Journal articles on the topic 'Parameterized quantum circuit'
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1
Li, Wei, Peng-Cheng Chu, Guang-Zhe Liu, Yan-Bing Tian, Tian-Hui Qiu, and Shu-Mei Wang. "An Image Classification Algorithm Based on Hybrid Quantum Classical Convolutional Neural Network." Quantum Engineering 2022 (July 14, 2022): 1–9. http://dx.doi.org/10.1155/2022/5701479.
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Quantum machine learning is emerging as a strategy to solve real-world problems. As a quantum computing model, parameterized quantum circuits provide an approach for constructing quantum machine learning algorithms, which may either realize computational acceleration or achieve better algorithm performance than classical algorithms. Based on the parameterized quantum circuit, we propose a hybrid quantum-classical convolutional neural network (HQCCNN) model for image classification that comprises both quantum and classical components. The quantum convolutional layer is designed using a parameterized quantum circuit. It is used to perform linear unitary transformation on the quantum state to extract hidden information. In addition, the quantum pooling unit is used to perform pooling operations. After the evolution of the quantum system, we measure the quantum state and input the measurement results into a classical fully connected layer for further processing. We demonstrate its potential by applying HQCCNN to the MNIST dataset. Compared to a convolutional neural network in a similar architecture, the results reveal that HQCCNN has a faster training speed and higher testing set accuracy than a convolutional neural network.
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Harwood, Stuart M., Dimitar Trenev, Spencer T. Stober, Panagiotis Barkoutsos, Tanvi P. Gujarati, Sarah Mostame, and Donny Greenberg. "Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing." ACM Transactions on Quantum Computing 3, no. 1 (March 31, 2022): 1–20. http://dx.doi.org/10.1145/3479197.
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The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization problem is in general nonconvex, the method can converge to suboptimal parameter values that do not yield the minimum eigenvalue. In this work, we address this shortcoming by adopting the concept of variational adiabatic quantum computing (VAQC) as a procedure to improve VQE. In VAQC, the ground state of a continuously parameterized Hamiltonian is approximated via a parameterized quantum circuit. We discuss some basic theory of VAQC to motivate the development of a hybrid quantum-classical homotopy continuation method. The proposed method has parallels with a predictor-corrector method for numerical integration of differential equations. While there are theoretical limitations to the procedure, we see in practice that VAQC can successfully find good initial circuit parameters to initialize VQE. We demonstrate this with two examples from quantum chemistry. Through these examples, we provide empirical evidence that VAQC, combined with other techniques (an adaptive termination criteria for the classical optimizer and a variance-based resampling method for the expectation evaluation), can provide more accurate solutions than “plain” VQE, for the same amount of effort.
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Zhu, D., N. M. Linke, M. Benedetti, K. A. Landsman, N. H. Nguyen, C. H. Alderete, A. Perdomo-Ortiz, et al. "Training of quantum circuits on a hybrid quantum computer." Science Advances 5, no. 10 (October 2019): eaaw9918. http://dx.doi.org/10.1126/sciadv.aaw9918.
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Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes.
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Jones, Tyson, and Simon C. Benjamin. "Robust quantum compilation and circuit optimisation via energy minimisation." Quantum 6 (January 24, 2022): 628. http://dx.doi.org/10.22331/q-2022-01-24-628.
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We explore a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. B∣in⟩=A∣in⟩. This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies B as a blank template: a layout of parameterised unitary gates configured to the identity. The compilation then proceeds using quantum hardware to perform an isomorphic energy-minimisation task, and an optional gate elimination phase to compress the circuit. If B is insufficient for perfect recompilation then the method will result in an approximate solution. We optimise using imaginary time evolution, and a recent extension of quantum natural gradient for noisy settings. We successfully recompile a 7-qubit circuit involving 186 gates of multiple types into an alternative form with a different topology, far fewer two-qubit gates, and a smaller family of gate types. Moreover we verify that the process is robust, finding that per-gate noise of up to 1% can still yield near-perfect recompilation. We test the scaling of our algorithm on up to 20 qubits, recompiling into circuits with up to 400 parameterized gates, and incorporate a custom adaptive timestep technique. We note that a classical simulation of the process can be useful to optimise circuits for today's prototypes, and more generally the method may enable `blind' compilation i.e. harnessing a device whose response to control parameters is deterministic but unknown.The code and resources used to generate our results are openly available online \cite{githubLink} \cite{mmaGithubLink}. A simple Mathematica demonstration of our algorithm can be found at questlink.qtechtheory.org.
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Chang, Su Yeon, Steven Herbert, Sofia Vallecorsa, Elías F. Combarro, and Ross Duncan. "Dual-Parameterized Quantum Circuit GAN Model in High Energy Physics." EPJ Web of Conferences 251 (2021): 03050. http://dx.doi.org/10.1051/epjconf/202125103050.
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Generative models, and Generative Adversarial Networks (GAN) in particular, are being studied as possible alternatives to Monte Carlo simulations. It has been proposed that, in certain circumstances, simulation using GANs can be sped-up by using quantum GANs (qGANs). We present a new design of qGAN, the dual-Parameterized Quantum Circuit (PQC) GAN, which consists of a classical discriminator and two quantum generators which take the form of PQCs. The first PQC learns a probability distribution over N-pixel images, while the second generates normalized pixel intensities of an individual image for each PQC input. With a view to HEP applications, we evaluated the dual-PQC architecture on the task of imitating calorimeter outputs, translated into pixelated images. The results demonstrate that the model can reproduce a fixed number of images with a reduced size as well as their probability distribution and we anticipate it should allow us to scale up to real calorimeter outputs.
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Liu, Huan-Yu, Tai-Ping Sun, Yu-Chun Wu, and Guo-Ping Guo. "Variational Quantum Algorithms for the Steady States of Open Quantum Systems." Chinese Physics Letters 38, no. 8 (September 1, 2021): 080301. http://dx.doi.org/10.1088/0256-307x/38/8/080301.
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The solutions of the problems related to open quantum systems have attracted considerable interest. We propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation, which can be efficiently evaluated with quantum circuits. We then optimize the parameters of the quantum circuit to find the steady state. Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels. The result shows that the fidelity between the optimal mixed state and the true steady state is over 99%. This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems.
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Nivelkar, Mukta, and S. G. Bhirud. "Modeling of Supervised Machine Learning using Mechanism of Quantum Computing." Journal of Physics: Conference Series 2161, no. 1 (January 1, 2022): 012023. http://dx.doi.org/10.1088/1742-6596/2161/1/012023.
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Abstract Mechanism of quantum computing helps to propose several task of machine learning in quantum technology. Quantum computing is enriched with quantum mechanics such as superposition and entanglement for making new standard of computation which will be far different than classical computer. Qubit is sole of quantum technology and help to use quantum mechanism for several tasks. Tasks which are non-computable by classical machine can be solved by quantum technology and these tasks are classically hard to compute and categorised as complex computations. Machine learning on classical models is very well set but it has more computational requirements based on complex and high-volume data processing. Supervised machine learning modelling using quantum computing deals with feature selection, parameter encoding and parameterized circuit formation. This paper highlights on integration of quantum computation and machine learning which will make sense on quantum machine learning modeling. Modelling of quantum parameterized circuit, Quantum feature set design and implementation for sample data is discussed. Supervised machine learning using quantum mechanism such as superposition and entanglement are articulated. Quantum machine learning helps to enhance the various classical machine learning methods for better analysis and prediction using complex measurement.
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Zeng, Yi, Hao Wang, Jin He, Qijun Huang, and Sheng Chang. "A Multi-Classification Hybrid Quantum Neural Network Using an All-Qubit Multi-Observable Measurement Strategy." Entropy 24, no. 3 (March 11, 2022): 394. http://dx.doi.org/10.3390/e24030394.
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Quantum machine learning is a promising application of quantum computing for data classification. However, most of the previous research focused on binary classification, and there are few studies on multi-classification. The major challenge comes from the limitations of near-term quantum devices on the number of qubits and the size of quantum circuits. In this paper, we propose a hybrid quantum neural network to implement multi-classification of a real-world dataset. We use an average pooling downsampling strategy to reduce the dimensionality of samples, and we design a ladder-like parameterized quantum circuit to disentangle the input states. Besides this, we adopt an all-qubit multi-observable measurement strategy to capture sufficient hidden information from the quantum system. The experimental results show that our algorithm outperforms the classical neural network and performs especially well on different multi-class datasets, which provides some enlightenment for the application of quantum computing to real-world data on near-term quantum processors.
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Miki, Tsukasa, Ryo Okita, Moe Shimada, Daisuke Tsukayama, and Jun-ichi Shirakashi. "Variational Ansatz preparation to avoid CNOT-gates on noisy quantum devices for combinatorial optimizations." AIP Advances 12, no. 3 (March 1, 2022): 035247. http://dx.doi.org/10.1063/5.0077706.
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The variational quantum eigensolver (VQE), which is a quantum–classical hybrid approach, has latent powers to leverage near-term quantum devices by effectively managing a limited number of qubits with finite coherent lifetimes. While it is generally argued that the quantum approximate optimization algorithm (QAOA), which is a special case of VQE with a variational Ansatz based on the adiabatic theorem, may enable practical applications of noisy quantum devices for classical combinatorial optimizations, the strategy to improve the performance of this algorithm by increasing the circuit depth conflicts with the limited coherence time of near-term quantum devices. Here, we introduce strategies involving the VQE to reduce the circuit resources required for solving combinatorial optimizations. Our concept of a parameterized quantum circuit allows the Ansatz preparation to be achieved by only single-qubit operation. We find that the variational Ansatz without controlled X-gates leads to quick convergence in a classical subroutine used to determine the variational parameters. In addition, the variational Ansatz with optimized parameters maintains performance over the problem sizes both on the numerical simulation and IBM 27-qubit processor “ibm_kawasaki.” Therefore, the variational Ansatz introduced in this study has several advantages considering the total calculation time and performance scaling over the problem sizes. We also show that the variational Ansatz consisting of a lower number of gate operations than that of QAOA can approximate the eigenstates of diagonal Hamiltonians with high accuracy. We illustrate our ideas with a maximum-cut problem and show that near-term quantum applications may be feasible using short-depth circuits.
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Nguyen, Tuyen, Incheon Paik, Yutaka Watanobe, and Truong Cong Thang. "An Evaluation of Hardware-Efficient Quantum Neural Networks for Image Data Classification." Electronics 11, no. 3 (February 1, 2022): 437. http://dx.doi.org/10.3390/electronics11030437.
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Quantum computing is expected to fundamentally change computer systems in the future. Recently, a new research topic of quantum computing is the hybrid quantum–classical approach for machine learning, in which a parameterized quantum circuit, also called quantum neural network (QNN), is optimized by a classical computer. This hybrid approach can have the benefits of both quantum computing and classical machine learning methods. In this early stage, it is of crucial importance to understand the new characteristics of quantum neural networks for different machine learning tasks. In this paper, we will study quantum neural networks for the task of classifying images, which are high-dimensional spatial data. In contrast to previous evaluations of low-dimensional or scalar data, we will investigate the impacts of practical encoding types, circuit depth, bias term, and readout on classification performance on the popular MNIST image dataset. Various interesting findings on learning behaviors of different QNNs are obtained through experimental results. To the best of our knowledge, this is the first work that considers various QNN aspects for image data.
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Huerga, Daniel. "Variational Quantum Simulation of Valence-Bond Solids." Quantum 6 (December 13, 2022): 874. http://dx.doi.org/10.22331/q-2022-12-13-874.
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We introduce a hybrid quantum-classical variational algorithm to simulate ground-state phase diagrams of frustrated quantum spin models in the thermodynamic limit. The method is based on a cluster-Gutzwiller ansatz where the wave function of the cluster is provided by a parameterized quantum circuit whose key ingredient is a two-qubit real XY gate allowing to efficiently generate valence-bonds on nearest-neighbor qubits. Additional tunable single-qubit Z- and two-qubit ZZ-rotation gates allow the description of magnetically ordered and paramagnetic phases while restricting the variational optimization to the U(1) subspace. We benchmark the method against the J1−J2 Heisenberg model on the square lattice and uncover its phase diagram, which hosts long-range ordered Neel and columnar anti-ferromagnetic phases, as well as an intermediate valence-bond solid phase characterized by a periodic pattern of 2×2 strongly-correlated plaquettes. Our results show that the convergence of the algorithm is guided by the onset of long-range order, opening a promising route to synthetically realize frustrated quantum magnets and their quantum phase transition to paramagnetic valence-bond solids with currently developed superconducting circuit devices.
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Sack, Stefan H., and Maksym Serbyn. "Quantum annealing initialization of the quantum approximate optimization algorithm." Quantum 5 (July 1, 2021): 491. http://dx.doi.org/10.22331/q-2021-07-01-491.
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The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with sub-optimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveals new connections between QAOA and quantum annealing.
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Sánchez, Fernando, Vicenta Sánchez, and Chumin Wang. "Coarse-Grained Quantum Theory of Organic Photovoltaic Devices." Nanomaterials 11, no. 2 (February 16, 2021): 495. http://dx.doi.org/10.3390/nano11020495.
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Understanding the exciton dissociation process in organic solar cells is a fundamental issue for the design of high-performance photovoltaic devices. In this article, a parameterized quantum theory based on a coarse-grained tight-binding model plus non-local electron-hole interactions is presented, while the diffusion and recombination of excitons are studied in a square lattice of excitonic states, where a real-space renormalization method on effective chains has been used. The Hamiltonian parameters are determined by fitting the measured quantum efficiency spectra and the theoretical short-circuit currents without adjustable parameters show a good agreement with the experimental ones obtained from several polymer:fullerene and polymer:polymer heterojunctions. Moreover, the present study reveals the degree of polymerization and the true driving force at donor-acceptor interface in each analyzed organic photovoltaic device.
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Wang, Haibin, Jiaojiao Zhao, Bosi Wang, and Lian Tong. "A Quantum Approximate Optimization Algorithm with Metalearning for MaxCut Problem and Its Simulation via TensorFlow Quantum." Mathematical Problems in Engineering 2021 (March 24, 2021): 1–11. http://dx.doi.org/10.1155/2021/6655455.
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A quantum approximate optimization algorithm (QAOA) is a polynomial-time approximate optimization algorithm used to solve combinatorial optimization problems. However, the existing QAOA algorithms have poor generalization performance in finding an optimal solution from a feasible solution set of combinatorial problems. In order to solve this problem, a quantum approximate optimization algorithm with metalearning for the MaxCut problem (MetaQAOA) is proposed. Specifically, a quantum neural network (QNN) is constructed in the form of the parameterized quantum circuit to detect different topological phases of matter, and a classical long short-term memory (LSTM) neural network is used as a black-box optimizer, which can quickly assist QNN to find the approximate optimal QAOA parameters. The experiment simulation via TensorFlow Quantum (TFQ) shows that MetaQAOA requires fewer iterations to reach the threshold of the loss function, and the threshold of the loss value after training is smaller than comparison methods. In addition, our algorithm can learn parameter update heuristics which can generalize to larger system sizes and still outperform other initialization strategies of this scale.
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Sweke, Ryan, Frederik Wilde, Johannes Jakob Meyer, Maria Schuld, Paul K. Fährmann, Barthélémy Meynard-Piganeau, and Jens Eisert. "Stochastic gradient descent for hybrid quantum-classical optimization." Quantum 4 (August 31, 2020): 314. http://dx.doi.org/10.22331/q-2020-08-31-314.
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Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore the consequences of the prior observation that estimation of these quantities on quantum hardware results in a form of stochastic gradient descent optimization. We formalize this notion, which allows us to show that in many relevant cases, including VQE, QAOA and certain quantum classifiers, estimating expectation values with k measurement outcomes results in optimization algorithms whose convergence properties can be rigorously well understood, for any value of k. In fact, even using single measurement outcomes for the estimation of expectation values is sufficient. Moreover, in many settings the required gradients can be expressed as linear combinations of expectation values -- originating, e.g., from a sum over local terms of a Hamiltonian, a parameter shift rule, or a sum over data-set instances -- and we show that in these cases k-shot expectation value estimation can be combined with sampling over terms of the linear combination, to obtain ``doubly stochastic'' gradient descent optimizers. For all algorithms we prove convergence guarantees, providing a framework for the derivation of rigorous optimization results in the context of near-term quantum devices. Additionally, we explore numerically these methods on benchmark VQE, QAOA and quantum-enhanced machine learning tasks and show that treating the stochastic settings as hyper-parameters allows for state-of-the-art results with significantly fewer circuit executions and measurements.
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Wang, Jiasu, Yulong Dong, and Lin Lin. "On the energy landscape of symmetric quantum signal processing." Quantum 6 (November 3, 2022): 850. http://dx.doi.org/10.22331/q-2022-11-03-850.
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Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given polynomial f, the parameters (called phase factors) can be obtained by solving an optimization problem. However, the cost function is non-convex, and has a very complex energy landscape with numerous global and local minima. It is therefore surprising that the solution can be robustly obtained in practice, starting from a fixed initial guess Φ0 that contains no information of the input polynomial. To investigate this phenomenon, we first explicitly characterize all the global minima of the cost function. We then prove that one particular global minimum (called the maximal solution) belongs to a neighborhood of Φ0, on which the cost function is strongly convex under the condition ‖f‖∞=O(d−1) with d=deg(f). Our result provides a partial explanation of the aforementioned success of optimization algorithms.
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Adebayo, Philip, Frederick Basaky, and Edgar Osaghae. "Developing a Model for Predicting Lung Cancer Using Variational Quantum-Classical Algorithm: A Survey." Journal of Applied Artificial Intelligence 3, no. 1 (June 30, 2022): 47–60. http://dx.doi.org/10.48185/jaai.v3i1.446.
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There are real life problems that currently proved hard for classical computers (even the best of supercomputers) to solve-the so called computationally intractable problems. Computers and computing devices are limited, by virtue of the fact that they cannot perform certain complex problems. For example, modern cryptography assumes that it is impossible to factorize a large number as the complexity of solving this problem increases exponentially. Even the best supercomputers of today cannot sufficiently find the prime factors of a number with 700-1,000 digits. With quantum computing, however, Shor’s algorithm proved that in principle, a quantum computer can be used to break the security of conventional cryptosystems. Quantum computing also promises exponential improvements for many optimization problems. Lov Grover algorithm was also designed to search for an element in unstructured database. Effort is currently on to leverage quantum computing and quantum mechanical phenomena to tackle complex machine learning problems. Using machine learning algorithm to solve problems is common place. What is however new is using quantum machine learning algorithm to solve problems such as detecting, classifying and predicting disease such as lung cancer. In this work, we highlight the limitations of classical computers to solve certain problems and then propose a hybrid model called the variational quantum-classical algorithm to predict the possibility of a patient developing lung cancer given a set of features which are spelt out in the dataset. The dataset is initially pre-processed, and made to pass through a Parameterized Quantum Circuit (PQC) and then post-processed. Finally, the output of the post-processing phase is used for prediction of lung cancer.
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Ostaszewski, Mateusz, Edward Grant, and Marcello Benedetti. "Structure optimization for parameterized quantum circuits." Quantum 5 (January 28, 2021): 391. http://dx.doi.org/10.22331/q-2021-01-28-391.
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We propose an efficient method for simultaneously optimizing both the structure and parameter values of quantum circuits with only a small computational overhead. Shallow circuits that use structure optimization perform significantly better than circuits that use parameter updates alone, making this method particularly suitable for noisy intermediate-scale quantum computers. We demonstrate the method for optimizing a variational quantum eigensolver for finding the ground states of Lithium Hydride and the Heisenberg model in simulation, and for finding the ground state of Hydrogen gas on the IBM Melbourne quantum computer.
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Ding, Li, and Lee Spector. "Multi-Objective Evolutionary Architecture Search for Parameterized Quantum Circuits." Entropy 25, no. 1 (January 3, 2023): 93. http://dx.doi.org/10.3390/e25010093.
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Recent work on hybrid quantum-classical machine learning systems has demonstrated success in utilizing parameterized quantum circuits (PQCs) to solve the challenging reinforcement learning (RL) tasks, with provable learning advantages over classical systems, e.g., deep neural networks. While existing work demonstrates and exploits the strength of PQC-based models, the design choices of PQC architectures and the interactions between different quantum circuits on learning tasks are generally underexplored. In this work, we introduce a Multi-objective Evolutionary Architecture Search framework for parameterized quantum circuits (MEAS-PQC), which uses a multi-objective genetic algorithm with quantum-specific configurations to perform efficient searching of optimal PQC architectures. Experimental results show that our method can find architectures that have superior learning performance on three benchmark RL tasks, and are also optimized for additional objectives including reductions in quantum noise and model size. Further analysis of patterns and probability distributions of quantum operations helps identify performance-critical design choices of hybrid quantum-classical learning systems.
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Benedetti, Marcello, Erika Lloyd, Stefan Sack, and Mattia Fiorentini. "Parameterized quantum circuits as machine learning models." Quantum Science and Technology 4, no. 4 (November 13, 2019): 043001. http://dx.doi.org/10.1088/2058-9565/ab4eb5.
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Katabarwa, Amara, Sukin Sim, Dax Enshan Koh, and Pierre-Luc Dallaire-Demers. "Connecting geometry and performance of two-qubit parameterized quantum circuits." Quantum 6 (August 23, 2022): 782. http://dx.doi.org/10.22331/q-2022-08-23-782.
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Parameterized quantum circuits (PQCs) are a central component of many variational quantum algorithms, yet there is a lack of understanding of how their parameterization impacts algorithm performance. We initiate this discussion by using principal bundles to geometrically characterize two-qubit PQCs. On the base manifold, we use the Mannoury-Fubini-Study metric to find a simple equation relating the Ricci scalar (geometry) and concurrence (entanglement). By calculating the Ricci scalar during a variational quantum eigensolver (VQE) optimization process, this offers us a new perspective to how and why Quantum Natural Gradient outperforms the standard gradient descent. We argue that the key to the Quantum Natural Gradient's superior performance is its ability to find regions of high negative curvature early in the optimization process. These regions of high negative curvature appear to be important in accelerating the optimization process.
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Barison, Stefano, Filippo Vicentini, and Giuseppe Carleo. "An efficient quantum algorithm for the time evolution of parameterized circuits." Quantum 5 (July 28, 2021): 512. http://dx.doi.org/10.22331/q-2021-07-28-512.
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We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected – Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.
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Sim, Sukin, Jonathan Romero, Jérôme F. Gonthier, and Alexander A. Kunitsa. "Adaptive pruning-based optimization of parameterized quantum circuits." Quantum Science and Technology 6, no. 2 (March 10, 2021): 025019. http://dx.doi.org/10.1088/2058-9565/abe107.
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Niu, Yun-Fei, Shuo Zhang, and Wan-Su Bao. "Warm Starting Variational Quantum Algorithms with Near Clifford Circuits." Electronics 12, no. 2 (January 9, 2023): 347. http://dx.doi.org/10.3390/electronics12020347.
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As a mainstream approach in the quantum machine learning field, variational quantum algorithms (VQAs) are frequently mentioned among the most promising applications for quantum computing. However, VQAs suffer from inefficient training methods. Here, we propose a pretraining strategy named near Clifford circuits warm start (NCC-WS) to find the initialization for parameterized quantum circuits (PQCs) in VQAs. We explored the expressibility of NCCs and the correlation between the expressibility and acceleration. The achieved results suggest that NCC-WS can find the correct initialization for the training of VQAs to achieve acceleration.
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Sim, Sukin, Peter D. Johnson, and Alán Aspuru‐Guzik. "Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms." Advanced Quantum Technologies 2, no. 12 (October 14, 2019): 1900070. http://dx.doi.org/10.1002/qute.201900070.
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Zhao, Chen, and Xiao-Shan Gao. "Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus." Quantum 5 (June 4, 2021): 466. http://dx.doi.org/10.22331/q-2021-06-04-466.
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In this paper, we propose a general scheme to analyze the gradient vanishing phenomenon, also known as the barren plateau phenomenon, in training quantum neural networks with the ZX-calculus. More precisely, we extend the barren plateaus theorem from unitary 2-design circuits to any parameterized quantum circuits under certain reasonable assumptions. The main technical contribution of this paper is representing certain integrations as ZX-diagrams and computing them with the ZX-calculus. The method is used to analyze four concrete quantum neural networks with different structures. It is shown that, for the hardware efficient ansatz and the MPS-inspired ansatz, there exist barren plateaus, while for the QCNN ansatz and the tree tensor network ansatz, there exists no barren plateau.
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Liu, Wen-Qiang, Xin-Jie Zhou, and Hai-Rui Wei. "Collective unitary evolution with linear optics by Cartan decomposition." Europhysics Letters 136, no. 6 (December 1, 2021): 60001. http://dx.doi.org/10.1209/0295-5075/ac483b.
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Abstract Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based on the results of decomposition, we design two compact architectures to deterministically implement arbitrary two-qubit polarization-spatial and spatial-polarization collective unitary operations, respectively. The involved linear optical elements are reduced from 25 to 20 and 21 to 20, respectively. Moreover, the parameterized quantum computation can be flexibly manipulated by wave plates and phase shifters. As an application, we construct the specific quantum circuits to realize two-dimensional quantum walk and quantum Fourier transformation. Our schemes are simple and feasible with the current technology.
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Xia, Rongxin, and Sabre Kais. "Hybrid Quantum-Classical Neural Network for Calculating Ground State Energies of Molecules." Entropy 22, no. 8 (July 29, 2020): 828. http://dx.doi.org/10.3390/e22080828.
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We present a hybrid quantum-classical neural network that can be trained to perform electronic structure calculation and generate potential energy curves of simple molecules. The method is based on the combination of parameterized quantum circuits and measurements. With unsupervised training, the neural network can generate electronic potential energy curves based on training at certain bond lengths. To demonstrate the power of the proposed new method, we present the results of using the quantum-classical hybrid neural network to calculate ground state potential energy curves of simple molecules such as H2, LiH, and BeH2. The results are very accurate and the approach could potentially be used to generate complex molecular potential energy surfaces.
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Arute, Frank, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Sergio Boixo, et al. "Hartree-Fock on a superconducting qubit quantum computer." Science 369, no. 6507 (August 27, 2020): 1084–89. http://dx.doi.org/10.1126/science.abb9811.
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The simulation of fermionic systems is among the most anticipated applications of quantum computing. We performed several quantum simulations of chemistry with up to one dozen qubits, including modeling the isomerization mechanism of diazene. We also demonstrated error-mitigation strategies based on N-representability that dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realized the Givens rotation approach to noninteracting fermion evolution, which we variationally optimized to prepare the Hartree-Fock wave function. This ubiquitous algorithmic primitive is classically tractable to simulate yet still generates highly entangled states over the computational basis, which allowed us to assess the performance of our hardware and establish a foundation for scaling up correlated quantum chemistry simulations.
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Vallury, Harish J., Michael A. Jones, Charles D. Hill, and Lloyd C. L. Hollenberg. "Quantum computed moments correction to variational estimates." Quantum 4 (December 15, 2020): 373. http://dx.doi.org/10.22331/q-2020-12-15-373.
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The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the results. There is now a clear focus on strategies that require fewer quantum circuit steps and are robust to device errors. Here we present an approach in which problem complexity is transferred to dynamic quantities computed on the quantum processor – Hamiltonian moments, ⟨Hn⟩. From these quantum computed moments, an estimate of the ground-state energy can be obtained using the ``infimum'' theorem from Lanczos cumulant expansions which manifestly corrects the associated variational calculation. With higher order effects in Hilbert space generated via the moments, the burden on the trial-state quantum circuit depth is eased. The method is introduced and demonstrated on 2D quantum magnetism models on lattices up to 5×5 (25 qubits) implemented on IBM Quantum superconducting qubit devices. Moments were quantum computed to fourth order with respect to a parameterised antiferromagnetic trial-state. A comprehensive comparison with benchmark variational calculations was performed, including over an ensemble of random coupling instances. The results showed that the infimum estimate consistently outperformed the benchmark variational approach for the same trial-state. These initial investigations suggest that the quantum computed moments approach has a high degree of stability against trial-state variation, quantum gate errors and shot noise, all of which bodes well for further investigation and applications of the approach.
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Wang, Xin, Zhixin Song, and Youle Wang. "Variational Quantum Singular Value Decomposition." Quantum 5 (June 29, 2021): 483. http://dx.doi.org/10.22331/q-2021-06-29-483.
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Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.
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Benedetti, Marcello, Erika Lloyd, Stefan Sack, and Mattia Fiorentini. "Erratum: Parameterized quantum circuits as machine learning models (2019 Quant. Sci. Tech. 4 043001)." Quantum Science and Technology 5, no. 1 (December 4, 2019): 019601. http://dx.doi.org/10.1088/2058-9565/ab5944.
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Huang, Zhaolong, Qiting Li, Junling Zhao, and Meimei Song. "Variational Quantum Algorithm Applied to Collision Avoidance of Unmanned Aerial Vehicles." Entropy 24, no. 11 (November 18, 2022): 1685. http://dx.doi.org/10.3390/e24111685.
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Mission planning for multiple unmanned aerial vehicles (UAVs) is a complex problem that is expected to be solved by quantum computing. With the increasing application of UAVs, the demand for efficient conflict management strategies to ensure airspace safety continues to increase. In the era of noisy intermediate-scale quantum (NISQ) devices, variational quantum algorithms (VQA) for optimizing parameterized quantum circuits with the help of classical optimizers are currently one of the most promising strategies to gain quantum advantage. In this paper, we propose a mathematical model for the UAV collision avoidance problem that maps the collision avoidance problem to a quadratic unconstrained binary optimization (QUBO) problem. The problem is formulated as an Ising Hamiltonian, then the ground state is solved using two kinds of VQAs: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We select conditional value-at-risk (CVaR) to further promote the performance of our model. Four examples are given to validate that with our method the probability of obtaining a feasible solution can exceed 90% based on appropriate parameters, and our method can enhance the efficiency of a UAVs’ collision avoidance model.
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Gyurik, Casper, Dyon Vreumingen, van, and Vedran Dunjko. "Structural risk minimization for quantum linear classifiers." Quantum 7 (January 13, 2023): 893. http://dx.doi.org/10.22331/q-2023-01-13-893.
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Quantum machine learning (QML) models based on parameterized quantum circuits are often highlighted as candidates for quantum computing's near-term “killer application''. However, the understanding of the empirical and generalization performance of these models is still in its infancy. In this paper we study how to balance between training accuracy and generalization performance (also called structural risk minimization) for two prominent QML models introduced by Havlíček et al. \cite{havlivcek:qsvm}, and Schuld and Killoran \cite{schuld:qsvm}. Firstly, using relationships to well understood classical models, we prove that two model parameters – i.e., the dimension of the sum of the images and the Frobenius norm of the observables used by the model – closely control the models' complexity and therefore its generalization performance. Secondly, using ideas inspired by process tomography, we prove that these model parameters also closely control the models' ability to capture correlations in sets of training examples. In summary, our results give rise to new options for structural risk minimization for QML models.
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Shi, Jinjing, Wenxuan Wang, Xiaoping Lou, Shichao Zhang, and Xuelong Li. "Parameterized Hamiltonian Learning With Quantum Circuit." IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022, 1–10. http://dx.doi.org/10.1109/tpami.2022.3203157.
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Hubregtsen, Thomas, Josef Pichlmeier, Patrick Stecher, and Koen Bertels. "Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility, and entangling capability." Quantum Machine Intelligence 3, no. 1 (March 11, 2021). http://dx.doi.org/10.1007/s42484-021-00038-w.
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AbstractAn active area of investigation in the search for quantum advantage is quantum machine learning. Quantum machine learning, and parameterized quantum circuits in a hybrid quantum-classical setup in particular, could bring advancements in accuracy by utilizing the high dimensionality of the Hilbert space as feature space. But is the ability of a quantum circuit to uniformly address the Hilbert space a good indicator of classification accuracy? In our work, we use methods and quantifications from prior art to perform a numerical study in order to evaluate the level of correlation. We find a moderate to strong correlation between the ability of the circuit to uniformly address the Hilbert space and the achieved classification accuracy for circuits that entail a single embedding layer followed by 1 or 2 circuit designs. This is based on our study encompassing 19 circuits in both 1- and 2-layer configurations, evaluated on 9 datasets of increasing difficulty. We also evaluate the correlation between entangling capability and classification accuracy in a similar setup, and find a weak correlation. Future work will focus on evaluating if this holds for different circuit designs.
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Shi, Jinjing, Yongze Tang, Yuhu Lu, Yanyan Feng, Ronghua Shi, and Shichao Zhang. "Quantum Circuit Learning with Parameterized Boson Sampling." IEEE Transactions on Knowledge and Data Engineering, 2021, 1. http://dx.doi.org/10.1109/tkde.2021.3095103.
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Jian, Guanlin, Yuan Yang, Ze Liu, Zhen Gang Zhu, and Zheng-Chuan Wang. "Towards simulating time evolution of specific quantum many-body system by lower counts of quantum gates." Europhysics Letters, December 20, 2022. http://dx.doi.org/10.1209/0295-5075/acad25.
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Abstract In the noisy intermediate-scale quantum (NISQ) era, quantum computers have become important tools to simulate the real-time evolution of strong correlated many-body systems. The general scheme of designing quantum circuits to simulate the quantum dynamics is based on the Trotter- Suzuki decomposition technique, which has its limitation because the accuracy of evolution process depends on the size of trotter steps when the evolution operator is decomposed as quantum gates. Going beyond the limitation of Trotter-Suzuki scheme, we design a parameterized quantum circuit named α-circuit with simple determined size and the only one control parameter θ to simulate the real-time evolution of the speci c XXX Heisenberg model with the speci c initial state │000 ●●● >. The α-circuit can accurately generate the time-evolution results by tuning parameter θ, which means the circuit can also be regarded as a good state preparation machine (SPM).
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Hubregtsen, Thomas, Wilde Frederik, Shozab Qasim, and J. Eisert. "Single-component gradient rules for variational quantum algorithms." Quantum Science and Technology, April 19, 2022. http://dx.doi.org/10.1088/2058-9565/ac6824.
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Abstract Many near-term quantum computing algorithms are conceived as variational quantum algorithms, in which parameterized quantum circuits are optimized in a hybrid quantum-classical setup. Examples are variational quantum eigensolvers, quantum approximate optimization algorithms as well as various algorithms in the context of quantum-assisted machine learning. A common bottleneck of any such algorithm is constituted by the optimization of the variational parameters. A popular set of optimization methods work on the estimate of the gradient, obtained by means of circuit evaluations. We will refer to the way in which one can combine these circuit evaluations as gradient rules. This work provides a comprehensive picture of the family of gradient rules that vary parameters of quantum gates individually. The most prominent known members of this family are the parameter shift rule and the finite differences method. To unite this family, we propose a generalized parameter shift rule that expresses all members of the aforementioned family as special cases, and discuss how all of these can be seen as providing access to a linear combination of exact first- and second-order derivatives. We further prove that a parameter shift rule with one non-shifted evaluation and only one shifted circuit evaluation does not exist, and introduce a novel perspective for approaching new gradient rules.
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Herrman, Rebekah, Phillip C. Lotshaw, James Ostrowski, Travis S. Humble, and George Siopsis. "Multi-angle quantum approximate optimization algorithm." Scientific Reports 12, no. 1 (April 26, 2022). http://dx.doi.org/10.1038/s41598-022-10555-8.
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AbstractThe quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we investigate a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time for a test dataset we consider. This new ansatz gives a 33% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.
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Herrman, Rebekah, Phillip C. Lotshaw, James Ostrowski, Travis S. Humble, and George Siopsis. "Multi-angle quantum approximate optimization algorithm." Scientific Reports 12, no. 1 (April 26, 2022). http://dx.doi.org/10.1038/s41598-022-10555-8.
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AbstractThe quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we investigate a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time for a test dataset we consider. This new ansatz gives a 33% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.
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Tamiya, Shiro, and Hayata Yamasaki. "Stochastic gradient line Bayesian optimization for efficient noise-robust optimization of parameterized quantum circuits." npj Quantum Information 8, no. 1 (July 27, 2022). http://dx.doi.org/10.1038/s41534-022-00592-6.
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AbstractOptimizing parameterized quantum circuits is a key routine in using near-term quantum devices. However, the existing algorithms for such optimization require an excessive number of quantum-measurement shots for estimating expectation values of observables and repeating many iterations, whose cost has been a critical obstacle for practical use. We develop an efficient alternative optimization algorithm, stochastic gradient line Bayesian optimization (SGLBO), to address this problem. SGLBO reduces the measurement-shot cost by estimating an appropriate direction of updating circuit parameters based on stochastic gradient descent (SGD) and further utilizing Bayesian optimization (BO) to estimate the optimal step size for each iteration in SGD. In addition, we formulate an adaptive measurement-shot strategy and introduce a technique of suffix averaging to reduce the effect of statistical and hardware noise. Our numerical simulation demonstrates that the SGLBO augmented with these techniques can drastically reduce the measurement-shot cost, improve the accuracy, and make the optimization noise-robust.
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Moussa, Charles, Hao Wang, Thomas Bäck, and Vedran Dunjko. "Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm." EPJ Quantum Technology 9, no. 1 (May 6, 2022). http://dx.doi.org/10.1140/epjqt/s40507-022-00131-4.
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AbstractAs combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of the quantum circuit output. One of these algorithms, the Quantum Approximate Optimization Algorithm stands out as a promising approach to tackling combinatorial problems. However, finding the appropriate parameters is a difficult task. Although QAOA exhibits concentration properties, they can depend on instances characteristics that may not be easy to identify, but may nonetheless offer useful information to find good parameters. In this work, we study unsupervised Machine Learning approaches for setting these parameters without optimization. We perform clustering with the angle values but also instances encodings (using instance features or the output of a variational graph autoencoder), and compare different approaches. These angle-finding strategies can be used to reduce calls to quantum circuits when leveraging QAOA as a subroutine. We showcase them within Recursive-QAOA up to depth 3 where the number of QAOA parameters used per iteration is limited to 3, achieving a median approximation ratio of 0.94 for MaxCut over 200 Erdős-Rényi graphs. We obtain similar performances to the case where we extensively optimize the angles, hence saving numerous circuit calls.
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Park, Gunhee, Joonsuk Huh, and Daniel Kyungdeock Park. "Variational quantum one-class classifier." Machine Learning: Science and Technology, January 3, 2023. http://dx.doi.org/10.1088/2632-2153/acafd5.
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Abstract One-class classification is a fundamental problem in pattern recognition with a wide range of applications. This work presents a semi-supervised quantum machine learning algorithm for such a problem, which we call a variational quantum one-class classifier (VQOCC). The algorithm is suitable for noisy intermediate-scale quantum computing because the VQOCC trains a fully-parameterized quantum autoencoder with a normal dataset and does not require decoding. The performance of the VQOCC is compared with that of the one-class support vector machine (OC-SVM), the kernel principal component analysis (PCA), and the deep convolutional autoencoder (DCAE) using handwritten digit and Fashion-MNIST datasets. The numerical experiment examined various structures of VQOCC by varying data encoding, the number of parameterized quantum circuit layers, and the size of the latent feature space. The benchmark shows that the classification performance of VQOCC is comparable to that of OC-SVM and PCA, although the number of model parameters grows only logarithmically with the data size. The quantum algorithm outperformed DCAE in most cases under similar training conditions. Therefore, our algorithm constitutes an extremely compact and effective machine learning model for one-class classification.
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Consiglio, Mirko, Wayne Jordan Chetcuti, Carlos Bravo-Prieto, Sergi Ramos-Calderer, Anna Minguzzi, José Ignacio Latorre, Luigi Amico, and Tony John George Apollaro. "Variational quantum eigensolver for SU(N) fermions." Journal of Physics A: Mathematical and Theoretical, May 16, 2022. http://dx.doi.org/10.1088/1751-8121/ac7016.
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Abstract Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum eigensolver is one of the aforementioned algorithms designed to determine the ground-state of many-body Hamiltonians. Here, we apply the variational quantum eigensolver to study the ground-state properties of N-component fermions. With such knowledge, we study the persistent current of interacting SU(N) fermions, which is employed to reliably map out the different quantum phases of the system. Our approach lays out the basis for a current-based quantum simulator of many-body systems that can be implemented on noisy intermediate-scale quantum computers.
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Miyahara, Hideyuki, and Vwani Roychowdhury. "Ansatz-Independent Variational Quantum Classifiers and the Price of Ansatz." Scientific Reports 12, no. 1 (November 14, 2022). http://dx.doi.org/10.1038/s41598-022-20688-5.
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AbstractThe paradigm of variational quantum classifiers (VQCs) encodes classical information as quantum states, followed by quantum processing and then measurements to generate classical predictions. VQCs are promising candidates for efficient utilizations of noisy intermediate scale quantum (NISQ) devices: classifiers involving M-dimensional datasets can be implemented with only $$\lceil \log _2 M \rceil $$ ⌈ log 2 M ⌉ qubits by using an amplitude encoding. A general framework for designing and training VQCs, however, is lacking. An encouraging specific embodiment of VQCs, quantum circuit learning (QCL), utilizes an ansatz: a circuit with a predetermined circuit geometry and parametrized gates expressing a time-evolution unitary operator; training involves learning the gate parameters through a gradient-descent algorithm where the gradients themselves can be efficiently estimated by the quantum circuit. The representational power of QCL, however, depends strongly on the choice of the ansatz, as it limits the range of possible unitary operators that a VQC can search over. Equally importantly, the landscape of the optimization problem may have challenging properties such as barren plateaus and the associated gradient-descent algorithm may not find good local minima. Thus, it is critically important to estimate (i) the price of ansatz; that is, the gap between the performance of QCL and the performance of ansatz-independent VQCs, and (ii) the price of using quantum circuits as classical classifiers: that is, the performance gap between VQCs and equivalent classical classifiers. This paper develops a computational framework to address both these open problems. First, it shows that VQCs, including QCL, fit inside the well-known kernel method. Next it introduces a framework for efficiently designing ansatz-independent VQCs, which we call the unitary kernel method (UKM). The UKM framework enables one to estimate the first known computationally-determined bounds on both the price of ansatz and the price of any speedup advantages of VQCs: numerical results with datatsets of various dimensions, ranging from 4 to 256, show that the ansatz-induced gap can vary between 10 and 20$$\%$$ % , while the VQC-induced gap (between VQC and kernel method) can vary between 10 and 16$$\%$$ % . To further understand the role of ansatz in VQCs, we also propose a method of decomposing a given unitary operator into a quantum circuit, which we call the variational circuit realization (VCR): given any parameterized circuit block (as for example, used in QCL), it finds optimal parameters and the number of layers of the circuit block required to approximate any target unitary operator with a given precision.
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Meitei, Oinam Romesh, Bryan T. Gard, George S. Barron, David P. Pappas, Sophia E. Economou, Edwin Barnes, and Nicholas J. Mayhall. "Gate-free state preparation for fast variational quantum eigensolver simulations." npj Quantum Information 7, no. 1 (October 27, 2021). http://dx.doi.org/10.1038/s41534-021-00493-0.
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AbstractThe variational quantum eigensolver is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. The algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state, and then measuring the molecular energy. Due to finite coherence times and gate errors, the number of gates that can be implemented remains limited. In this work, we propose an alternative algorithm where device-level pulse shapes are variationally optimized for the state preparation rather than using an abstract-level quantum circuit. In doing so, the coherence time required for the state preparation is drastically reduced. We numerically demonstrate this by directly optimizing pulse shapes which accurately model the dissociation of H2 and HeH+, and we compute the ground state energy for LiH with four transmons where we see reductions in state preparation times of roughly three orders of magnitude compared to gate-based strategies.
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Sun, Zheng-Hang, Yong-Yi Wang, Jian Cui, and Heng Fan. "Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry." New Journal of Physics, January 11, 2023. http://dx.doi.org/10.1088/1367-2630/acb22c.
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Abstract The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamiltonians near the critical points of their quantum phase transitions, and generating Greenberger-Horne-Zeilinger (GHZ) states. We reveal that the performance of QAOA is related to the translational invariance of the target Hamiltonian: Without the translational symmetry, for instance due to the open boundary condition (OBC) or randomness in the system, the QAOA becomes less efficient. We then propose a generalized QAOA assisted by the parameterized resource Hamiltonian (PRH-QAOA), to achieve a better performance. In addition, based on the PRH-QAOA, we design a low-depth quantum circuit beyond one-dimensional geometry, to generate GHZ states with perfect fidelity. The experimental realization of the proposed scheme for generating GHZ states on Rydberg-dressed atoms is discussed. Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry, especially for recently developed two-dimensional quantum processors with OBC.
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Caro, Matthias C., Hsin-Yuan Huang, M. Cerezo, Kunal Sharma, Andrew Sornborger, Lukasz Cincio, and Patrick J. Coles. "Generalization in quantum machine learning from few training data." Nature Communications 13, no. 1 (August 22, 2022). http://dx.doi.org/10.1038/s41467-022-32550-3.
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AbstractModern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as $$\sqrt{T/N}$$ T / N . When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to $$\sqrt{K/N}$$ K / N . Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.
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Liu, Wenjie, Ying Zhang, Zhiliang Deng, Jiaojiao Zhao, and Lian Tong. "A hybrid quantum-classical conditional generative adversarial network algorithm for human-centered paradigm in cloud." EURASIP Journal on Wireless Communications and Networking 2021, no. 1 (February 22, 2021). http://dx.doi.org/10.1186/s13638-021-01898-3.
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AbstractAs an emerging field that aims to bridge the gap between human activities and computing systems, human-centered computing (HCC) in cloud, edge, fog has had a huge impact on the artificial intelligence algorithms. The quantum generative adversarial network (QGAN) is considered to be one of the quantum machine learning algorithms with great application prospects, which also should be improved to conform to the human-centered paradigm. The generation process of QGAN is relatively random and the generated model does not conform to the human-centered concept, so it is not quite suitable for real scenarios. In order to solve these problems, a hybrid quantum-classical conditional generative adversarial network (QCGAN) algorithm is proposed, which is a knowledge-driven human–computer interaction computing mode that can be implemented in cloud. The purposes of stabilizing the generation process and realizing the interaction between human and computing process are achieved by inputting artificial conditional information in the generator and discriminator. The generator uses the parameterized quantum circuit with an all-to-all connected topology, which facilitates the tuning of network parameters during the training process. The discriminator uses the classical neural network, which effectively avoids the “input bottleneck” of quantum machine learning. Finally, the BAS training set is selected to conduct experiment on the quantum cloud computing platform. The result shows that the QCGAN algorithm can effectively converge to the Nash equilibrium point after training and perform human-centered classification generation tasks.