Journal articles: 'Qubits simulation'

1

Ivanyos, G., A. B. Nagy, and L. Ronyai. "Constructions for quantum computing with symmetrized gates." Quantum Information and Computation 8, no. 5 (May 2008): 411–29. http://dx.doi.org/10.26421/qic8.5-4.

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We investigate constructions for simulating quantum computers with a polynomial slowdown on ensembles composed of qubits on which symmetrized versions of one- and two-qubit gates can be performed. The simulation is based on taking Lie commutators of symmetrized Hamiltonians to extract Hamiltonians at desired local positions. During the simulation, only a part of the qubits can be used for storing information, the others are left unchanged by the commutators. We propose constructions for various symmetry groups where a pretty large fraction of the qubits can be used. As a few of the other qubits need to be set to one, our construction requires individual initialization of some of the qubits.

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Bluvstein, Dolev, Harry Levine, Giulia Semeghini, Tout T. Wang, Sepehr Ebadi, Marcin Kalinowski, Alexander Keesling, et al. "A quantum processor based on coherent transport of entangled atom arrays." Nature 604, no. 7906 (April 20, 2022): 451–56. http://dx.doi.org/10.1038/s41586-022-04592-6.

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AbstractThe ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems1,2. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation3–5. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state6,7. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits8 and a toric code state on a torus with sixteen data and eight ancillary qubits9. Finally, we use this architecture to realize a hybrid analogue–digital evolution2 and use it for measuring entanglement entropy in quantum simulations10–12, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars13,14. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology.

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Essammouni, K., A. Chouikh, T. Said, and M. Bennai. "niSWAP and NTCP gates realized in a circuit QED system." International Journal of Geometric Methods in Modern Physics 14, no. 07 (March 7, 2017): 1750100. http://dx.doi.org/10.1142/s0219887817501006.

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Based on superconducting qubit coupled to a resonator driven by a strong microwave field, we propose a method to implement two quantum logic gates ([Formula: see text]SWAP and NTCP gates) of one qubit simultaneously controlling [Formula: see text] qubits selected from [Formula: see text] qubits in a circuit QED [Formula: see text] by introducing qubit–qubit interaction. The interaction between the qubits and the circuit QED can be achieved by tuning the gate voltage and the external flux. The operation times of the logic gates are much smaller than the decoherence time and dephasing time. Moreover, the numerical simulation under the influence of the gates operations shows that the scheme could be achieved efficiently with presently available techniques.

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Caraiman, Simona, and Vasile Manta. "Parallel Simulation of Quantum Search." International Journal of Computers Communications & Control 5, no. 5 (December 1, 2010): 634. http://dx.doi.org/10.15837/ijccc.2010.5.2219.

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Simulation of quantum computers using classical computers is a computationally hard problem, requiring a huge amount of operations and storage. Parallelization can alleviate this problem, allowing the simulation of more qubits at the same time or the same number of qubits to be simulated in less time. A promising approach is represented by executing these simulators in Grid systems that can provide access to high performance resources. In this paper we present a parallel implementation of the QC-lib quantum computer simulator deployed as a Grid service. Using a specific scheme for partitioning the terms describing quantum states and efficient parallelization of the general singe qubit operator and of the controlled operators, very good speed-ups were obtained for the simulation of the quantum search problem.

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Said, Taoufik, Abdelhaq Chouikh, Karima Essammouni, and Mohamed Bennai. "Realizing an N-two-qubit quantum logic gate in a cavity QED with nearest qubit--qubit interaction." Quantum Information and Computation 16, no. 5&6 (April 2016): 465–82. http://dx.doi.org/10.26421/qic16.5-6-4.

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We propose an effective way for realizing a three quantum logic gates (NTCP gate, NTCP-NOT gate and NTQ-NOT gate) of one qubit simultaneously controlling N target qubits based on the qubit-qubit interaction. We use the superconducting qubits in a cavity QED driven by a strong microwave field. In our scheme, the operation time of these gates is independent of the number N of qubits involved in the gate operation. These gates are insensitive to the initial state of the cavity QED and can be used to produce an analogous CNOT gate simultaneously acting on N qubits. The quantum phase gate can be realized in a time (nanosecond-scale) much smaller than decoherence time and dephasing time (microsecond-scale) in cavity QED. Numerical simulation under the influence of the gate operations shows that the scheme could be achieved efficiently within current state-of-the-art technology.

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Said, T., A. Chouikh, K. Essammouni, and M. Bennai. "Implementing N-quantum phase gate via circuit QED with qubit–qubit interaction." Modern Physics Letters B 30, no. 05 (February 20, 2016): 1650050. http://dx.doi.org/10.1142/s0217984916500500.

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We propose a method for realizing a quantum phase gate of one qubit simultaneously controlling [Formula: see text] target qubits based on the qubit–qubit interaction. We show how to implement the proposed gate with one transmon qubit simultaneously controlling [Formula: see text] transmon qubits in a circuit QED driven by a strong microwave field. In our scheme, the operation time of this phase gate is independent of the number [Formula: see text] of qubits. On the other hand, this gate can be realized in a time of nanosecond-scale much smaller than the decoherence time and dephasing time both being the time of microsecond-scale. Numerical simulation of the occupation probabilities of the second excited lever shows that the scheme could be achieved efficiently within current technology.

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7

Yan, Zhiguang, Yu-Ran Zhang, Ming Gong, Yulin Wu, Yarui Zheng, Shaowei Li, Can Wang, et al. "Strongly correlated quantum walks with a 12-qubit superconducting processor." Science 364, no. 6442 (May 2, 2019): 753–56. http://dx.doi.org/10.1126/science.aaw1611.

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Quantum walks are the quantum analogs of classical random walks, which allow for the simulation of large-scale quantum many-body systems and the realization of universal quantum computation without time-dependent control. We experimentally demonstrate quantum walks of one and two strongly correlated microwave photons in a one-dimensional array of 12 superconducting qubits with short-range interactions. First, in one-photon quantum walks, we observed the propagation of the density and correlation of the quasiparticle excitation of the superconducting qubit and quantum entanglement between qubit pairs. Second, when implementing two-photon quantum walks by exciting two superconducting qubits, we observed the fermionization of strongly interacting photons from the measured time-dependent long-range anticorrelations, representing the antibunching of photons with attractive interactions. The demonstration of quantum walks on a quantum processor, using superconducting qubits as artificial atoms and tomographic readout, paves the way to quantum simulation of many-body phenomena and universal quantum computation.

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8

Bashkirov, Evgeny K. "Entanglement of two superconducting qubits induced by a thermal noise of a cavity with Kerr medium taking into account the atomic coherence." Physics of Wave Processes and Radio Systems 25, no. 1 (March 29, 2022): 7–15. http://dx.doi.org/10.18469/1810-3189.2022.25.1.7-15.

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The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.

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9

Huang, Xing Kui. "The Construction and Simulation Analysis of Three-Qubit Hxx Chain Refrigerator Based on Quantum Entangled States." Applied Mechanics and Materials 380-384 (August 2013): 4849–55. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.4849.

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Quantum entangled state theory is combined with quantum thermodynamics theory to build quantum entangled state heat engine. The basic nature of three-qubit Hxx chain, and all parameters of the orbit are analyzed. Energy model of quantum entangled state refrigerator in working process is taken as as a theoretical basis to construct three qubits Hxx chain refrigerator based on quantum entangled states. The working nature of the new quantum entangled state refrigerator under different field strength is studied. Compaired with two-qubit Hxxx chain refrigerator based on quantum entangled states and mapping analysis, the working efficiency of three qubits Hxx chain refrigerator based on quantum entangled states is much higher when the field strength is not zero and its working state is more stable.

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10

Bertoni, A., P. Bordone, R. Brunetti, C. Jacoboni, and S. Reggiani. "Numerical Simulation of Quantum Logic Gates Based on Quantum Wires." VLSI Design 13, no. 1-4 (January 1, 2001): 97–102. http://dx.doi.org/10.1155/2001/86126.

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A system based on frontier mesoscopic semiconductor technology, able to perform the basic quantum operations needed for quantum computation, is proposed. The elementary quantum bit (qubit) is defined as the state of an electron running along a couple of quantum wires coupled through a potential barrier with variable height and/ or width. A proper design of the system, together with the action of Coulomb interaction of two electrons representing two different qubits, allows the implementation of basic one-qubit and two-qubit quantum logic gates. Numerical simulations confirm the correctness of the hypothesis.

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11

Takahashi, Yasuhiro, Takeshi Yamazaki, and Kazuyuki Tanaka. "Hardness of classically simulating quantum circuits with unbounded Toffoli and fan-out gates." Quantum Information and Computation 14, no. 13&14 (October 2014): 1149–64. http://dx.doi.org/10.26421/qic14.13-14-7.

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We study the classical simulatability of constant-depth polynomial-size quantum circuits followed by only one single-qubit measurement, where the circuits consist of universal gates on at most two qubits and additional gates on an unbounded number of qubits. First, we consider unbounded Toffoli gates as additional gates and deal with the weak simulation, i.e., sampling the output probability distribution. We show that there exists a constant-depth quantum circuit with only one unbounded Toffoli gate that is not weakly simulatable, unless $\bqp \subseteq \postbpp \cap \am$. Then, we consider unbounded fan-out gates as additional gates and deal with the strong simulation, i.e., computing the output probability. We show that there exists a constant-depth quantum circuit with only two unbounded fan-out gates that is not strongly simulatable, unless $\p = \pp$. These results are in contrast to the fact that any constant-depth quantum circuit without additional gates on an unbounded number of qubits is strongly and weakly simulatable.

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12

Bagrov, A. R., and E. K. Bashkirov. "DYNAMICS OF THE THREE-QUBITS TAVIS — CUMMINGS MODEL." Vestnik of Samara University. Natural Science Series 28, no. 1-2 (December 29, 2022): 95–105. http://dx.doi.org/10.18287/2541-7525-2022-28-1-2-95-105.

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In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.

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13

Olaya-Castro, A., C. F. Lee, and N. F. Johnson. "Exact simulation of multi-qubit dynamics with only three qubits." Europhysics Letters (EPL) 74, no. 2 (April 2006): 208–14. http://dx.doi.org/10.1209/epl/i2006-10005-1.

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14

Ferraro, Elena, and Marco De Michielis. "Bandwidth-Limited and Noisy Pulse Sequences for Single Qubit Operations in Semiconductor Spin Qubits." Entropy 21, no. 11 (October 26, 2019): 1042. http://dx.doi.org/10.3390/e21111042.

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Spin qubits are very valuable and scalable candidates in the area of quantum computation and simulation applications. In the last decades, they have been deeply investigated from a theoretical point of view and realized on the scale of few devices in the laboratories. In semiconductors, spin qubits can be built confining the spin of electrons in electrostatically defined quantum dots. Through this approach, it is possible to create different implementations: single electron spin qubit, singlet–triplet spin qubit, or a three-electron architecture, e.g., the hybrid qubit. For each qubit type, we study the single qubit rotations along the principal axis of Bloch sphere including the mandatory non-idealities of the control signals that realize the gate operations. The realistic transient of the control signal pulses are obtained by adopting an appropriate low-pass filter function. In addition. the effect of disturbances on the input signals is taken into account by using a Gaussian noise model.

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APPN Editorial Office. "Highlights from the Asia Pacific Region." Asia Pacific Physics Newsletter 02, no. 02 (August 2013): 29–46. http://dx.doi.org/10.1142/s2251158x13000271.

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Quantum information technologies hold the promise of greatly outperforming traditional approaches in, e.g., cryptography, metrology and simulation. However, the ultimate goal of realizing scalable quantum computing has so far remained elusive, largely owing to the formidable difficulty in "wiring up" suitable quantum bits (qubits). In recent years, individual nitrogen-vacancy (NV-) defects in diamond have emerged as one of the most promising candidates for a solidstate qubit for two reasons. First, they possess the longest observed room-temperature coherence time of an electron spin (the qubit) to date; second, their spin can be initialized and measured with a nanoscale resolution using optical techniques under ambient conditions. However, interconnecting different NV- centres remains a big challenge. This problem is further exacerbated by the need for a large spatial separation between adjacent qubits, required for individual qubit addressability.

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Sabín, Carlos. "Digital Quantum Simulation of Linear and Nonlinear Optical Elements." Quantum Reports 2, no. 1 (March 4, 2020): 208–20. http://dx.doi.org/10.3390/quantum2010013.

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We provide a recipe for the digitalization of linear and nonlinear quantum optics in networks of superconducting qubits. By combining digital techniques with boson-qubit mappings, we address relevant problems that are typically considered in analog simulators, such as the dynamical Casimir effect or molecular force fields, including nonlinearities. In this way, the benefits of digitalization are extended in principle to a new realm of physical problems. We present preliminary examples launched in IBM Q 5 Tenerife.

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Zakharov, Rodion K., and Evgeny K. Bashkirov. "Entanglement of two dipole-couples qubits induced by a thermal field of a cavity with Kerr medium." Physics of Wave Processes and Radio Systems 24, no. 3 (November 18, 2021): 9–17. http://dx.doi.org/10.18469/1810-3189.2021.24.3.9-17.

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In the present work, we investigated the dynamics of two identical superconducting qubits interacting with the mode of the quantum electromagnetic field of a microwave coplanar cavity with a Kerr medium in the presence of an effective dipole-dipole interaction of the qubits. We have found an exact solution of the quantum Liouville equation for the complete density matrix of the system under consideration for the Fock and thermal chaotic initial states of the cavityr field. The exact solution for the full density matrix was used to determine the reduced qubit density matrix and to calculate the entanglement parameter concurrence. Computer simulation of the time dependence of the concurrshowed that for certain initial states of qubits, their entanglement can be significantly increased in the presence of a Kerr medium and direct dipole-dipole interaction.

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Menegasso Pires, Otto, Eduardo Inacio Duzzioni, Jerusa Marchi, and Rafael De Santiago. "Quantum Circuit Synthesis Using Projective Simulation." Inteligencia Artificial 24, no. 67 (April 13, 2021): 90–101. http://dx.doi.org/10.4114/intartif.vol24iss67pp90-101.

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Quantum Computing has been evolving in the last years. Although nowadays quantum algorithms performance has shown superior to their classical counterparts, quantum decoherence and additional auxiliary qubits needed for error tolerance routines have been huge barriers for quantum algorithms efficient use.These restrictions lead us to search for ways to minimize algorithms costs, i.e the number of quantum logical gates and the depth of the circuit. For this, quantum circuit synthesis and quantum circuit optimization techniques are explored.We studied the viability of using Projective Simulation, a reinforcement learning technique, to tackle the problem of quantum circuit synthesis. The agent had the task of creating quantum circuits up to 5 qubits. Our simulations demonstrated that the agent had a good performance but its capacity for learning new circuits decreased as the number of qubits increased.

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Sun, Bo, Abdullah M. Iliyasu, Fei Yan, Fangyan Dong, and Kaoru Hirota. "An RGB Multi-Channel Representation for Images on Quantum Computers." Journal of Advanced Computational Intelligence and Intelligent Informatics 17, no. 3 (May 20, 2013): 404–17. http://dx.doi.org/10.20965/jaciii.2013.p0404.

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RGB multi channel representation is proposed for images on quantum computers (MCQI) that captures information about colors (RGB channels) and their corresponding positions in an image in a normalized quantum state. The proposed representation makes it possible to store the RGB information about an image simultaneously by using 2n+3 qubits for encoding 2n× 2npixel images, whereas pixel-wise processing is necessary in many other quantum image representations, e.g., qubit lattice, grid qubit, and quantum lattice. Simulation of storage and retrieval of MCQI images using human facial images demonstrated that 15 qubits are required for encoding 64 × 64 colored images, and encoded information is retrieved by measurement. Perspectives of designing quantum image operators are also discussed based onMCQI representation, e.g., channel of interest, channel swapping, and restrict version of color transformation.

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Jiang, Zhang, Amir Kalev, Wojciech Mruczkiewicz, and Hartmut Neven. "Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning." Quantum 4 (June 4, 2020): 276. http://dx.doi.org/10.22331/q-2020-06-04-276.

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We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an n-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on ⌈log3⁡(2n+1)⌉ qubits. The mapping has a simple structure and is optimal in the sense that it is impossible to construct Pauli operators in any fermion-to-qubit mapping acting nontrivially on less than log3⁡(2n) qubits on average. We apply it to the problem of learning k-fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show that one can determine individual elements of all k-fermion RDMs in parallel, to precision ϵ, by repeating a single quantum circuit for ≲(2n+1)kϵ−2 times. This result is based on a method we develop here that allows one to determine individual elements of all k-qubit RDMs in parallel, to precision ϵ, by repeating a single quantum circuit for ≲3kϵ−2 times, independent of the system size. This improves over existing schemes for determining qubit RDMs.

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21

Vlasov, Alexander Yu. "Quantum circuits and Spin(3n) groups." Quantum Information and Computation 15, no. 3&4 (March 2015): 235–59. http://dx.doi.org/10.26421/qic15.3-4-3.

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All quantum gates with one and two qubits may be described by elements of Spin groups due to isomorphisms Spin(3)\isomSU(2) and Spin(6)\isomSU(4). However, the group of n-qubit gates SU(2^n) for n>2 has bigger dimension than Spin(3n). A quantum circuit with one- and two-qubit gates may be used for construction of arbitrary unitary transformation SU(2^n). Analogously, the `$Spin(3n)$ circuits' are introduced in this work as products of elements associated with one- and two-qubit gates with respect to the above-mentioned isomorphisms. The matrix tensor product implementation of the Spin(3n) group together with relevant models by usual quantum circuits with 2n qubits are investigated in such a framework. A certain resemblance with well-known sets of non-universal quantum gates (e.g., matchgates, noninteracting-fermion quantum circuits) related with Spin(2n) may be found in presented approach. Finally, a possibility of the classical simulation of such circuits in polynomial time is discussed.

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Woolfe, Kieran J., Charles D. Hill, and Lloyd C. L. Hollenberg. "Scaling and efficient classical simulation of the quantum Fourier transform." Quantum Information and Computation 17, no. 1&2 (January 2017): 1–14. http://dx.doi.org/10.26421/qic17.1-2-1.

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We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors in the operator converge to a common tensor as the number of qubits in the transform increases. Together these results imply that the application of the quantum Fourier transform to a matrix product state with n qubits of maximum Schmidt rank χ can be simulated in O(n (log(n))2 χ 2 ) time. We perform such simulations and quantify the error involved in representing the transform as a matrix product operator and simulating the quantum Fourier transform of periodic states.

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23

Zhang, Xu, Wenjie Jiang, Jinfeng Deng, Ke Wang, Jiachen Chen, Pengfei Zhang, Wenhui Ren, et al. "Digital quantum simulation of Floquet symmetry-protected topological phases." Nature 607, no. 7919 (July 20, 2022): 468–73. http://dx.doi.org/10.1038/s41586-022-04854-3.

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AbstractQuantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals1–8, in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions9,10, solid-state spin systems11–15, ultracold atoms16,17 and superconducting qubits18–20. Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors21.

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Jozsa, Richard, and Akimasa Miyake. "Matchgates and classical simulation of quantum circuits." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2100 (July 22, 2008): 3089–106. http://dx.doi.org/10.1098/rspa.2008.0189.

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Let G ( A , B ) denote the two-qubit gate that acts as the one-qubit SU (2) gates A and B in the even and odd parity subspaces, respectively, of two qubits. Using a Clifford algebra formalism, we show that arbitrary uniform families of circuits of these gates, restricted to act only on nearest neighbour (n.n.) qubit lines, can be classically efficiently simulated. This reproduces a result originally proved by Valiant using his matchgate formalism, and subsequently related by others to free fermionic physics. We further show that if the n.n. condition is slightly relaxed, to allow the same gates to act only on n.n. and next n.n. qubit lines, then the resulting circuits can efficiently perform universal quantum computation. From this point of view, the gap between efficient classical and quantum computational power is bridged by a very modest use of a seemingly innocuous resource (qubit swapping). We also extend the simulation result above in various ways. In particular, by exploiting properties of Clifford operations in conjunction with the Jordan–Wigner representation of a Clifford algebra, we show how one may generalize the simulation result above to provide further classes of classically efficiently simulatable quantum circuits, which we call Gaussian quantum circuits.

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Acharya, Nikita, Miroslav Urbanek, Wibe A. De Jong, and Samah Mohamed Saeed. "Test Points for Online Monitoring of Quantum Circuits." ACM Journal on Emerging Technologies in Computing Systems 18, no. 1 (January 31, 2022): 1–19. http://dx.doi.org/10.1145/3477928.

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Noisy Intermediate-Scale Quantum (NISQ) computers consisting of tens of inherently noisy quantum bits (qubits) suffer from reliability problems. Qubits and their gates are susceptible to various types of errors. Due to limited numbers of qubits and high error rates, quantum error correction cannot be applied. Physical constraints of quantum hardware including the error rates are used to guide the design and the layout of quantum circuits. The error rates determine the selection of qubits and their operations. The resulting circuit is executed on the quantum computer. This study explores the risk of unexpected changes in the error rates of NISQ computers post-calibration. We show that unexpected changes in error rates can alter the output state of a quantum circuit. To detect these changes, we propose the insertion of test points into the quantum circuit to enable online monitoring of the physical qubit behavior. We utilize classical, superposition, and uncompute test points. Furthermore, we use a gate error coverage metric to assess the quality of the tests. We verify the effectiveness of the proposed scheme on different IBM quantum computers (IBM Q), in addition to a noisy simulation that shows the scalability of the proposed approach.

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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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Wang, Qingfeng, Ming Li, Christopher Monroe, and Yunseong Nam. "Resource-Optimized Fermionic Local-Hamiltonian Simulation on a Quantum Computer for Quantum Chemistry." Quantum 5 (July 26, 2021): 509. http://dx.doi.org/10.22331/q-2021-07-26-509.

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The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing the power of quantum computers. Here, we address this problem in two aspects. In the fault-tolerant regime, we optimize the Rz and T gate counts along with the ancilla qubit counts required, assuming the use of a product-formula algorithm for implementation. We obtain a savings ratio of two in the gate counts and a savings ratio of eleven in the number of ancilla qubits required over the state of the art. In the pre-fault tolerant regime, we optimize the two-qubit gate counts, assuming the use of the variational quantum eigensolver (VQE) approach. Specific to the latter, we present a framework that enables bootstrapping the VQE progression towards the convergence of the ground-state energy of the fermionic system. This framework, based on perturbation theory, is capable of improving the energy estimate at each cycle of the VQE progression, by about a factor of three closer to the known ground-state energy compared to the standard VQE approach in the test-bed, classically-accessible system of the water molecule. The improved energy estimate in turn results in a commensurate level of savings of quantum resources, such as the number of qubits and quantum gates, required to be within a pre-specified tolerance from the known ground-state energy. We also explore a suite of generalized transformations of fermion to qubit operators and show that resource-requirement savings of up to more than 20%, in small instances, is possible.

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He, Kaiyong, Xiao Geng, Rutian Huang, Jianshe Liu, and Wei Chen. "Quantum computation and simulation with superconducting qubits*." Chinese Physics B 30, no. 8 (August 1, 2021): 080304. http://dx.doi.org/10.1088/1674-1056/ac16cf.

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29

Lee, Y. H., M. Khalil-Hani, and M. N. Marsono. "An FPGA-based quantum circuit emulation framework using heisenberg representation." International Journal of Quantum Information 16, no. 06 (September 2018): 1850052. http://dx.doi.org/10.1142/s0219749918500521.

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While physical realization of practical large-scale quantum computers is still ongoing, theoretical research of quantum computing applications is facilitated on classical computing platforms through simulation and emulation methods. Nevertheless, the exponential increase in resource requirement with the increase in the number of qubits is an inherent issue in classical modeling of quantum systems. In the effort to alleviate the critical scalability issue in existing FPGA emulation works, a novel FPGA-based quantum circuit emulation framework based on Heisenberg representation is proposed in this paper. Unlike previous works that are restricted to the emulations of quantum circuits of small qubit sizes, the proposed FPGA emulation framework can scale-up to 120-qubit on Altera Stratix IV FPGA for the stabilizer circuit case study while providing notable speed-up over the equivalent simulation model.

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30

Wang, Ruixia, Peng Zhao, Yirong Jin, and Haifeng Yu. "Control and mitigation of microwave crosstalk effect with superconducting qubits." Applied Physics Letters 121, no. 15 (October 10, 2022): 152602. http://dx.doi.org/10.1063/5.0115393.

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Improving gate performance is vital for scalable quantum computing. Universal quantum computing also requires gate fidelity to reach a high level. For a superconducting quantum processor, which operates in the microwave band, the single-qubit gates are usually realized with microwave driving. The crosstalk between microwave pulses is a non-negligible error source. In this article, we propose an error mitigation scheme to address this crosstalk issue for single-qubit gates. There are three steps in our method. First, by controlling the detuning between qubits, the microwave induced classical crosstalk error can be constrained within the computational subspace. Second, by applying the general decomposition procedure, the arbitrary single-qubit gate can be decomposed as a sequence of [Formula: see text] and virtual Z gates. Finally, by optimizing the parameters in virtual Z gates, the error constrained in the computational space can be corrected. Using our method, no additional compensation signals are needed, arbitrary single-qubit gate time will not be prolonged, and the circuit depth containing simultaneous single-qubit gates will also not increase. The simulation results show that, in a specific regime of qubit–qubit detuning, the infidelities of simultaneous single-qubit gates can be as low as that without microwave crosstalk.

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31

Ye, Yangsen, Sirui Cao, Yulin Wu, Xiawei Chen, Qingling Zhu, Shaowei Li, Fusheng Chen, et al. "Realization of High-Fidelity Controlled-Phase Gates in Extensible Superconducting Qubits Design with a Tunable Coupler." Chinese Physics Letters 38, no. 10 (November 1, 2021): 100301. http://dx.doi.org/10.1088/0256-307x/38/10/100301.

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High-fidelity two-qubit gates are essential for the realization of large-scale quantum computation and simulation. Tunable coupler design is used to reduce the problem of parasitic coupling and frequency crowding in many-qubit systems and thus thought to be advantageous. Here we design an extensible 5-qubit system in which center transmon qubit can couple to every four near-neighboring qubits via a capacitive tunable coupler and experimentally demonstrate high-fidelity controlled-phase (CZ) gate by manipulating central qubit and one near-neighboring qubit. Speckle purity benchmarking and cross entropy benchmarking are used to assess the purity fidelity and the fidelity of the CZ gate. The average purity fidelity of the CZ gate is 99.69±0.04% and the average fidelity of the CZ gate is 99.65±0.04%, which means that the control error is about 0.04%. Our work is helpful for resolving many challenges in implementation of large-scale quantum systems.

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32

Su, Fei-Fan, Zhao-Hua Yang, Shou-Kuan Zhao, Hai-Sheng Yan, Ye Tian, and Shi-Ping Zhao. "Fabrication of superconducting qubits and auxiliary devices with niobium base layer." Acta Physica Sinica 71, no. 5 (2022): 050303. http://dx.doi.org/10.7498/aps.71.20211865.

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Over the past two decades significant advances have been made in the research of superconducting quantum computing and quantum simulation, in particular of the device design and fabrication that leads to ever-increasing superconducting qubit coherence times and scales. With Google’s announcement of the realization of “quantum supremacy”, superconducting quantum computing has attracted even more attention. Superconducting qubits are macroscopic objects with quantum properties such as quantized energy levels and quantum-state superposition and entanglement. Their quantum states can be precisely manipulated by tuning the magnetic flux, charge, and phase difference of the Josephson junctions with nonlinear inductance through electromagnetic pulse signals, thereby implementing the quantum information processing. They have advantages in many aspects and are expected to become the central part of universal quantum computing. Superconducting qubits and auxiliary devices prepared with niobium or other hard metals like tantalum as bottom layers of large-area components have unique properties and potentials for further development. In this paper the research work in this area is briefly reviewed, starting from the design and working principle of a variety of superconducting qubits, to the detailed procedures of substrate selection and pretreatment, film growth, pattern transfer, etching, and Josephson junction fabrication, and finally the practical superconducting qubit and their auxiliary device fabrications with niobium base layers are also presented. We aim to provide a clear overview for the fabrication process of these superconducting devices as well as an outlook for further device improvement and optimization in order to help establish a perspective for future progress.

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33

Abu-Nada, Ali. "Quantum computing simulation of the hydrogen molecular ground-state energies with limited resources." Open Physics 19, no. 1 (January 1, 2021): 628–33. http://dx.doi.org/10.1515/phys-2021-0071.

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Abstract In this article, the hydrogen molecular ground-state energies using our algorithm based on quantum variational principle are calculated. They are calculated through a simulator since the system of the present study (i.e., the hydrogen molecule) is relatively small and hence the ground-state energies for this molecule are efficiently classically simulable using a simulator. Complete details of this algorithm are elucidated. For this, a full description on the fermions–qubits and the molecular Hamiltonian–qubit Hamiltonian transformations, is given. The authors search for qubit system parameters ( θ 0 {\theta }_{0} and θ 1 {\theta }_{1} ) that yield the minimum energies for the system and also study the ground state energies as a function of the molecular bond length. Proposed circuit is humble and does not include many parameters compared with that of Kandala et al., the authors control only two parameters ( θ 0 {\theta }_{0} and θ 1 {\theta }_{1} ).

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34

Sripakdee, Chatchawal. "Qubit Noise within Micro PANDA Ring Resonator in QKD Process." Applied Mechanics and Materials 879 (March 2018): 178–82. http://dx.doi.org/10.4028/www.scientific.net/amm.879.178.

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The aim of this work is about establishing and analyzing the Hamiltonian for entangled photon generation in a micro PANDA ring resonator for a quantum key generation unit in quantum cryptography processing. The reduced density matrix for two level states of qubits is also analyzed by using dynamics Heisenberg equation of motion. The master equation in the thermal effect shows fluctuation of the corresponding c-operators in phase space. The optimum simulation result for probability of qubit states survive for the existence of a surrounding heat bath is also showed and discussed.

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35

Simoni, Mario, Giovanni Amedeo Cirillo, Giovanna Turvani, Mariagrazia Graziano, and Maurizio Zamboni. "Towards Compact Modeling of Noisy Quantum Computers: A Molecular-Spin-Qubit Case of Study." ACM Journal on Emerging Technologies in Computing Systems 18, no. 1 (January 31, 2022): 1–26. http://dx.doi.org/10.1145/3474223.

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Classical simulation of Noisy Intermediate Scale Quantum computers is a crucial task for testing the expected performance of real hardware. The standard approach, based on solving Schrödinger and Lindblad equations, is demanding when scaling the number of qubits in terms of both execution time and memory. In this article, attempts in defining compact models for the simulation of quantum hardware are proposed, ensuring results close to those obtained with standard formalism. Molecular Nuclear Magnetic Resonance quantum hardware is the target technology, where three non-ideality phenomena—common to other quantum technologies—are taken into account: decoherence, off-resonance qubit evolution, and undesired qubit-qubit residual interaction. A model for each non-ideality phenomenon is embedded into a MATLAB simulation infrastructure of noisy quantum computers. The accuracy of the models is tested on a benchmark of quantum circuits, in the expected operating ranges of quantum hardware. The corresponding outcomes are compared with those obtained via numeric integration of the Schrödinger equation and the Qiskit’s QASMSimulator. The achieved results give evidence that this work is a step forward towards the definition of compact models able to provide fast results close to those obtained with the traditional physical simulation strategies, thus paving the way for their integration into a classical simulator of quantum computers.

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36

Morgado, M., and S. Whitlock. "Quantum simulation and computing with Rydberg-interacting qubits." AVS Quantum Science 3, no. 2 (June 2021): 023501. http://dx.doi.org/10.1116/5.0036562.

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37

Borzenkova, O. V., G. I. Struchalin, A. S. Kardashin, V. V. Krasnikov, N. N. Skryabin, S. S. Straupe, S. P. Kulik, and J. D. Biamonte. "Variational simulation of Schwinger's Hamiltonian with polarization qubits." Applied Physics Letters 118, no. 14 (April 5, 2021): 144002. http://dx.doi.org/10.1063/5.0043322.

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38

JANZING, DOMINIK, PAWEL WOCJAN, and THOMAS BETH. "ON THE COMPUTATIONAL POWER OF PHYSICAL INTERACTIONS: BOUNDS ON THE NUMBER OF TIME STEPS FOR SIMULATING ARBITRARY INTERACTION GRAPHS." International Journal of Foundations of Computer Science 14, no. 05 (October 2003): 889–903. http://dx.doi.org/10.1142/s0129054103002072.

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The most popular model of quantum computation is the quantum circuit model using single and two qubit gates as elementary transformations. Definitions of quantum complexity usually refer to this model. In contrast, we consider the physical interactions among the qubits as the basic computational resource that allows to carry out complex transformations on the quantum register. One method to compare the computational power of different interactions is to examine the complexity of the so-called mutual simulation of interaction Hamiltonians. The physical interaction can simulate other interactions by interspersing the natural time evolution with external control operations. In previous papers we have considered mutual simulation of n-partite pair-interaction Hamiltonians. We have focussed on the running time overhead of general simulations, while considering the required number of time steps only for special cases (decoupling and time-reversal). These two complexity measures differ significantly. Here we derive lower bounds on the number of time steps for simulations of general interaction graphs. In particular, the simulation of interaction graphs with irrational spectrum requires at least n steps. We discuss as examples graphs that correspond to graph codes and nearest neighbor interactions in 1- and 2-dimensional lattices. In the latter case the lower bounds are almost tight.

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39

Atzori, Matteo, Alessandro Chiesa, Elena Morra, Mario Chiesa, Lorenzo Sorace, Stefano Carretta, and Roberta Sessoli. "A two-qubit molecular architecture for electron-mediated nuclear quantum simulation." Chemical Science 9, no. 29 (2018): 6183–92. http://dx.doi.org/10.1039/c8sc01695j.

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40

Bravyi, Sergey, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard. "Simulation of quantum circuits by low-rank stabilizer decompositions." Quantum 3 (September 2, 2019): 181. http://dx.doi.org/10.22331/q-2019-09-02-181.

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Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizerrank, which for a pure state ψ is defined to be the smallest integer χ such that ψ is a superposition of χ stabilizer states. Here we develop a comprehensive mathematical theory of the stabilizer rank and the related approximate stabilizer rank. We also present a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art. A new feature is the capability to simulate circuits composed of Clifford gates and arbitrary diagonal gates, extending the reach of a previous algorithm specialized to the Clifford+T gate set. We implemented the new simulation methods and used them to simulate quantum algorithms with 40-50 qubits and over 60 non-Clifford gates, without resorting to high-performance computers. We report a simulation of the Quantum Approximate Optimization Algorithm in which we process superpositions of χ∼106 stabilizer states and sample from the full n-bit output distribution, improving on previous simulations which used ∼103 stabilizer states and sampled only from single-qubit marginals. We also simulated instances of the Hidden Shift algorithm with circuits including up to 64 T gates or 16 CCZ gates; these simulations showcase the performance gains available by optimizing the decomposition of a circuit's non-Clifford components.

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41

Ellinas, Demosthenes. "Operational Algorithms for Separable Qubit X States." Condensed Matter 4, no. 3 (July 2, 2019): 64. http://dx.doi.org/10.3390/condmat4030064.

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This work motivates and applies operational methodology to simulation of quantum statistics of separable qubit X states. Three operational algorithms for evaluating separability probability distributions are put forward. Building on previous findings, the volume function characterizing the separability distribution is determined via quantum measurements of multi-qubit observables. Three measuring states, one for each algorithm are generated via (i) a multi-qubit channel map, (ii) a unitary operator generated by a Hamiltonian describing a non-uniform hypergraph configuration of interactions among 12 qubits, and (iii) a quantum walk CP map in a extended state space. Higher order CZ gates are the only tools of the algorithms hence the work associates itself computationally with the Instantaneous Quantum Polynomial-time Circuits (IQP), while wrt possible implementation the work relates to the Lechner-Hauke-Zoller (LHZ) architecture of higher order coupling. Finally some uncertainty aspects of the quantum measurement observables are discussed together with possible extensions to non-qubit separable bipartite systems.

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42

Shen, Ze-Song, and Fang-Yu Hong. "Electrically tunable quantum interfaces between photons and spin qubits in carbon nanotube quantum dots." International Journal of Quantum Information 14, no. 08 (December 2016): 1650047. http://dx.doi.org/10.1142/s0219749916500477.

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We present a new scheme for quantum interfaces (QIs) to accomplish the interconversion of photonic qubits and spin qubits based on optomechanical resonators and the spin–orbit-induced interactions in suspended carbon nanotube quantum dots (CNTQDs). This interface implements quantum spin transducers and further enables electrical manipulation of local electron spin qubits, which lays the foundation for all-electrical control of state transfer protocols between two distant quantum nodes in a quantum network. We numerically evaluate the state transfer processes and proceed to estimate the effect of each coupling strength on the operation fidelities. The simulation suggests that high operation fidelities are obtainable under realistic experimental conditions.

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43

Dalzell, Alexander M., Aram W. Harrow, Dax Enshan Koh, and Rolando L. La Placa. "How many qubits are needed for quantum computational supremacy?" Quantum 4 (May 11, 2020): 264. http://dx.doi.org/10.22331/q-2020-05-11-264.

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Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of classical computation. One common assumption is that the polynomial hierarchy (PH) does not collapse, a stronger version of the statement that P≠NP, which leads to the conclusion that any classical simulation of certain families of quantum circuits requires time scaling worse than any polynomial in the size of the circuits. However, the asymptotic nature of this conclusion prevents us from calculating exactly how many qubits these quantum circuits must have for their classical simulation to be intractable on modern classical supercomputers. We refine these quantum computational supremacy arguments and perform such a calculation by imposing fine-grained versions of the non-collapse conjecture. Our first two conjectures poly3-NSETH(a) and per-int-NSETH(b) take specific classical counting problems related to the number of zeros of a degree-3 polynomial in n variables over F2 or the permanent of an n×n integer-valued matrix, and assert that any non-deterministic algorithm that solves them requires 2cn time steps, where c∈{a,b}. A third conjecture poly3-ave-SBSETH(a′) asserts a similar statement about average-case algorithms living in the exponential-time version of the complexity class SBP. We analyze evidence for these conjectures and argue that they are plausible when a=1/2, b=0.999 and a′=1/2.Imposing poly3-NSETH(1/2) and per-int-NSETH(0.999), and assuming that the runtime of a hypothetical quantum circuit simulation algorithm would scale linearly with the number of gates/constraints/optical elements, we conclude that Instantaneous Quantum Polynomial-Time (IQP) circuits with 208 qubits and 500 gates, Quantum Approximate Optimization Algorithm (QAOA) circuits with 420 qubits and 500 constraints and boson sampling circuits (i.e. linear optical networks) with 98 photons and 500 optical elements are large enough for the task of producing samples from their output distributions up to constant multiplicative error to be intractable on current technology. Imposing poly3-ave-SBSETH(1/2), we additionally rule out simulations with constant additive error for IQP and QAOA circuits of the same size. Without the assumption of linearly increasing simulation time, we can make analogous statements for circuits with slightly fewer qubits but requiring 104 to 107 gates.

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Khatri, Sumeet, Ryan LaRose, Alexander Poremba, Lukasz Cincio, Andrew T. Sornborger, and Patrick J. Coles. "Quantum-assisted quantum compiling." Quantum 3 (May 13, 2019): 140. http://dx.doi.org/10.22331/q-2019-05-13-140.

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Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitaryUand a trainable unitaryVas the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost involves not only the global overlapTr(V†U)but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we prove that our cost cannot be efficiently approximated with a classical algorithm under reasonable complexity assumptions. We present both gradient-free and gradient-based approaches to minimizing this cost. As a demonstration of QAQC, we compile various one-qubit gates on IBM's and Rigetti's quantum computers into their respective native gate alphabets. Furthermore, we successfully simulate QAQC up to a problem size of 9 qubits, and these simulations highlight both the scalability of our cost function as well as the noise resilience of QAQC. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking.

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45

Lee, Donggeun, and Wonmin Son. "Simulation of qubits in 1D array using MPS method." Current Applied Physics 16, no. 12 (December 2016): 1631–36. http://dx.doi.org/10.1016/j.cap.2016.09.008.

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46

Beaudrap, Niel de, and Steven Herbert. "Fast Stabiliser Simulation with Quadratic Form Expansions." Quantum 6 (September 15, 2022): 803. http://dx.doi.org/10.22331/q-2022-09-15-803.

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This paper builds on the idea of simulating stabiliser circuits through transformations of {quadratic form expansions}. This is a representation of a quantum state which specifies a formula for the expansion in the standard basis, describing real and imaginary relative phases using a degree-2 polynomial over the integers. We show how, with deft management of the quadratic form expansion representation, we may simulate individual stabiliser operations in O(n2) time matching the overall complexity of other simulation techniques \cite{Aaronson2004,Anders2006,Bravyi2016}. Our techniques provide economies of scale in the time to simulate simultaneous measurements of all (or nearly all) qubits in the standard basis. Our techniques also allow single-qubit measurements with deterministic outcomes to be simulated in constant time. We also describe throughout how these bounds may be tightened when the expansion of the state in the standard basis has relatively few terms (has low `rank'), or can be specified by sparse matrices. Specifically, this allows us to simulate a `local' stabiliser syndrome measurement in time O(n), for a stabiliser code subject to Pauli noise --- matching what is possible using techniques developed by Gidney \cite{gidney2021stim} without the need to store which operations have thus far been simulated.

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47

Bertlmann, Reinhold A., and Beatrix C. Hiesmayr. "Kaonic Qubits." Quantum Information Processing 5, no. 5 (July 12, 2006): 421–40. http://dx.doi.org/10.1007/s11128-006-0026-1.

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48

Shahbeigi, Fereshte, Mahsa Karimi, and Vahid Karimipour. "Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer." Physica Scripta 97, no. 2 (January 20, 2022): 025101. http://dx.doi.org/10.1088/1402-4896/ac49b0.

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Abstract Two qubit density matrices which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this Hamiltonian, we show that by only two qubits, one can simulate the dynamics of this system on the IBM quantum computer.

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Rudi, Alessandro, Leonard Wossnig, Carlo Ciliberto, Andrea Rocchetto, Massimiliano Pontil, and Simone Severini. "Approximating Hamiltonian dynamics with the Nyström method." Quantum 4 (February 20, 2020): 234. http://dx.doi.org/10.22331/q-2020-02-20-234.

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Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation technique whose runtime scales polynomially in the number of qubits and the Frobenius norm of the Hamiltonian. As an immediate application, we show that sample based quantum simulation, a type of evolution where the Hamiltonian is a density matrix, can be efficiently classically simulated under specific structural conditions. Our main technical contribution is a randomized algorithm for approximating Hermitian matrix exponentials. The proof leverages a low-rank, symmetric approximation via the Nyström method. Our results suggest that under strong sampling assumptions there exist classical poly-logarithmic time simulations of quantum computations.

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Avila, Anderson, Renata Hax Sander Reiser, Maurício Lima Pilla, and Adenauer Correa Yamin. "Improving in situ GPU simulation of quantum computing in the D-GM environment." International Journal of High Performance Computing Applications 33, no. 3 (January 16, 2019): 462–72. http://dx.doi.org/10.1177/1094342018823251.

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Exponential increase and global access to read/write memory states in quantum computing (QC) simulation limit both the number of qubits and quantum transformations which can be currently simulated. Although QC simulation is parallel by nature, spatial and temporal complexity are major performance hazards, making this a nontrivial application for high performance computing. A new methodology employing reduction and decomposition optimizations has shown relevant results, but its GPU implementation could be further improved. In this work, we develop a new kernel for in situ GPU simulation that better explores its resources without requiring further hardware. Shor’s and Grover’s algorithms are simulated up to 25 and 21 qubits respectively and compared to our previous version, to [Formula: see text] simulator and to ProjectQ framework, showing better results with relative speedups up to 4.38×, 3357.76× and 333× respectively.

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Journal articles on the topic 'Qubits simulation'

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