Journal articles: 'Computational quantum theory'

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KRISHNAMURTHY, E. V., and VIKRAM KRISHNAMURTHY. "QUANTUM FIELD THEORY AND COMPUTATIONAL PARADIGMS." International Journal of Modern Physics C 12, no. 08 (October 2001): 1179–205. http://dx.doi.org/10.1142/s0129183101002437.

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We introduce the basic theory of quantization of radiation field in quantum physics and explain how it relates to the theory of recursive functions in computer science. We outline the basic differences between quantum mechanics (QM) and quantum field theory (QFT) and explain why QFT is better suited for a computational paradigm — based on algorithmic requirement, countably infinite degrees of freedom and the creation of macroscopic output objects. The quanta of the radiation field correspond to the non-negative integers and the harmonic oscillator spectra correspond to the recursive computation — with the creation and annihilation operators, respectively, playing the same role as the successor and predecessor in computability theory. Accordingly, this approach relates the classical computational model and the quantum physical model more directly than the Turing machine approach used earlier. Also, the application of Lambda calculus formalism and the associated denotational semantics (that is widely used in the classical computational paradigm involving recursive functions) for applications to computational paradigm based on quantum field theory is described. Finally, we explain where QFT and conventional paradigm depart from each other, and examine the concept of fixed points, phase transitions, programmability, emergent computation and related open problems.

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Potvin, Jean, Harvey Gould, and Jan Tobochnik. "Computational Quantum-Field Theory." Computers in Physics 7, no. 2 (1993): 149. http://dx.doi.org/10.1063/1.4823157.

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Stephen, David T., Hendrik Poulsen Nautrup, Juani Bermejo-Vega, Jens Eisert, and Robert Raussendorf. "Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter." Quantum 3 (May 20, 2019): 142. http://dx.doi.org/10.22331/q-2019-05-20-142.

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Quantum phases of matter are resources for notions of quantum computation. In this work, we establish a new link between concepts of quantum information theory and condensed matter physics by presenting a unified understanding of symmetry-protected topological (SPT) order protected by subsystem symmetries and its relation to measurement-based quantum computation (MBQC). The key unifying ingredient is the concept of quantum cellular automata (QCA) which we use to define subsystem symmetries acting on rigid lower-dimensional lines or fractals on a 2D lattice. Notably, both types of symmetries are treated equivalently in our framework. We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the structure of entanglement that is uniformly present throughout these phases. By also formulating schemes of MBQC based on these QCA, we are able to prove that most of the phases we construct are computationally universal phases of matter, in which every state is a resource for universal MBQC. Interestingly, our approach allows us to construct computational phases which have practical advantages over previous examples, including a computational speedup. The significance of the approach stems from constructing novel computationally universal phases of matter and showcasing the power of tensor networks and quantum information theory in classifying subsystem SPT order.

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Park, Buhm Soon. "Between Accuracy and Manageability: Computational Imperatives in Quantum Chemistry." Historical Studies in the Natural Sciences 39, no. 1 (2009): 32–62. http://dx.doi.org/10.1525/hsns.2009.39.1.32.

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This article explores the place of computation in the history of quantum theory by examining the development of several approximation methods to solve the Schröödinger equation without using empirical information, as these were worked out in the years from 1927 to 1933. These ab initio methods, as they became known, produced the results that helped validate the use of quantum mechanics in many-body atomic and molecular systems, but carrying out the computations became increasingly laborious and difficult as better agreement between theory and experiment was pursued and more complex systems were tackled. I argue that computational work in the early years of quantum chemistry shows an emerging practice of theory that required human labor, technological improvement (computers), and mathematical ingenuity.

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BERTINI, CESARINO, and ROBERTO LEPORINI. "QUANTUM COMPUTATIONAL FINITE-VALUED LOGICS." International Journal of Quantum Information 05, no. 05 (October 2007): 641–65. http://dx.doi.org/10.1142/s0219749907003109.

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The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quantum information quantity, represented by a quregister (a system of qudits) or, more generally, by a mixture of quregisters (called qumix), whose dimension depends on the logical complexity of the sentence. At the same time, the logical connectives are interpreted as logical operations defined in terms of quantum logical gates. Physical models of quantum computational logics can be built by means of Mach-Zehnder interferometers.

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Potvin, Jean, Harvey Gould, and Jan Tobochnik. "Computational Quantum Field Theory. Part II: Lattice Gauge Theory." Computers in Physics 8, no. 2 (1994): 170. http://dx.doi.org/10.1063/1.4823280.

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DALLA CHIARA, MARIA LUISA, ROBERTO GIUNTINI, and ROBERTO LEPORINI. "LOGICS FROM QUANTUM COMPUTATION." International Journal of Quantum Information 03, no. 02 (June 2005): 293–337. http://dx.doi.org/10.1142/s0219749905000943.

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The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits) or, more generally, with a mixture of quregisters (called qumix). In this framework, any sentence α of the language gives rise to a quantum tree: a kind of quantum circuit that transforms the quregister (qumix) associated to the atomic subformulas of α into the quregister (qumix) associated to α. A variant of the quantum computational semantics is represented by the quantum holistic semantics, which permits us to represent entangled meanings. Physical models of quantum computational logics can be built by means of Mach–Zehnder interferometers.

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Krishnamurthy, E. V. "Computational Power of Quantum Machines, Quantum Grammars and Feasible Computation." International Journal of Modern Physics C 09, no. 02 (March 1998): 213–41. http://dx.doi.org/10.1142/s0129183198000170.

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This paper studies the computational power of quantum computers to explore as to whether they can recognize properties which are in nondeterministic polynomial-time class (NP) and beyond. To study the computational power, we use the Feynman's path integral (FPI) formulation of quantum mechanics. From a computational point of view the Feynman's path integral computes a quantum dynamical analogue of the k-ary relation computed by an Alternating Turing machine (ATM) using AND-OR Parallelism. Hence, if we can find a suitable mapping function between an instance of a mathematical problem and the corresponding interference problem, using suitable potential functions for which FPI can be integrated exactly, the computational power of a quantum computer can be bounded to that of an alternating Turing machine that can solve problems in NP (e.g, factorization problem) and in polynomial space. Unfortunately, FPI is exactly integrable only for a few problems (e.g., the harmonic oscillator) involving quadratic potentials; otherwise, they may be only approximately computable or noncomputable. This means we cannot in general solve all quantum dynamical problems exactly except for those special cases of quadratic potentials, e.g., harmonic oscillator. Since there is a one to one correspondence between the quantum mechanical problems that can be analytically solved and the path integrals that can be exactly evaluated, we can say that the noncomputability of FPI implies quantum unsolvability. This is the analogue of classical unsolvability. The Feynman's path graph can be considered as a semantic parse graph for the quantum mechanical sentence. It provides a semantic valuation function of the terminal sentence based on probability amplitudes to disambiguate a given quantum description and obtain an interpretation in a linear time. In Feynman's path integral, the kernels are partially ordered over time (different alternate paths acting concurrently at the same time) and multiplied. The semantic valuation is computable only if the FPI is computable. Thus both the expressive power and complexity aspects quantum computing are mirrored by the exact and efficient integrability of FPI.

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DATTA, ANIMESH, and ANIL SHAJI. "QUANTUM DISCORD AND QUANTUM COMPUTING — AN APPRAISAL." International Journal of Quantum Information 09, no. 07n08 (October 2011): 1787–805. http://dx.doi.org/10.1142/s0219749911008416.

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We discuss models of computing that are beyond classical. The primary motivation is to unearth the cause of non-classical advantages in computation. Completeness results from computational complexity theory lead to the identification of very disparate problems, and offer a kaleidoscopic view into the realm of quantum enhancements in computation. Emphasis is placed on the "power of one qubit" model, and the boundary between quantum and classical correlations as delineated by quantum discord. A recent result by Eastin on the role of this boundary in the efficient classical simulation of quantum computation is discussed. Perceived drawbacks in the interpretation of quantum discord as a relevant certificate of quantum enhancements are addressed.

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Raussendorf, Robert. "Cohomological framework for contextual quantum computations." quantum Information and Computation 19, no. 13&14 (November 2019): 1141–70. http://dx.doi.org/10.26421/qic19.13-14-4.

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We describe a cohomological framework for measurement-based quantum computation in which symmetry plays a central role. Therein, the essential information about the computation is contained in either of two topological invariants, namely two cohomology groups. One of them applies only to deterministic quantum computations, and the other to general probabilistic ones. Those invariants characterize the computational output, and at the same time witness quantumness in the form of contextuality. In result, they give rise to fundamental algebraic structures underlying quantum computation.

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Miszczak, J. "Models of quantum computation and quantum programming languages." Bulletin of the Polish Academy of Sciences: Technical Sciences 59, no. 3 (September 1, 2011): 305–24. http://dx.doi.org/10.2478/v10175-011-0039-5.

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Models of quantum computation and quantum programming languagesThe goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.

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Morimae, Tomoyuki, and Suguru Tamaki. "Fine-grained quantum computational supremacy." quantum Information and Computation 19, no. 13&14 (November 2019): 1089–115. http://dx.doi.org/10.26421/qic19.13-14-2.

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(pp1089-1115) Tomoyuki Morimae and Suguru Tamaki doi: https://doi.org/10.26421/QIC19.13-14-2 Abstracts: Output probability distributions of several sub-universal quantum computing models cannot be classically efficiently sampled unless some unlikely consequences occur in classical complexity theory, such as the collapse of the polynomial-time hierarchy. These results, so called quantum supremacy, however, do not rule out possibilities of super-polynomial-time classical simulations. In this paper, we study ``fine-grained" version of quantum supremacy that excludes some exponential-time classical simulations. First, we focus on two sub-universal models, namely, the one-clean-qubit model (or the DQC1 model) and the HC1Q model. Assuming certain conjectures in fine-grained complexity theory, we show that for any a>0 output probability distributions of these models cannot be classically sampled within a constant multiplicative error and in 2^{(1-a)N+o(N)} time, where N is the number of qubits. Next, we consider universal quantum computing. For example, we consider quantum computing over Clifford and T gates, and show that under another fine-grained complexity conjecture, output probability distributions of Clifford-T quantum computing cannot be classically sampled in 2^{o(t)} time within a constant multiplicative error, where t is the number of T gates.

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DALLA CHIARA, MARIA LUISA, ROBERTO GIUNTINI, and ROBERTO LEPORINI. "QUANTUM COMPUTATIONAL LOGICS AND FOCK SPACE SEMANTICS." International Journal of Quantum Information 03, no. 01 (March 2005): 9–16. http://dx.doi.org/10.1142/s0219749905000372.

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The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence α is identified with a quantum information quantity, represented by a density operator of a Hilbert space, whose dimension depends on the logical complexity of α. At the same time, the logical connectives of the language are interpreted as operations defined in terms of quantum logical gates. Standard quantum computational models can be described as special cases of Fock space models, where the meaning of any sentence is localized in a precise sector of a Fock space ℱ. From an intuitive point of view, the increasing number of particles described in the different sectors of ℱ can be interpreted as increasing information.

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Hasler, Jennifer, and Eric Black. "Physical Computing: Unifying Real Number Computation to Enable Energy Efficient Computing." Journal of Low Power Electronics and Applications 11, no. 2 (March 26, 2021): 14. http://dx.doi.org/10.3390/jlpea11020014.

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Physical computing unifies real value computing including analog, neuromorphic, optical, and quantum computing. Many real-valued techniques show improvements in energy efficiency, enable smaller area per computation, and potentially improve algorithm scaling. These physical computing techniques suffer from not having a strong computational theory to guide application development in contrast to digital computation’s deep theoretical grounding in application development. We consider the possibility of a real-valued Turing machine model, the potential computational and algorithmic opportunities of these techniques, the implications for implementation applications, and the computational complexity space arising from this model. These techniques have shown promise in increasing energy efficiency, enabling smaller area per computation, and potentially improving algorithm scaling.

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Lee, Ciarán M., and Matty J. Hoban. "Bounds on the power of proofs and advice in general physical theories." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2190 (June 2016): 20160076. http://dx.doi.org/10.1098/rspa.2016.0076.

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Quantum theory presents us with the tools for computational and communication advantages over classical theory. One approach to uncovering the source of these advantages is to determine how computation and communication power vary as quantum theory is replaced by other operationally defined theories from a broad framework of such theories. Such investigations may reveal some of the key physical features required for powerful computation and communication. In this paper, we investigate how simple physical principles bound the power of two different computational paradigms which combine computation and communication in a non-trivial fashion: computation with advice and interactive proof systems. We show that the existence of non-trivial dynamics in a theory implies a bound on the power of computation with advice. Moreover, we provide an explicit example of a theory with no non-trivial dynamics in which the power of computation with advice is unbounded. Finally, we show that the power of simple interactive proof systems in theories where local measurements suffice for tomography is non-trivially bounded. This result provides a proof that Q M A is contained in P P , which does not make use of any uniquely quantum structure—such as the fact that observables correspond to self-adjoint operators—and thus may be of independent interest.

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Whyman, Richard. "Physical Computational Complexity and First-order Logic." Fundamenta Informaticae 181, no. 2-3 (August 4, 2021): 129–61. http://dx.doi.org/10.3233/fi-2021-2054.

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We present the concept of a theory machine, which is an atemporal computational formalism that is deployable within an arbitrary logical system. Theory machines are intended to capture computation on an arbitrary system, both physical and unphysical, including quantum computers, Blum-Shub-Smale machines, and infinite time Turing machines. We demonstrate that for finite problems, the computational power of any device characterisable by a finite first-order theory machine is equivalent to that of a Turing machine. Whereas for infinite problems, their computational power is equivalent to that of a type-2 machine. We then develop a concept of complexity for theory machines, and prove that the class of problems decidable by a finite first order theory machine with polynomial resources is equal to 𝒩𝒫 ∩ co-𝒩𝒫.

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Juba, Brendan. "On learning finite-state quantum sources." Quantum Information and Computation 12, no. 1&2 (January 2012): 105–18. http://dx.doi.org/10.26421/qic12.1-2-7.

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We examine the complexity of learning the distributions produced by finite-state quantum sources. We show how prior techniques for learning hidden Markov models can be adapted to the {\em quantum generator} model to find that the analogous state of affairs holds: information-theoretically, a polynomial number of samples suffice to approximately identify the distribution, but computationally, the problem is as hard as learning parities with noise, a notorious open question in computational learning theory.

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KRISHNAMURTHY, E. V. "INTEGRABILITY, ENTROPY AND QUANTUM COMPUTATION." International Journal of Modern Physics C 10, no. 07 (October 1999): 1205–28. http://dx.doi.org/10.1142/s012918319900098x.

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The important requirements are stated for the success of quantum computation. These requirements involve coherent preserving Hamiltonians as well as exact integrability of the corresponding Feynman path integrals. Also we explain the role of metric entropy in dynamical evolutionary system and outline some of the open problems in the design of quantum computational systems. Finally, we observe that unless we understand quantum nondemolition measurements, quantum integrability, quantum chaos and the direction of time arrow, the quantum control and computational paradigms will remain elusive and the design of systems based on quantum dynamical evolution may not be feasible.

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CLARK, JOHN W., DENNIS G. LUCARELLI, and TZYH-JONG TARN. "CONTROL OF QUANTUM SYSTEMS." International Journal of Modern Physics B 17, no. 28 (November 10, 2003): 5397–411. http://dx.doi.org/10.1142/s021797920302051x.

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A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed against the background of recent ideas and advances in two seemingly disparate endeavours: (i) laser control of chemical reactions and (ii) quantum computation. Using Lie-algebraic methods, sufficient conditions have been derived for global controllability on a finite-dimensional manifold of an infinite-dimensional Hilbert space, in the case that the Hamiltonian and control operators, possibly unbounded, possess a common dense domain of analytic vectors. Some simple examples are presented. A synergism between quantum control and quantum computation is creating a host of exciting new opportunities for both activities. The impact of these developments on computational many-body theory could be profound.

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Bugrimov, Anatolii L’vovich, and Nikolai Vital’evich Zverev. "FEATURES OF THE COMPUTATIONAL TECHNIQUES IN THE QUANTUM FIELD THEORY." Bulletin of the Moscow State Regional University (Physics and mathematics), no. 2 (2016): 8–17. http://dx.doi.org/10.18384/2310-7251-2016-2-08-17.

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Ashtiani, Mehrdad, and Mohammad Abdollahi Azgomi. "A formulation of computational trust based on quantum decision theory." Information Systems Frontiers 18, no. 4 (April 30, 2015): 735–64. http://dx.doi.org/10.1007/s10796-015-9555-4.

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Jordan, Stephen P., Keith S. M. Lee, and John Preskill. "Quantum computation of scattering in scalar quantum field theories." Quantum Information and Computation 14, no. 11&12 (September 2014): 1014–80. http://dx.doi.org/10.26421/qic14.11-12-8.

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Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive $\phi^4$ theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling.

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Jozsa, Richard, Barbara Kraus, Akimasa Miyake, and John Watrous. "Matchgate and space-bounded quantum computations are equivalent." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2115 (November 11, 2009): 809–30. http://dx.doi.org/10.1098/rspa.2009.0433.

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Matchgates are an especially multiflorous class of two-qubit nearest-neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions and one-dimensional spin chains. We show that the computational power of circuits of matchgates is equivalent to that of space-bounded quantum computation with unitary gates, with space restricted to being logarithmic in the width of the matchgate circuit. In particular, for the conventional setting of polynomial-sized (logarithmic-space generated) families of matchgate circuits, known to be classically simulatable, we characterize their power as coinciding with polynomial-time and logarithmic-space-bounded universal unitary quantum computation.

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Potgieter, P. H. "The pre-history of quantum computation." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 23, no. 1/2 (September 23, 2004): 2–6. http://dx.doi.org/10.4102/satnt.v23i1/2.186.

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The main ideas behind developments in the theory and technology of quantum computation were formulated in the late 1970s and early 1980s by two physicists in the West and a mathematician in the former Soviet Union. It is not generally known in the West that the subject has roots in the Russian technical literature. The idea, as propagated by Benioff and (especially) Feynman, is reviewed along with the proposition of a foundation for this kind of computation by Manin in the Russian literature. The author hopes to present as impartial a synthesis as possible of the early history of thought on this subject. The role of reversible and irreversible computational processes will be examined brieﬂy as it relates to the origins of quantum computing and the so-called Information Paradox in physics. Information theory and physics, as this paradox shows, have much to communicate to each other.

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Lloyd, Seth. "A Turing test for free will." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1971 (July 28, 2012): 3597–610. http://dx.doi.org/10.1098/rsta.2011.0331.

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Before Alan Turing made his crucial contributions to the theory of computation, he studied the question of whether quantum mechanics could throw light on the nature of free will. This paper investigates the roles of quantum mechanics and computation in free will. Although quantum mechanics implies that events are intrinsically unpredictable, the ‘pure stochasticity’ of quantum mechanics adds randomness only to decision-making processes, not freedom. By contrast, the theory of computation implies that, even when our decisions arise from a completely deterministic decision-making process, the outcomes of that process can be intrinsically unpredictable, even to—especially to—ourselves. I argue that this intrinsic computational unpredictability of the decision-making process is what gives rise to our impression that we possess free will. Finally, I propose a ‘Turing test’ for free will: a decision-maker who passes this test will tend to believe that he, she, or it possesses free will, whether the world is deterministic or not.

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Metger, Tony, and Thomas Vidick. "Self-testing of a single quantum device under computational assumptions." Quantum 5 (September 16, 2021): 544. http://dx.doi.org/10.22331/q-2021-09-16-544.

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Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.

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Fiorini, Rodolfo A. "Towards Advanced Quantum Cognitive Computation." International Journal of Software Science and Computational Intelligence 9, no. 1 (January 2017): 1–19. http://dx.doi.org/10.4018/ijssci.2017010101.

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Computational information conservation theory (CICT) can help us to develop competitive applications and even advanced quantum cognitive computational application and systems towards deep computational cognitive intelligence. CICT new awareness of a discrete HG (hyperbolic geometry) subspace (reciprocal space, RS) of coded heterogeneous hyperbolic structures, underlying the familiar Q Euclidean (direct space, DS) system surface representation can open the way to holographic information geometry (HIG) to recover lost coherence information in system description and to develop advanced quantum cognitive systems. This paper is a relevant contribution towards an effective and convenient “Science 2.0” universal computational framework to achieve deeper cognitive intelligence at your fingertips and beyond.

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Rocchetto, Andrea, Scott Aaronson, Simone Severini, Gonzalo Carvacho, Davide Poderini, Iris Agresti, Marco Bentivegna, and Fabio Sciarrino. "Experimental learning of quantum states." Science Advances 5, no. 3 (March 2019): eaau1946. http://dx.doi.org/10.1126/sciadv.aau1946.

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The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be “probably approximately learned” with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.

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Morgante, Pierpaolo, and Roberto Peverati. "Statistically representative databases for density functional theory via data science." Physical Chemistry Chemical Physics 21, no. 35 (2019): 19092–103. http://dx.doi.org/10.1039/c9cp03211h.

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Balasubramanian, Krishnan. "Mathematical and Computational Techniques for Drug Discovery: Promises and Developments." Current Topics in Medicinal Chemistry 18, no. 32 (March 5, 2019): 2774–99. http://dx.doi.org/10.2174/1568026619666190208164005.

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We review various mathematical and computational techniques for drug discovery exemplifying some recent works pertinent to group theory of nested structures of relevance to phylogeny, topological, computational and combinatorial methods for drug discovery for multiple viral infections. We have reviewed techniques from topology, combinatorics, graph theory and knot theory that facilitate topological and mathematical characterizations of protein-protein interactions, molecular-target interactions, proteomics, genomics and statistical data reduction procedures for a large set of starting chemicals in drug discovery. We have provided an overview of group theoretical techniques pertinent to phylogeny, protein dynamics especially in intrinsically disordered proteins, DNA base permutations and related algorithms. We consider computational techniques derived from high level quantum chemical computations such as QM/MM ONIOM methods, quantum chemical optimization of geometries complexes, and molecular dynamics methods for providing insights into protein-drug interactions. We have considered complexes pertinent to Hepatitis Virus C non-structural protein 5B polymerase receptor binding of C5-Arylidebne rhodanines, complexes of synthetic potential vaccine molecules with dengue virus (DENV) and HIV-1 virus as examples of various simulation studies that exemplify the utility of computational tools. It is demonstrated that these combinatorial and computational techniques in conjunction with experiments can provide promising new insights into drug discovery. These techniques also demonstrate the need to consider a new multiple site or allosteric binding approach to drug discovery, as these studies reveal the existence of multiple binding sites.

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Jozsa, Richard, and Marrten Van den Nest. "Classical simulation complexity of extended Clifford circuits." Quantum Information and Computation 14, no. 7&8 (May 2014): 633–48. http://dx.doi.org/10.26421/qic14.7-8-7.

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Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true only in a suitably restricted setting. Here we consider Clifford computations with a variety of additional ingredients: (a) strong vs. weak simulation, (b) inputs being computational basis states vs. general product states, (c) adaptive vs. non-adaptive choices of gates for circuits involving intermediate measurements, (d) single line outputs vs. multi-line outputs. We consider the classical simulation complexity of all combinations of these ingredients and show that many are not classically efficiently simulatable (subject to common complexity assumptions such as P not equal to NP). Our results reveal a surprising proximity of classical to quantum computing power viz. a class of classically simulatable quantum circuits which yields universal quantum computation if extended by a purely classical additional ingredient that does not extend the class of quantum processes occurring.

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Tamukong, Patrick K., Wadumesthrige D. N. Peiris, and Svetlana Kilina. "Computational insights into CdSe quantum dots' interactions with acetate ligands." Physical Chemistry Chemical Physics 18, no. 30 (2016): 20499–510. http://dx.doi.org/10.1039/c6cp01665k.

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Carrera, Edmundo M., Nelson Flores-Gallegos, and Rodolfo O. Esquivel. "Natural atomic probabilities in quantum information theory." Journal of Computational and Applied Mathematics 233, no. 6 (January 2010): 1483–90. http://dx.doi.org/10.1016/j.cam.2009.02.086.

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Hallgren, Sean, Adam Smith, and Fang Song. "Classical cryptographic protocols in a quantum world." International Journal of Quantum Information 13, no. 04 (June 2015): 1550028. http://dx.doi.org/10.1142/s0219749915500288.

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Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is the most realistic model of physically feasible computation, then we must ask: What classical protocols remain secure against quantum attackers? Our main contribution is showing the existence of classical two-party protocols for the secure evaluation of any polynomial-time function under reasonable computational assumptions (for example, it suffices that the learning with errors problem be hard for quantum polynomial time). Our result shows that the basic two-party feasibility picture from classical cryptography remains unchanged in a quantum world.

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Johnston, I. D. "Photon states made easy: A computational approach to quantum radiation theory." American Journal of Physics 64, no. 3 (March 1996): 245–55. http://dx.doi.org/10.1119/1.18212.

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ARRIGHI, PABLO, and LOUIS SALVAIL. "BLIND QUANTUM COMPUTATION." International Journal of Quantum Information 04, no. 05 (October 2006): 883–98. http://dx.doi.org/10.1142/s0219749906002171.

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We investigate the possibility of having someone carry out the work of executing a function for you, but without letting him learn anything about your input. Say Alice wants Bob to compute some known function f upon her input x, but wants to prevent Bob from learning anything about x. The situation arises for instance if client Alice has limited computational resources in comparison with mistrusted server Bob, or if x is an inherently mobile piece of data. Could there be a protocol whereby Bob is forced to compute ,f(x)blindly, i.e. without observing x? We provide such a blind computation protocol for the class of functions which admit an efficient procedure to generate random input–output pairs, e.g. factorization. The cheat-sensitive security achieved relies only upon quantum theory being true. The security analysis carried out assumes the eavesdropper performs individual attacks.

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ORTIZ, GERARDO, ROLANDO SOMMA, HOWARD BARNUM, and EMANUEL KNILL. "LIMITS ON THE POWER OF SOME MODELS OF QUANTUM COMPUTATION." International Journal of Modern Physics B 20, no. 30n31 (December 20, 2006): 5122–31. http://dx.doi.org/10.1142/s0217979206036181.

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We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end. We show that these models can be efficiently simulated on a classical computer in time polynomial in the dimension of the algebra, regardless of the dimension of the Hilbert space where the algebra acts. Similar results hold for the computation of the expectation value of operators implemented by a gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field Hamiltonians and show that they are efficiently (exactly) solvable by means of a Jacobi-like diagonalization method. Our results generalize earlier ones on fermionic linear optics computation and provide insight into the source of the power of the conventional model of quantum computation.

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BERTINI, CESARINO, and ROBERTO LEPORINI. "LOGICS FROM QUANTUM COMPUTATION WITH BOUNDED ADDITIVE OPERATORS." International Journal of Quantum Information 10, no. 03 (April 2012): 1250036. http://dx.doi.org/10.1142/s0219749912500360.

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The theory of gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics, where the meaning of a sentence is identified with a system of qubits in a pure or, more generally, mixed state. In this framework, any formula of the language gives rise to a quantum circuit that transforms the state associated to the atomic subformulas into the state associated to the formula and vice versa. On this basis, some holistic semantic situations can be described, where the meaning of whole determines the meaning of the parts, by non-linear and anti-unitary operators. We prove that the semantics with such operators and the semantics with unitary operators turn out to characterize the same logic.

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Love, Bradley C. "Grounding quantum probability in psychological mechanism." Behavioral and Brain Sciences 36, no. 3 (May 14, 2013): 296. http://dx.doi.org/10.1017/s0140525x12003147.

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AbstractPothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data.

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Kotukh, E. V., O. V. Severinov, A. V. Vlasov, L. S. Kozina, A. O. Tenytska, and E. O. Zarudna. "Methods of construction and properties of logariphmic signatures." Radiotekhnika, no. 205 (July 2, 2021): 94–99. http://dx.doi.org/10.30837/rt.2021.2.205.09.

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Development and promising areas of research in the construction of practical models of quantum computers contributes to the search and development of effective cryptographic primitives. Along with the growth of the practical possibilities of using quantum computing, the threat to classical encryption and electronic signature schemes using classical mathematical problems as a basis, being overcome by the computational capabilities of quantum computers. This fact motivates the study of fundamental theorems concerning the mathematical and computational aspects of candidate post-quantum cryptosystems. Development of a new quantum-resistant asymmetric cryptosystem is one of the urgent problems. The use of logarithmic signatures and coverings of finite groups a promising direction in the development of asymmetric cryptosystems. The current state of this area and the work of recent years suggest that the problem of factorizing an element of a finite group in the theory of constructing cryptosystems based on non-Abelian groups using logarithmic signatures is computationally complex; it potentially provides the necessary level of cryptographic protection against attacks using the capabilities of quantum calculations. The paper presents logarithmic signatures as a special type of factorization in finite groups; it also considers their properties and construction methods.

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Dawson, C. M., H. L. Haselgrove, A. P. Hines, D. Mortimer, M. A. Nielsen, and T. J. Osborne. "Quantum computing and polynomial equations over Z_2." Quantum Information and Computation 5, no. 2 (May 2005): 102–12. http://dx.doi.org/10.26421/qic5.2-2.

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What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP/P/\#P and BQP/PP.

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Dalla Chiara, Maria, Hector Freytes, Roberto Giuntini, Roberto Leporini, and Giuseppe Sergioli. "Probabilities and Epistemic Operations in the Logics of Quantum Computation." Entropy 20, no. 11 (October 31, 2018): 837. http://dx.doi.org/10.3390/e20110837.

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Quantum computation theory has inspired new forms of quantum logic, called quantum computational logics, where formulas are supposed to denote pieces of quantum information, while logical connectives are interpreted as special examples of quantum logical gates. The most natural semantics for these logics is a form of holistic semantics, where meanings behave in a contextual way. In this framework, the concept of quantum probability can assume different forms. We distinguish an absolute concept of probability, based on the idea of quantum truth, from a relative concept of probability (a form of transition-probability, connected with the notion of fidelity between quantum states). Quantum information has brought about some intriguing epistemic situations. A typical example is represented by teleportation-experiments. In some previous works we have studied a quantum version of the epistemic operations “to know”, “to believe”, “to understand”. In this article, we investigate another epistemic operation (which is informally used in a number of interesting quantum situations): the operation “being probabilistically informed”.

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Sutton, A. P., P. D. Godwin, and A. P. Horsfield. "Tight-Binding Theory and Computational Materials Synthesis." MRS Bulletin 21, no. 2 (February 1996): 42–48. http://dx.doi.org/10.1557/s0883769400046297.

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At the heart of any atomistic simulation is a description of the atomic interactions. A whole hierarchy of models of atomic interactions has been developed over the last twenty years or so, ranging from ab initio density-functional techniques, to simple empirical potentials such as the embedded-atom method and Finnis-Sinclair potentials in metals, valence force fields in covalently bonded materials, and the somewhat older shell model in ionic systems. Between the ab initio formulations and empirical potentials lies the tight-binding approximation: It involves the solution of equations that take into account the electronic structure of the system, but at a small fraction of the cost of an ab initio simulation, because those equations contain simplifying approximations and parameters that are usually fitted empirically.Tight binding may be characterized as the simplest formulation of atomic interactions that incorporates the quantum-mechanical nature of bonding. The particular features that it captures are as follows: (1) the strength of a bond being dependent not only on the interatomic separation but also on the angles it forms with respect to other bonds, which arises fundamentally from the spatially directed characters of p and d atomic orbitals, (2) the filling of bonding (and possibly antibonding) states with electrons, which controls the bond strengths, and (3) changes in the energy distribution of bonding and antibonding states as a result of atomic displacements. These features enable one to obtain considerable improvements in accuracy compared to the simple “glue models” of bonding since use is made of the physics and chemistry of bonding.

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Patra, Dr Indrajit. "Computation is Existence — A Brief Overview of the Multi-faceted Implications of Quantum Mechanical Description of Black holes as hyper computational Entities." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (April 11, 2021): 944–56. http://dx.doi.org/10.17762/turcomat.v12i2.1105.

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The article attempts to deal with the newly emerging paradigm of black hole computers in which adopting a quantum-mechanical perspective of information enables us to assess the computational power of black holes. Viewing space-time itself as a computational entity and black holes as the supreme forms of serial computers can help us to gain insight into the ideas from gravitational thermodynamics and the emergent nature of space-time and gravity. The idea of black holes as computational entities also relates to quantum gravity which views space-time and foamy and fuzzy due to quantum fluctuations and divided into discrete, Planck-scale blocks.

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Crosby, Lonnie D., Shawn M. Kathmann, and Theresa L. Windus. "Implementation of dynamical nucleation theory with quantum potentials." Journal of Computational Chemistry 30, no. 5 (April 15, 2009): 743–49. http://dx.doi.org/10.1002/jcc.21098.

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Rocchetto, Andrea. "Stabiliser states are efficiently PAC-learnable." Quantum Information and Computation 18, no. 7&8 (June 2018): 541–52. http://dx.doi.org/10.26421/qic18.7-8-1.

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The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state tomography. State tomography, whose objective is to obtain an approximate description of a quantum system, can be analysed in the framework of computational learning theory. In this model, Aaronson (2007) showed that quantum states are Probably Approximately Correct (PAC)-learnable with sample complexity linear in the number of qubits. However, it is conjectured that in general quantum states require an exponential amount of computation to be learned. Here, using results from the literature on the efficient classical simulation of quantum systems, we show that stabiliser states are efficiently PAC-learnable. Our results solve an open problem formulated by Aaronson (2007) and establish a connection between classical simulation of quantum systems and efficient learnability.

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Aaronson, Scott. "The learnability of quantum states." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2088 (September 11, 2007): 3089–114. http://dx.doi.org/10.1098/rspa.2007.0113.

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Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n . But using ideas from computational learning theory, we show that one can do exponentially better in a statistical setting. In particular, to predict the outcomes of most measurements drawn from an arbitrary probability distribution, one needs only a number of sample measurements that grows linearly with n . This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense. The theorem also has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.

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Król, Jerzy, and Paweł Klimasara. "Black Holes and Complexity via Constructible Universe." Universe 6, no. 11 (October 27, 2020): 198. http://dx.doi.org/10.3390/universe6110198.

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The relation of randomness and classical algorithmic computational complexity is a vast and deep subject by itself. However, already, 1-randomness sequences call for quantum mechanics in their realization. Thus, we propose to approach black hole’s quantum computational complexity by classical computational classes and randomness classes. The model of a general black hole is proposed based on formal tools from Zermelo–Fraenkel set theory like random forcing or minimal countable constructible model Lα. The Bekenstein–Hawking proportionality rule is shown to hold up to a multiplicative constant. Higher degrees of randomness and algorithmic computational complexity are derived in the model. Directions for further studies are also formulated. The model is designed for exploring deep quantum regime of spacetime.

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D'Ariano, Giacomo Mauro, Franco Manessi, Paolo Perinotti, and Alessandro Tosini. "The Feynman problem and fermionic entanglement: Fermionic theory versus qubit theory." International Journal of Modern Physics A 29, no. 17 (June 26, 2014): 1430025. http://dx.doi.org/10.1142/s0217751x14300257.

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The present paper is both a review on the Feynman problem, and an original research presentation on the relations between Fermionic theories and qubits theories, both regarded in the novel framework of operational probabilistic theories. The most relevant results about the Feynman problem of simulating Fermions with qubits are reviewed, and in the light of the new original results, the problem is solved. The answer is twofold. On the computational side, the two theories are equivalent, as shown by Bravyi and Kitaev [S. B. Bravyi and A. Y. Kitaev, Ann. Phys. 298, 210 (2002)]. On the operational side, the quantum theory of qubits and the quantum theory of Fermions are different, mostly in the notion of locality, with striking consequences on entanglement. Thus the emulation does not respect locality, as it was suspected by Feynman [R. Feynman, Int. J. Theor. Phys. 21, 467 (1982)].

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Raussendorf, R., and H. Briegel. "Computational model underlying the one-way quantum computer." Quantum Information and Computation 2, no. 6 (October 2002): 443–86. http://dx.doi.org/10.26421/qic2.6-3.

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In this paper we present the computational model underlying the one-way quantum computer which we introduced recently [Phys. Rev. Lett. {\bf{86}}, 5188 (2001)]. The one-way quantum computer has the property that any quantum logic network can be simulated on it. Conversely, not all ways of quantum information processing that are possible with the one-way quantum computer can be understood properly in network model terms. We show that the logical depth is, for certain algorithms, lower than has so far been known for networks. For example, every quantum circuit in the Clifford group can be performed on the one-way quantum computer in a single step.

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Journal articles on the topic 'Computational quantum theory'

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