In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice gas automata--and show how to implement them efficiently on standard quantum computers.
T. D. Kieu has claimed that a quantum computing procedure can solve a classically unsolvable problem. Recent work of W. D. Smith has shown that Kieu's central mathematical claim cannot be sustained. Here, a more general critique is given of Kieu's proposal and some suggestions are made regarding the Church-Turing thesis.
We present a quantumly-enhanced protocol to achieve unconditionally secure delegated classical computation where the client and the server have both limited classical and quantum computing capacity. We prove the same task cannot be achieved using only classical protocols. This extends the work of Anders and Browne on the computational power of correlations to a security setting. Concretely, we present how a client with access to a non-universal classical gate such as a parity gate could achieve unconditionally secure delegated universal classical computation by exploiting minimal quantum gadge…
This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the case where the mapping is of order k, we prove a theorem that gives us the function of the entangled state. A useful generalization beyond this research will be the implementation of quantum states with arbitrary probability amplitude functions.
Instead of producing quantum languages that are fit for current quantum computers, we build a language from standard classical assembler and augment it with quantum capabilities so that quantum algorithms become a subset of it. This paves the way for the development of hybrid algorithms directly from classical software, which is not feasible on today's hardware but might inspire future quantum programmers.
To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towa…
In our previous work, we presented a Blahut-Arimoto type algorithm for computing the discrete memoryless (DM) classical-quantum channel capacity. And the speed of convergence is analyzed. In this paper, we present numerical experiment to show that the algorithm converged much faster than the theoretical prediction. Also we present an explicit approximate solution for the binary inputs, two dimensional outputs classical-quantum channel, which has an error within $3\times10^{-4}$
Blind quantum computing protocols enable a client, who can generate or measure single-qubit states, to delegate quantum computing to a remote quantum server protecting the client's privacy (i.e., input, output, and program). With current technologies, generations or measurements of single-qubit states are not too much burden for the client. In other words, secure delegated quantum computing is possible for "almost classical" clients. However, is it possible for a "completely classical" client? Here we consider a one-round perfectly-secure delegated quantum computing, and show that the protocol…
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical computers continue to advance, but those …
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. The quantum machine learning includes hybrid methods that involve both classical and quantum algorithms. Quantum approaches can be used to analyze quantum states instead of classical data. On other side, quantum algorithms can exponentially improve classical data science algorithm. Here, we show basic ideas of quantum machine learning. …
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems theoretical perspective and applied to the formulation of quantum gates. Then quantum systems are defined by introducing feedback to the gates. In Part III, quantum gates and systems are reformulated from a quantum field theoretical perspective using S-matrices. We also discuss how gauge fields are related to feedback.
Python is a popular programming language known for its flexibility, usability, readability, and focus on developer productivity. The quantum software community has adopted Python on a number of large-scale efforts due to these characteristics, as well as the remote nature of near-term quantum processors. The use of Python has enabled quick prototyping for quantum code that directly benefits pertinent research and development efforts in quantum scientific computing. However, this rapid prototyping ability comes at the cost of future performant integration for tightly-coupled CPU-QPU architectur…
A long-standing question is whether it is possible to delegate computational tasks securely. Recently, both a classical and a quantum solution to this problem were found. Here, we study the interplay of classical and quantum approaches and show how coherence can be used as a tool for secure delegated classical computation. We show that a client with limited computational capacity - restricted to an XOR gate - can perform universal classical computation by manipulating information carriers that may occupy superpositions of two states. Using single photonic qubits or coherent light, we experimen…
In the discussion about the quantumness of NMR computation a conclusion is done that computational states are separable and therefore can not be entangled. This conclusion is based on the assumption that the initial density matrix of an individual molecule coincides with whole sample molecules distribution over single molecule energy levels. This means that quantum stochasticity is replaced by classical stochasticity. In the present paper it is shown, that quantum NMR computation can create genuine entangled states if initial system states are thermodynamical equilibrium ones. A separability a…
Quantum computing represents a paradigm shift for computation requiring an entirely new computer architecture. However, there is much that can be learned from traditional classical computer engineering. In this paper, we describe the Parallel Research Kernels (PRK), a tool that was very useful for designing classical parallel computing systems. The PRK are simple kernels written to expose bottlenecks that limit classical parallel computing performance. We hypothesize that an analogous tool for quantum computing, Quantum Research Kernels (QRK), may similarly aid the co-design of software and ha…
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the P/NP problem are reviewed. Section 2 introduces the notion of quantum parallelism and explains the main issues of quantum computing. Section 3 is devoted to four quantum subroutines: initialization, quantum computing of classical Boolean functions, quantum Fourier transform, and Grover's search algorithm. The central Section 4 explains Shor's factoring algorith…
Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on t…
Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation is that there is an oracle which is of no assistance to a classical computer but which allows a quantum computer to solve undecidable problems. Thus useful relativized separations between quantum and classical complexity classes must exclude the transmission of phase information from oracle to computer.
In this manuscript, we provide an overview of the recent developments of the coupled cluster (CC) downfolding methods, where the ground-state problem of a quantum system is represented through effective/downfolded Hamiltonians defined using active spaces. All CC downfolding techniques discussed here are derived from a single-reference exponential ansatz for the ground-state problem. We discuss several extensions of the non-Hermitian and Hermitian downfolding approaches to the time domain and the so-called quantum flows. We emphasize the important role of downfolding formalisms in transitioning…
The rapid progress in quantum computing witnessed in recent years has sparked widespread interest in developing scalable quantum information theoretic methods to work with large quantum systems. For instance, several approaches have been proposed to bypass tomographic state reconstruction, and yet retain to a certain extent the capability to estimate multiple physical properties of a given state previously measured. In this paper, we introduce the Virtual Linear Map Algorithm (VILMA), a new method that enables not only to estimate multiple operator averages using classical post-processing of i…
Optimal measurement is required to obtain the quantum and classical correlations of a quantum state, and the crucial difficulty is how to acquire the maximal information about one system by measuring the other part; in other words, getting the maximum information corresponds to preparing the best measurement operators. Within a general setup, we designed a variational hybrid quantum-classical (VHQC) algorithm to achieve classical and quantum correlations for system states under the Noisy-Intermediate Scale Quantum (NISQ) technology. To employ, first, we map the density matrix to the vector rep…
Heterogeneous high-performance computing (HPC) systems offer novel architectures which accelerate specific workloads through judicious use of specialized coprocessors. A promising architectural approach for future scientific computations is provided by heterogeneous HPC systems integrating quantum processing units (QPUs). To this end, we present XACC (eXtreme-scale ACCelerator) --- a programming model and software framework that enables quantum acceleration within standard or HPC software workflows. XACC follows a coprocessor machine model that is independent of the underlying quantum computin…
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or non-trivial high-dimensional classical optimization. Here we introduce a quantum solver of contracted eigenvalue equations, the quantum analogue of classical m…
Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013)]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the Hilbert space for such an interferometer and show that its dimension scales exponentially with all the physical resources. We also show in a simple example just how the Schrödinger and Heisenberg pictu…
Quantum computing is an emerging field of science which will eventually lead us to new and powerful logic devices with capabilities far beyond the limits of current transistor-based technology. There are certain types of problems which quantum computers can solve fundamentally faster than the tradition digital computers. There are quantum algorithms which require both superposition and entanglement (e.g. Shor algorithm). But neither the Grover algorithm nor the very first quantum algorithm due to Deutsch and Jozsa need entanglement. Is it possible to utilize classical wave superposition to spe…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum algorithms perform a select set of tasks vastly more efficiently than any classical algorithm, but for many tasks it has been proved that quantum algorithms provide no advantage. The breadth of quantum computing applications is still being explored. Major application areas include security and the many fields that would benefit from efficient quantum simula…
Recently, the paper B. Georgeot and D.L. Shepelyansky, Phys. Rev. Lett._86_, 5393 (2001) has been criticized [C. Zalka, quant-ph/0110019; L. Di'osi, quant-ph/0110026]. The Letter claims an exponential speedup and reduction in error sensitivity, when phase-space density evolution under the Arnold cat map is performed on a quantum computer. On the one hand, some points have not yet been made by previous respondents. On the other, the authors' reaction [quant-ph/0110142] raises new issues. The present note addresses both.
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been successfully tested on two computational tasks. Several basic logic gates have been analyzed and the nonlocal content of the associate quantum transformations have been calculated. The results provide us with new interesting insight into the notion of complexity of logic operations.
Dedicated research into the design and construction of a large scale Quantum Information Processing (QIP) system is a complicated task. The design of an experimentally feasible quantum processor must draw upon results in multiple fields; from experimental efforts in system control and fabrication through to far more abstract areas such as quantum algorithms and error correction. Recently, the adaptation of topological coding models to physical systems in optics has illustrated a possible long term pathway to truly large scale QIP. As the topological model has well defined protocols for Quantum…
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving messages from the quantum simulator, classical computing devic…
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case. This is a fundamental step towards the construction of a quantum computer because a time efficient quantum computation is a reversible physical process. The paper is organized as follows. The first section reviews the classical theory of reversible computing. In the second section it is showed that the designs used in the classical framework to decrease the…
Locally-biased classical shadows allow rapid estimation of energies of quantum Hamiltonians. Recently, derandomised classical shadows have emerged claiming to be even more accurate. This accuracy comes at a cost of introducing classical computing resources into the energy estimation procedure. This present note shows, by adding a fraction of this classical computing resource to the locally-biased classical shadows setting, that the modified algorithm, termed Adaptive Pauli Shadows is state-of-the-art for energy estimation.
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.
We discuss models of computing that are beyond classical. The primary motivation is to unearth the cause of nonclassical 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 c…
Quantum programming techniques and software have advanced significantly over the past five years, with a majority focusing on high-level language frameworks targeting remote REST library APIs. As quantum computing architectures advance and become more widely available, lower-level, system software infrastructures will be needed to enable tighter, co-processor programming and access models. Here we present XACC, a system-level software infrastructure for quantum-classical computing that promotes a service-oriented architecture to expose interfaces for core quantum programming, compilation, and …
Quantum computing has attracted much attention in recent decades, since it is believed to solve certain problems substantially faster than traditional computing methods. Theoretically, such an advance can be obtained by networks of the quantum operators in universal gate sets, one famous example of which is formed by CNOT gate and single qubit gates. However, realizing a device that performs practical quantum computing is tricky. This is because it requires a scalable qubit system with long coherence time and good controls, which is harsh for most current platforms. Here, we demonstrate that t…
