QuEST and High Performance Simulation of Quantum Computers
Tyson Jones, Anna Brown, Ian Bush, Simon Benjamin
备注：
8 pages, 8 figures; fixed typos; updated QuEST URL and fixed typo in Fig. 4 caption where ProjectQ and QuEST were swapped in speedup subplot explanation; added explanation of simulation algorithm, updated bibliography; stressed technical novelty of QuEST; mentioned new density matrix support
We introduce QuEST, the Quantum Exact Simulation Toolkit, and compare it to ProjectQ, qHipster and a recent distributed implementation of Quantum++. QuEST is the first open source, OpenMP and MPI hybridised, GPU accelerated simulator of universal quantum circuits. Embodied as a C library, it is designed so that a user's code can be deployed seamlessly to any platform from a laptop to a supercomputer. QuEST is capable of simulating generic quantum circuits of general single-qubit gates and multi-qubit controlled gates, on pure and mixed states, represented as state-vectors and density matrices, and under the presence of decoherence. Using the ARCUS Phase-B and ARCHER supercomputers, we benchmark QuEST's simulation of random circuits of up to 38 qubits, distributed over up to 2048 compute nodes, each with up to 24 cores. We directly compare QuEST's performance to ProjectQ's on single machines, and discuss the differences in distribution strategies of QuEST, qHipster and Quantum++. QuEST shows excellent scaling, both strong and weak, on multicore and distributed architectures.
Quantum simulation can beat current classical computers with minimally a few tens of qubits and will likely become the first practical use of a quantum computer. One promising application of quantum simulation is to attack challenging quantum chemistry problems. Here we report an experimental demonstration that a small nuclear-magnetic-resonance (NMR) quantum computer is already able to simulate the dynamics of a prototype chemical reaction. The experimental results agree well with classical simulations. We conclude that the quantum simulation of chemical reaction dynamics not computable on cu…
In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Dualit…
We have developed a concrete quantum simulation scheme and experimentally simulated a pairing model on an NMR quantum computer. The design of our experiment includes choosing an appropriate initial state in order to make our scheme scalable in near future, and the accomplishment of our experiment makes use of twice Fourier transforms so that our method is applicable to other physical models. Our results show that the experimental simulation can give the spectrum of the simulated Hamiltonian. Consequently, the potential power of a quantum computer on the simulation of complex physical systems i…
We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers, or quantum Turing machines(QTM), and (2) parallel quantum computers, or quantum circuits. This paper shows that the computational power of decohered quantum computers depends strongly on the amount of parallelism in the computation. The expected slowdown of the simulation of a QTM is polynomial in time and space of the quantum computation, for any non zero d…
Using a numerical simulation of the evolution of a qubit interacting with the environment we show that quantum error detection and correction can work effectively even when the recovery procedure introduces errors.
This paper shows a novel way of simulating a Markov process by a quantum computer. The main purpose of the paper is to show a particular application of quantum computing in the field of stochastic processes analysis. Using a Quantum computer, the process could be superposed, where the random variables of the Markov chain are represented by entangled qubit states, which gives the great opportunity of having all the possible scenarios simultaneously.
A construction is given for simulating any deterministic finite state machine (FSM) on a quantum computer in a space-efficient manner. By constructing a superposition of input strings of lengths K or less, questions can be asked about the FSM, such as the inputs that reach particular nodes, and the answers can be found using a search algorithm such as Grover's. This has implications for the eventual utility of quantum computers for software validation.
To efficiently implement many-qubit gates for use in quantum simulations on quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2 + ...) Δt] as a product of factors exp[-i H_1 Δt], exp[-i H_2 Δt], ... which is accurate to 3rd or 4th order in Δt. The methods we derive are an extended form of symplectic method and can also be used for the integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases.
We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In order to accommodate fermions using a first quantized Hamiltonian, an efficient quantum algorithm for anti-symmetrization is given. Finally, a simulation of the Hubbard model is discussed in detail.
Simulation of time dynamical physical problems has been a challenge for classical computers due to their time-complexity. To demonstrate the dominance of quantum computers over classical computers in this regime, here we simulate a semi-empirical model where two neutral particles interact through Lennard-Jones potential in a one-dimensional system. We implement the above scenario on the IBM quantum experience platform using a 5-qubit real device. We construct the Hamiltonian and then efficiently map it to quantum operators onto quantum gates using the time-evolutionary unitary matrix obtained …
We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a conventional simulation of the corresponding classical system. We then sketch how results of interest, like the energy spectrum of a system, can be obtained. We also indicate that ultimately the simulation of quantum field theory might be possible on large quantum computers. We want to demonstrate that in principle various interesting things can be done. Actual appl…
Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation and optimization techniques that massively reduce the entangling-gate counts. We exploit the well-studied non-quantum optimization algorithms to achieve up to 24\% savings over the state of the art for several small-molecule simulations, with no loss of accuracy or hidden costs. Our methodologies straightforwardly generalize to wider classes of near-term simu…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation ar…
We design a quantum circuit in IBM quantum computer that mimics the dynamics of single photon in a coupled cavity system. By suitably choosing the gate parameters in the quantum circuit, we could transfer an unknown qubit state between the qubits. The condition for perfect state transfer is obtained by solving the unitary time dynamics governed by the Hamiltonian of the coupled cavity system. We then demonstrate the dynamics of entanglement between the two-qubits and show violation of Bell's inequality in IBM quantum computer.
It is exponentially hard to simulate quantum systems by classical algorithms, while quantum computer could in principle solve this problem polynomially. We demonstrate such an quantum-simulation algorithm on our NMR system to simulate an hydrogen molecule and calculate its ground-state energy. We utilize the NMR interferometry method to measure the phase shift and iterate the process to get a high precision. Finally we get 17 precise bits of the energy value, and we also analyze the source of the error in the simulation.
In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial scale but by pushing the envelope as far as possible through optimal choices of algorithms and hardware the value of the simulator tool is maximized. This work reviews the state-of-the-art numerical simulation methods i.e. the classical algorithms that emulate quantum computer evolution under specific operations. We focus on the mainstream state-vector and te…
We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance. We believe this to be the first explicit physical realization of such a simulation.
Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the fermionic problem in a bosonic system of qubits. By exploiting the block diagonality of a fermionic Hamiltonian, we show that the number of required qubits can be reduced by a factor of two or more. There is no need to go into the basis of the Hilbert space for this reduction because all operations can be performed in the operator space. The scheme is conceived as a pre-computational step that would be performed on a classical computer prior to the actual quantum simulation. We apply this schem…
Recent development in quantum information sciences and technologies, especially building programmable quantum computers, provide us new opportunities to study fundamental aspects of quantum mechanics. We propose qubit models to emulate the quantum measurement process, in which the quantum information of a qubit is mapped to a collection of qubits acting as the measurement device. One model is motivated by single-photon detection and the other by spin measurement. Both models are scalable to generate Schrödinger cat-like state, and their corresponding quantum circuits are shown explicitly. Larg…
The feasibility of computationally superior quantum computers is one of the most exciting and clear-cut scientific questions of our time. The question touches on fundamental issues regarding probability, physics, and computability, as well as on exciting problems in experimental physics, engineering, computer science, and mathematics. We propose three related directions towards a negative answer. The first is a conjecture about physical realizations of quantum codes, the second has to do with correlations in stochastic physical systems, and the third proposes a model for quantum evolutions whe…
Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be simulated by a quantum computer. A basis mapping between the systems dictates the average Hamiltonian in the quantum computer needed to implement the desired Hamiltonian in the simulated system. The flexibility of the procedure is illustrated with NMR on 13-C labelled Alanine by creating the non-physical Hamiltonian ZZZ corresponding to a three body interaction.
We present a computer simulation model of Wheeler's delayed choice experiment that is a one-to-one copy of an experiment reported recently (V. Jacques {\sl et al.}, Science 315, 966 (2007)). The model is solely based on experimental facts, satisfies Einstein's criterion of local causality and does not rely on any concept of quantum theory. Nevertheless, the simulation model reproduces the averages as obtained from the quantum theoretical description of Wheeler's delayed choice experiment. Our results prove that it is possible to give a particle-only description of Wheeler's delayed choice expe…
We present an exact simulation of a one-dimensional transverse Ising spin chain with a quantum computer. We construct an efficient quantum circuit that diagonalizes the Ising Hamiltonian and allows to obtain all eigenstates of the model by just preparing the computational basis states. With an explicit example of that circuit for $n=4$ spins, we compute the expected value of the ground state magnetization, the time evolution simulation and provide a method to also simulate thermal evolution. All circuits are run in IBM and Rigetti quantum devices to test and compare them qualitatively.
One of the major approaches to neuromorphic computing is using memristors as analogue synapses. We propose unitary quantum gates that exhibit memristive behaviours, including Ohm's law, pinched hysteresis loop and synaptic plasticity. Hysteresis depending on the quantum phase and long-term plasticity that encodes the quantum state are observed. We also propose a three-layer neural network with the capability of universal quantum computing. Quantum state classification on the memristive neural network is demonstrated. Our results pave the way towards brain-inspired quantum computing. We obtain …
Simulating quantum systems is believed to be one of the first applications for which quantum computers may demonstrate a useful advantage. For many problems in physics, we are interested in studying the evolution of the electron-phonon Hamiltonian, for which efficient digital quantum computing schemes exist. Yet to date, no accurate simulation of this system has been produced on real quantum hardware. In this work, we consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems as dictated by the number of Trotter steps and bosonic energy levels necess…
Dymanics of spin dimers in multiple quantum NMR experiment is studied on the 5-qubit superconducting quantum processor of IBM {Quantum Experience} for the both {pure} ground and thermodynamic equilibrium (mixed) initial states. The work can be considered as a first step towards an application of quantum computers to solving problems of magnetic resonance. This article is dedicated to Prof. Klaus Möbius and Prof. Kev Salikhov on the occasion of their 85th birthdays.
State-of-the-art cosmological simulations on classical computers are limited by time, energy, and memory usage. Quantum computers can perform some calculations exponentially faster than classical computers, using exponentially less energy and memory, and may enable extremely large simulations that accurately capture the whole dynamic range of structure in the Universe within statistically representative cosmic volumes. However, not all computational tasks exhibit a `quantum advantage'. Quantum circuits act linearly on quantum states, so nonlinearities (e.g. self-gravity in cosmological simulat…
Comment on the Letter ``Polynomial-Time Simulation of Pairing Models on a Quantum Computer'', L. A. Wu, M. S. Byrd and D. A. Lidar, Phys. Rev. Lett. 89, 057904 (2002).
Classical simulation is important because it sets a benchmark for quantum computer performance. Classical simulation is currently the only way to exercise larger numbers of qubits. To achieve larger simulations, sparse matrix processing is emphasized below while trading memory for processing. It performed well within NCSA supercomputers, giving a state vector in convenient continuous portions ready for post processing.
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms and the avenue of its application in multiple domains. Availability of efficient quantum simulators will enable the researchers to quickly verify their results and concepts in order to establish a working proof of correctness. One important algorithm that has become one of the basic ingredients to build other algorithms and models is the Grover's search Algor…
We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between ground and first excited states, and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultra-small metallic grains.
Max Planck Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Leiden University（莱顿大学）
Suppose we have a small quantum computer with only M qubits. Can such a device genuinely speed up certain algorithms, even when the problem size is much larger than M? Here we answer this question to the affirmative. We present a hybrid quantum-classical algorithm to solve 3SAT problems involving n>>M variables that significantly speeds up its fully classical counterpart. This question may be relevant in view of the current quest to build small quantum computers.
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness the power of near-term quantum computers for simulations of larger systems, it is desirable to develop hybrid quantum-classical methods where the quantum computation is restricted to a small portion of the system. This is of particular relevance for molecules and solids where an active region requires a higher level of theoretical accuracy than its environme…
We present a hybrid quantum-classical algorithm for the time evolution of out-of-equilibrium thermal states. The method depends upon classically computing a sparse approximation to the density matrix, and then time-evolving each matrix element via the quantum computer. For this exploratory study, we investigate the time-dependent Heisenberg model with five spins on the Rigetti Forest quantum virtual machine and a one spin system on the Rigetti 8Q-Agave quantum processor.
Photosynthesis is an important and complex physical process in nature, whose comprehensive understanding would have many relevant industrial applications, for instance in the field of energy production. In this paper we propose a quantum algorithm for the simulation of the excitonic transport of energy, occurring in the first stage of the process of photosynthesis. The algorithm takes in account the quantum and environmental effects (pure-dephasing), influencing the quantum transport. We performed quantum simulations of such phenomena, for a proof of concept scenario, in an actual quantum comp…
It is shown that under reasonable assumptions a Drake-style equation can be obtained for the probability that our universe is the result of a deliberate simulation. Evaluating loose bounds for certain terms in the equation shows that the probability is unlikely to be as high as previously reported in the literature, especially in a scenario where the simulations are recursive. Furthermore, we investigate the possibility of eavesdropping from the outside of such a simulation and introduce a general attack that can circumvent attempts at quantum cryptography inside the simulation, even if the qu…
