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GPU-accelerated simulations of quantum annealing and the quantum approximate optimization algorithm
TL;DR: In this article, the authors study large-scale applications using a GPU-accelerated version of the massively parallel Julich universal quantum computer simulator (JUQCS--G) using a very coarsely discretized version of QA, termed approximate quantum annealing (AQA), and find that AQA performs surprisingly well in comparison to the quantum approximate optimization algorithm (QAOA).
Abstract: We study large-scale applications using a GPU-accelerated version of the massively parallel Julich universal quantum computer simulator (JUQCS--G) First, we benchmark JUWELS Booster, a GPU cluster with 3744 NVIDIA A100 Tensor Core GPUs Then, we use JUQCS--G to study the relation between quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) We find that a very coarsely discretized version of QA, termed approximate quantum annealing (AQA), performs surprisingly well in comparison to the QAOA It can either be used to initialize the QAOA, or to avoid the costly optimization procedure altogether Furthermore, we study the scaling of the success probability when using AQA for problems with 30 to 40 qubits We find that the case with largest discretization error performs most favorably, surpassing the best result obtained from the QAOA
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TL;DR: In this paper, the authors benchmark the quantum processing units of the largest quantum annealers to date, the 5000+ qubit Quantum Annealer Advantage and its 2000-qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios.
Abstract: We benchmark the quantum processing units of the largest quantum annealers to date, the 5000+ qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find that D-Wave 2000Q can only achieve better success rates for a few very sparsely connected problems.
15 citations
TL;DR: In this paper , the authors compared the performance of the 5000+ qubit quantum annealer Advantage and its 2000-qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios.
Abstract: We benchmark the quantum processing units of the largest quantum annealers to date, the 5000+ qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find, however, that D-Wave 2000Q can achieve better success rates for sparsely connected problems that do not require the many new couplers present on Advantage, so improving the connectivity of a quantum annealer does not per se improve its performance.
12 citations
TL;DR: In this article, the authors benchmark the 5000+ qubit system Advantage coupled with the hybrid solver Service 2 released by D-Wave Systems Inc. in September 2020 by using a new class of optimization problems called garden optimization problems and derive their QUBO formulation and illustrate their relation to the quadratic assignment problem.
Abstract: We benchmark the 5000+ qubit system Advantage coupled with the Hybrid Solver Service 2 released by D-Wave Systems Inc. in September 2020 by using a new class of optimization problems called garden optimization problems. These problems are scalable to an arbitrary number of variables and intuitively find application in real-world scenarios. We derive their QUBO formulation and illustrate their relation to the quadratic assignment problem. We demonstrate that the Advantage system and the new hybrid solver can solve larger problems in less time than their predecessors. However, we also show that the solvers based on the 2000+ qubit system DW2000Q sometimes produce more favourable results if they can solve the problems.
3 citations
TL;DR: In this article , the authors proposed a chaotic equilibrium optimization (CEO) method to deal with the temperature-dependent optimal power flow (TDOPF) problem in IEEE 30-bus and 118-bus networks with different objective functions, including generating fuel cost, total active power losses, voltage profile enhancement, voltage stability improvement and emission reduction.
Abstract: ABSTRACT Optimal power flow (OPF) is one of the common problems in power systems. In general, the branch resistance of the system is assumed to be constant with respect to temperature variation in conventional optimal power flow. However, the temperature correlation of the branch resistance should be taken into account to enhance the accurate calculation of the power flow and branch losses. This paper suggests a new and efficient method, which is chaotic equilibrium optimization (CEO) to deal with the temperature-dependent optimal power flow (TDOPF) problem. The CEO is validated on IEEE 30-bus and 118-bus networks with different objective functions, including generating fuel cost, total active power losses, voltage profile enhancement, voltage stability improvement, and emission reduction. Furthermore, the temperature effect on the TDOPF problem is also analyzed. In the case of fuel cost optimization in the 30-bus network, fuel cost increases from 799.85 $/h to 802.9474 $/h when the temperature increases from 0°C to 100°C, corresponding to a fuel cost increase of 0.04% for each 10°C. From the obtained outcomes, the efficacy of the CEO has been proven in finding accurate solutions for the TDOPF problem. GRAPHICAL ABSTRACT
1 citations
01 Jul 2021
TL;DR: In this article, the authors report the performance gains obtained by using CuPy, a general purpose library (linear algebra) developed specifically for CUDA-based GPUs, to simulate quantum circuits.
Abstract: Quantum circuit simulators have a long tradition of exploiting massive hardware parallelism. Most of the times, parallelism has been supported by special purpose libraries tailored specifically for the quantum circuits. Quantum circuit simulators are integral part of quantum software stacks, which are mostly written in Python. Our focus has been on ease of use, implementation and maintainability within the Python ecosystem. We report the performance gains we obtained by using CuPy, a general purpose library (linear algebra) developed specifically for CUDA-based GPUs, to simulate quantum circuits. For supremacy circuits the speedup is around 2x, and for quantum multipliers almost 22x compared to state-of-the-art C++-based simulators.
References
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TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Abstract: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.
27,271 citations
01 Dec 2010
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Abstract: Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.
14,825 citations
TL;DR: L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables, intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems.
Abstract: L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be used for unconstrained problems and in this case performs similarly to its predessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.
2,776 citations
06 Aug 2018
TL;DR: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future, and the 100-qubit quantum computer will not change the world right away - but it should be regarded as a significant step toward the more powerful quantum technologies of the future.
Abstract: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the
near future. Quantum computers with 50-100 qubits may be able to perform tasks
which surpass the capabilities of today's classical digital computers, but
noise in quantum gates will limit the size of quantum circuits that can be
executed reliably. NISQ devices will be useful tools for exploring many-body
quantum physics, and may have other useful applications, but the 100-qubit
quantum computer will not change the world right away --- we should regard it
as a significant step toward the more powerful quantum technologies of the
future. Quantum technologists should continue to strive for more accurate
quantum gates and, eventually, fully fault-tolerant quantum computing.
2,598 citations
Google1, University of Massachusetts Amherst2, Ames Research Center3, California Institute of Technology4, University of California, Santa Barbara5, University of Erlangen-Nuremberg6, Oak Ridge National Laboratory7, University of California, Riverside8, RWTH Aachen University9, Forschungszentrum Jülich10, University of Michigan11, University of Illinois at Urbana–Champaign12
TL;DR: Quantum supremacy is demonstrated using a programmable superconducting processor known as Sycamore, taking approximately 200 seconds to sample one instance of a quantum circuit a million times, which would take a state-of-the-art supercomputer around ten thousand years to compute.
Abstract: The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy8-14 for this specific computational task, heralding a much-anticipated computing paradigm.
2,527 citations