Classical Optimizers for Noisy Intermediate-Scale Quantum Devices

Lavrijsen, W.; Tudor, Ana; Müller, Juliane; Iancu, Costin; Jong, Wibe A. de

doi:10.1109/qce49297.2020.00041

Cited by 76 publications

(61 citation statements)

References 22 publications

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“…Error amounts are drawn independently from err ≈ N(0, ) at each round of the classical optimizer. We used BOBYQA (Bound Optimization BY Quadratic Approximation) as implemented in SKQuant-Opt, [49] a standard optimizer package for near term hybrid quantum classical algorithms. Although we have simulated the results under a ion trap model, hidden inverse can be applied to other systems too(as an example to reduce errors in ZX gates for a superconducting hardware).…”

Section: Discussionmentioning

confidence: 99%

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

et al. 2021

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Quantum chemistry is a key application area for noisy-intermediate scale quantum (NISQ) devices, and therefore serves as an important benchmark for current and future quantum computer performance. Previous benchmarks in this field have focused on variational methods for computing ground and excited states of various molecules, including a benchmarking suite focused on the performance of computing ground states for alkali-hydrides under an array of error mitigation methods. State-of-the-art methods to reach chemical accuracy in hybrid quantum-classical electronic structure calculations of alkali hydride molecules on NISQ devices from IBM are outlined here. It is demonstrated how to extend the reach of variational eigensolvers with symmetry preserving Ansätze. Next, it is outlined how to use quantum imaginary time evolution and Lanczos as a complementary method to variational techniques, highlighting the advantages of each approach. Finally, a new error mitigation method is demonstrated which uses systematic error cancellation via hidden inverse gate constructions, improving the performance of typical variational algorithms. These results show that electronic structure calculations have advanced rapidly, to routine chemical accuracy for simple molecules, from their inception on quantum computers a few short years ago, and they point to further rapid progress to larger molecules as the power of NISQ devices grows.

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Section: Discussionmentioning

confidence: 99%

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

et al. 2021

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“…One possible area for exploration could be finding an ansatz that would result in a smoother cost function landscape with shallower circuits. More adapted classical optimization methods may also bring significant improvements in the optimization process as it was found that a considerable fraction of optimization runs got stuck in local minimas [28,46]. Improvement on that front may also substantially decrease the number of measurements required to reach comparable quality of solutions.…”

Section: Discussionmentioning

confidence: 99%

Qubit-efficient encoding schemes for binary optimisation problems

Tan

Lemonde

Thanasilp

et al. 2021

Quantum

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We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of nc classical variables can be implemented on O(log⁡nc) number of qubits. The underlying encoding scheme allows for a systematic increase in correlations among the classical variables captured by a variational quantum state by progressively increasing the number of qubits involved. We first examine the simplest limit where all correlations are neglected, i.e. when the quantum state can only describe statistically independent classical variables. We apply this minimal encoding to find approximate solutions of a general problem instance comprised of 64 classical variables using 7 qubits. Next, we show how two-body correlations between the classical variables can be incorporated in the variational quantum state and how it can improve the quality of the approximate solutions. We give an example by solving a 42-variable Max-Cut problem using only 8 qubits where we exploit the specific topology of the problem. We analyze whether these cases can be optimized efficiently given the limited resources available in state-of-the-art quantum platforms. Lastly, we present the general framework for extending the expressibility of the probability distribution to any multi-body correlations.

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“…Firstly, the one-dimensional state returned by the quantum computer has to be translated into the X matrix from Equation (6). This is done via the f function defined for each encoding in Equations ( 12), (14), and (21) respectively. Similarly, the Y slack matrix also has to be unflattened.…”

Section: Encoding and Workflow Schedulingmentioning

confidence: 99%

Variational Algorithms for Workflow Scheduling Problem in Gate-Based Quantum Devices

Plewa

Sieńko

Rycerz

2021

cai

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In this paper we consider the combinatorial optimization problem known as workflow scheduling. We compare three encoding schemes of varying density: one-hot, binary, and domain wall, and test their performance against two wellknown hybrid quantum-classical algorithms: Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). In an attempt to obtain the best results possible, we investigate various parameters of the algorithms and test out other state-of-the-art improvements, such as dedicated QAOA mixers. Ultimately, we prove that, despite its popularity, one-hot encoding is not always the best, and using a denser encoding scheme, such as binary or domain wall, can allow for solving larger instances of workflow scheduling. Additionally, combining the above-mentioned encodings with dedicated QAOA mixers reduces the number of infeasible solutions, leading to better results.

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Classical Optimizers for Noisy Intermediate-Scale Quantum Devices

Cited by 76 publications

References 22 publications

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

Qubit-efficient encoding schemes for binary optimisation problems

Variational Algorithms for Workflow Scheduling Problem in Gate-Based Quantum Devices

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