Quantum Error Mitigation using Symmetry Expansion

Cai, Zhenyu

doi:10.22331/q-2021-09-21-548

Cited by 45 publications

(34 citation statements)

References 29 publications

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“…The current ones based on superconductor units are, unfortunately, quite noisy, partly due to their quantum nature [ 34 ], but mostly due to unresolved issues related to the technical complexity of physical realizations of quantum processors; for details, see, e.g., [ 35 ]. Consequently, there is a tremendous effort focused on various error-mitigation methods [ 36 , 37 , 38 , 39 , 40 , 41 ].…”

Section: Resultsmentioning

confidence: 99%

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

et al. 2022

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Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting the best-practice aspects of these calculations. In order to compare the performance of different setups, the ground-state energy of the hydrogen molecule was chosen as a benchmark for which the exact solution exists in the literature. Applying the variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi–Kitaev transformation, we analyzed the impact of various computational technicalities. These included (i) the choice of the optimization methods, (ii) the architecture of the quantum circuits, as well as (iii) the different types of noise when simulating real quantum processors. On these, we eventually performed a series of experimental runs as a complement to our simulations. The simultaneous perturbation stochastic approximation (SPSA) and constrained optimization by linear approximation (COBYLA) optimization methods clearly outperformed the Nelder–Mead and Powell methods. The results obtained when using the Ry variational form were better than those obtained when the RyRz form was used. The choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization method. The circular entangling layer was found to worsen the performance of the COBYLA method, while the full-entangling layer improved it. All four optimization methods sometimes led to an energy that corresponded to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight.

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Section: Resultsmentioning

confidence: 99%

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

et al. 2022

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“…[48]. Consequently, there is a tremendous effort focused on various error-mitigation methods [49][50][51][52][53][54].…”

Section: Simulations Of Noisy Runsmentioning

confidence: 99%

Best-practice aspects of quantum-computer calculations: A case study of hydrogen molecule

Miháliková,

Friák,

Pivoluska

et al. 2021

Preprint

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Quantum computers are reaching one crucial milestone after another. Motivated by their 1 progress in quantum chemistry, we have performed an extensive series of simulations of quantum-2 computer runs that were aimed at inspecting best-practice aspects of these calculations. In order to 3 compare the performance of different set-ups, the ground-state energy of hydrogen molecule has 4 been chosen as a benchmark for which the exact solution exists in literature. Applying variational 5 quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi-Kitaev transformation 6 we have analyzed the impact of various computational technicalities. These include (i) the choice 7 of optimization methods, (ii) the architecture of quantum circuits, as well as (iii) different types 8 of noise when simulating real quantum processors. On these we eventually performed a series 9 of experimental runs as a complement to our simulations. The SPSA and COBYLA optimization 10 methods have clearly outperformed the Nelder-Mead and Powell methods. The results obtained when 11 using the R y variational form were better than those obtained when the R y R z form was used. The 12 choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization 13 method. The circular entangling layer has been found to worsen the performance of the COBYLA 14 method while the full entangling layer improved it. All four optimization methods sometimes lead 15 to an energy that corresponds to an excited state rather than the ground state. We also show that a 16 similarity analysis of measured probabilities can provide a useful insight.

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“…There are many different approaches to correcting the noisy results (see Refs. [27][28][29][30][31][32][33][34][35][36] and references therein), based on different techniques of noise characterization.…”

Section: Introductionmentioning

confidence: 99%

The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

et al. 2022

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New approaches into computational quantum chemistry can be developed through the use of quantum computing. While universal, fault-tolerant quantum computers are still not available, and we want to utilize today’s noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE)—an algorithm for calculating the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, and physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal method of running the hybrid classical-quantum optimization is to: (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but ensure a high final readout precision; (ii) emphasize efficient problem encoding and ansatz parametrization; and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently, it is quite difficult to perform trustworthy calculations of molecular energies.

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Quantum Error Mitigation using Symmetry Expansion

Cited by 45 publications

References 29 publications

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

Best-practice aspects of quantum-computer calculations: A case study of hydrogen molecule

The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

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