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Physical Review A

Guaranteed-accuracy quantum annealing

Takashi Imoto, Yuya Seki, Yuichiro Matsuzaki, Shiro Kawabata

Published Oct 28, 2022• 1 citation
Publisher

Abstract

Quantum chemistry calculations constitute an important application of quantum annealing (QA). For practical applications in quantum chemistry, it is essential to estimate the ground-state energy of the Hamiltonian with chemical accuracy. However, there is no known method for guaranteeing the accuracy of the energy estimated via QA. Here, we propose a method for guaranteeing the accuracy of the energy estimated via QA using the Weinstein and Temple bounds. In our scheme, before QA is performed, the energies of the ground state and first excited state must be preestimated with some error bars (corresponding to the possible estimation error) via classical computation with some approximations. We show that, if the expectation value and standard deviation of the energy of the state after QA are lower than certain threshold values (that we can calculate from the preestimation), the ground-state energy estimated by QA is closer to the ground-state energy than the preestimation. As the expectation value and standard deviation of the energy can be experimentally measured via QA, our results pave the way for accurate estimation of the ground-state energy using QA.

DOI
10.1103/physreva.106.042615

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Quantum chemistry calculations constitute an important application of quantum annealing (QA). For practical applications in quantum chemistry, it is essential to estimate the ground-state energy of the Hamiltonian with chemical accuracy. However, there is no known method for guaranteeing the accuracy of the energy estimated via QA. Here, we propose a method for guaranteeing the accuracy of the energy estimated via QA using the Weinstein and Temple bounds. In our scheme, before QA is performed, the energies of the ground state and first excited state must be preestimated with some error bars (corresponding to the possible estimation error) via classical computation with some approximations. We show that, if the expectation value and standard deviation of the energy of the state after QA are lower than certain threshold values (that we can calculate from the preestimation), the ground-state energy estimated by QA is closer to the ground-state energy than the preestimation. As the expectation value and standard deviation of the energy can be experimentally measured via QA, our results pave the way for accurate estimation of the ground-state energy using QA.
Quantum chemistry calculations are important applications of quantum annealing. For practical applications in quantum chemistry, it is essential to estimate a ground state energy of the Hamiltonian with chemical accuracy. However, there are no known methods to guarantee the accuracy of the estimation of the energy calculated by quantum annealing. Here, we propose a way to improve the accuracy of the estimate of the ground state energy by combining quantum annealing with classical computation. In our scheme, before running the QA, we need a pre-estimation of the energies of the ground state and first excited state with some error bars (corresponding to possible estimation error) by performing classical computation with some approximations. We show that, if an expectation value and variance of the energy of the state after the QA are smaller than certain threshold values (that we can calculate from the pre-estimation), the QA provides us with a better estimate of the ground state energy than that of the pre-estimation. Since the expectation value and variance of the energy can be experimentally measurable by the QA, our results pave the way for accurate estimation of the ground state energy with the QA.
Abstract In quantum chemistry, it is important to estimate an energy gap between a ground state and an excited state of molecular Hamiltonians. In previous researches, it was necessary to measure the energy of the ground state and that of the excited state separately, and the energy gap was estimated from the subtraction between them. Here, we show a novel scheme to estimate such an energy gap in a more direct manner. We use a concept of a Ramsey type measurement in the quantum annealing (QA) for such a direct estimation of the energy gap. In our scheme, the measured signal oscillates with a frequency of the energy gap. To study the performance of our scheme, we perform numerical simulations. The results show our scheme is robust against non-adiabatic transitions between the ground state and first excited state. Our scheme paves the way for the practical application of QA in quantum chemistry.
Quantum chemistry is one of the important applications of quantum information technology. Especially, an estimation of the energy gap between a ground state and excited state of a target Hamiltonian corresponding to a molecule is essential. In the previous approach, an energy of the ground state and that of the excited state are estimated separately, and the energy gap can be calculated from the subtraction between them. Here, we propose a direct estimation of the energy gap between the ground state and excited state of the target Hamiltonian with quantum annealing. The key idea is to combine a Ramsey type measurement with the quantum annealing. This provides an oscillating signal with a frequency of the energy gap, and a Fourier transform of the signal let us know the energy gap. Based on typical parameters of superconducting qubits, we numerically investigate the performance of our scheme when we estimate an energy gap between the ground state and first excited state of the Hamiltonian. We show robustness against non-adiabatic transitions between the ground state and first-excited state. Our results pave a new way to estimate the energy gap of the Hamiltonian for quantum chemistry.
Quantum chemistry is one of the important applications of quantum information technology.Especially, an estimation of the energy gap between a ground state and excited state of a target Hamiltonian corresponding to a molecule is essential.In the previous approach, an energy of the ground state and that of the excited state are estimated separately, and the energy gap can be calculated from the subtraction between them.Here, we propose a direct estimation of the energy gap between the ground state and excited state of the target Hamiltonian with quantum annealing.The key idea is to combine a Ramsey type measurement with the quantum annealing.This provides an oscillating signal with a frequency of the energy gap, and a Fourier transform of the signal let us know the energy gap.Based on typical parameters of superconducting qubits, we numerically investigate the performance of our scheme when we estimate an energy gap between the ground state and first excited state of the Hamiltonian.We show robustness against non-adiabatic transitions between the ground state and first-excited state.Our results pave a new way to estimate the energy gap of the Hamiltonian for quantum chemistry.
Quantum annealing (QA) is one of the methods to prepare a ground state of a problem Hamiltonian. In the absence of noise, QA can accurately estimate the ground-state energy if the adiabatic condition is satisfied. However, in practice, systems are known to suffer from decoherence. Meanwhile, considerable research effort has been devoted to noisy intermediate-scale quantum (NISQ) computation. For practical NISQ computation, many error-mitigation (EM) methods have been proposed to mitigate the effects of noise. This paper proposes a QA strategy combined with an EM method, namely, dual-state purification, to suppress the effects of decoherence. Our protocol consists of four parts: the conventional dynamics, single-qubit projective measurements, the Hamiltonian dynamics corresponding to an inverse map of the first dynamics, and postprocessing of the measurement results. Importantly, our protocol works without two-qubit gates that require pulse operations; hence, it is suitable for devices designed for practical QA. In addition, we present numerical calculations to show that our protocol is more accurate than the conventional QA in estimating the ground-state energy under decoherence.
Calculating the molecular ground-state energy is a central challenge in computational chemistry. Conventional methods such as the Complete Active Space Configuration Interaction scale exponentially with molecular size, limiting their applicability to large molecules. Quantum computing offers a promising alternative by mapping molecular Hamiltonians by qubits, enabling cheaper computational scaling. Previous studies have shown that it is possible to formulate molecular ground state calculations as discrete optimization problems, addressable by quantum annealing. However, these efforts have been limited by previous generations of hardware and suboptimal annealing techniques. Here, the H2OH_{2}OH2​O ground-state problem is mapped to an Ising Hamiltonian using the Xian-Bias-Kas (XBK) method. By taking advantage of enhanced qubit connectivity and shorter embedding chains, it is solved with a more than doubled probability of achieving Hartree-Fock-level solutions with respect to the most advanced predecessor. Advanced annealing strategies extend Hartree-Fock-level accuracy to significantly larger problem instances, enabling solutions that use nearly 2.5 times more physically embedded qubits than the largest cases previously reported and allowing to improve annealing results by two orders of magnitude, reaching an energy difference of 0.120~Hartree relative to Hartree-Fock. These results show tangible progress toward practical quantum annealing applications in NISQ era.