Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2208.02553 · Scientific Reports

How to experimentally evaluate the adiabatic condition for quantum annealing

Yuichiro Mori, Shiro Kawabata, Yuichiro Matsuzaki

Published Apr 8, 2024• 5 citations
arXivHTMLPDF

Abstract

We propose an experimental method for evaluating the adiabatic condition during quantum annealing (QA), which will be essential for solving practical problems. The adiabatic condition consists of the transition matrix element and the energy gap, and our method simultaneously provides information about these components without diagonalizing the Hamiltonian. The key idea is to measure the power spectrum of a time domain signal by adding an oscillating field during QA, and we can estimate the values of the transition matrix element and energy gap from the measurement output. Our results provides a powerful experimental basis for analyzing the performance of QA.

DOI
10.1038/s41598-024-58286-2

Related papers

Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy

Hiroshi Hayasaka, Takashi Imoto, Yuichiro Matsuzaki +1 more

Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using what is referred to as the adiabatic condition derived from the adiabatic theorem. The adiabatic condition consists of two parts: an energy gap and a transition matrix. Most past studies have focused on the relationship between the energy gap and computational time. The success probability of QA is considered to decrease exponentially owing to the exponentially decreasing energy gap at the first-order phase-transition point. In this study, through a detailed analysis of the relationship between the energy gap, transition matrix, and computational cost during QA, we propose a general method for constructing counterintuitive models wherein QA with a constant annealing time fails despite a constant energy gap, based on polynomial energy. We assume that the energy of the total Hamiltonian is at most $\mathrm{\ensuremath{\Theta}}(L)$, where $L$ is the number of qubits. In our formalism, we choose a known model that exhibits an exponentially small energy gap during QA, and modify the model by adding a specific penalty term to the Hamiltonian. In the modified model, the transition matrix in the adiabatic condition becomes exponentially large as the number of qubits increases, while the energy gap remains constant. Moreover, we achieve a quadratic speedup, for which the upper bound for improvement in the adiabatic condition is determined by the polynomial energy. For concrete examples, we consider the adiabatic Grover search and the ferromagnetic $p$-spin model. In these cases, with the addition of the penalty term, although the success probability of QA on the modified models becomes exponentially small despite a constant energy gap, we are able to achieve a success probability considerably higher than that of conventional QA. Moreover, in concrete examples, we numerically show the scaling of the computational cost is quadratically improved compared to the conventional QA. Our findings pave the way for a better understanding of QA performance.

arXiv:2212.09995•Physical Review A•Aug 26, 2024•4 citations

Proposal to experimentally evaluate the adiabatic condition of quantum annealing in coupled systems of Kerr parametric oscillators

Yuichiro Mori, Harunobu Hiratsuka, Yuichiro Matsuzaki

Quantum annealing (QA) is an algorithm to find the ground state of the problem Hamiltonian by using an adiabatic time evolution. An approach to evaluate adiabaticity in the experiment by applying spectroscopic techniques has recently been suggested. However, this method requires temporal oscillation of interaction strength during QA, posing challenges for experimental demonstration. Here, we propose an experimental method for evaluating adiabaticity when performing QA with a parametric oscillator with Kerr nonlinearity (KPO). Importantly, our proposal offers a significant advantage by eliminating the need for temporal oscillation of interactions during QA. We investigate its performance through numerical simulations, and we show the feasibility of our method.

arXiv:2408.09363•Aug 18, 2024•0 citations

Direct estimation of the energy gap between the ground state and excited state with quantum annealing

Yuichiro Matsuzaki, Hideaki Hakoshima, Kenji Sugisaki +2 more

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.

International Conference on Solid State Devices and Materials (SSDM)•Sep 29, 2020•2 citations

Direct estimation of the energy gap between the ground state and excited state with quantum annealing

Yuichiro Matsuzaki, Hideaki Hakoshima, Kenji Sugisaki +2 more

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.

Japanese Journal of Applied Physics•Jan 22, 2021•22 citations

Direct estimation of the energy gap between the ground state and excited state with quantum annealing

Yuichiro Matsuzaki, Hideaki Hakoshima, Kenji Sugisaki +2 more

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.

arXiv:2007.10561•Jul 21, 2020•0 citations

Excited State Search Using Quantum Annealing

Yuya Seki, Yuichiro Matsuzaki, Shiro Kawabata

Quantum annealing (QA) is one of the ways to search the ground state of the problem Hamiltonian. Here, we propose the QA scheme to search arbitrary excited states of the problem Hamiltonian. In our scheme, an $n$-th excited state of the trivial Hamiltonian is initially prepared and is adiabatically changed into an $n$-th excited state of the target Hamiltonian. Although our scheme is general such that we can search any excited states, we especially discuss the first excited state search in this paper. As a comparison, we consider a non-adiabatic scheme to find the first excited state with non-adiabatic transitions from the ground state. By solving the Lindblad master equation, we evaluate the performance of each scheme under the influence of decoherence. Our conclusion is that the adiabatic scheme show better performance than the non-adiabatic scheme as long as the coherence time of qubits is sufficiently long. These results are important for applications in the area of quantum chemistry, quantum simulation, and post-quantum cryptography.

arXiv:2002.12621•Journal of the Physical Society of Japan•Apr 7, 2021•6 citations
We propose an experimental method for evaluating the adiabatic condition during quantum annealing (QA), which will be essential for solving practical problems. The adiabatic condition consists of the transition matrix element and the energy gap, and our method simultaneously provides information about these components without diagonalizing the Hamiltonian. The key idea is to measure the power spectrum of a time domain signal by adding an oscillating field during QA, and we can estimate the values of the transition matrix element and energy gap from the measurement output. Our results provides a powerful experimental basis for analyzing the performance of QA.
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using what is referred to as the adiabatic condition derived from the adiabatic theorem. The adiabatic condition consists of two parts: an energy gap and a transition matrix. Most past studies have focused on the relationship between the energy gap and computational time. The success probability of QA is considered to decrease exponentially owing to the exponentially decreasing energy gap at the first-order phase-transition point. In this study, through a detailed analysis of the relationship between the energy gap, transition matrix, and computational cost during QA, we propose a general method for constructing counterintuitive models wherein QA with a constant annealing time fails despite a constant energy gap, based on polynomial energy. We assume that the energy of the total Hamiltonian is at most $\mathrm{\ensuremath{\Theta}}(L)$, where LLL is the number of qubits. In our formalism, we choose a known model that exhibits an exponentially small energy gap during QA, and modify the model by adding a specific penalty term to the Hamiltonian. In the modified model, the transition matrix in the adiabatic condition becomes exponentially large as the number of qubits increases, while the energy gap remains constant. Moreover, we achieve a quadratic speedup, for which the upper bound for improvement in the adiabatic condition is determined by the polynomial energy. For concrete examples, we consider the adiabatic Grover search and the ferromagnetic ppp-spin model. In these cases, with the addition of the penalty term, although the success probability of QA on the modified models becomes exponentially small despite a constant energy gap, we are able to achieve a success probability considerably higher than that of conventional QA. Moreover, in concrete examples, we numerically show the scaling of the computational cost is quadratically improved compared to the conventional QA. Our findings pave the way for a better understanding of QA performance.
Quantum annealing (QA) is an algorithm to find the ground state of the problem Hamiltonian by using an adiabatic time evolution. An approach to evaluate adiabaticity in the experiment by applying spectroscopic techniques has recently been suggested. However, this method requires temporal oscillation of interaction strength during QA, posing challenges for experimental demonstration. Here, we propose an experimental method for evaluating adiabaticity when performing QA with a parametric oscillator with Kerr nonlinearity (KPO). Importantly, our proposal offers a significant advantage by eliminating the need for temporal oscillation of interactions during QA. We investigate its performance through numerical simulations, and we show the feasibility of our method.
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.
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 annealing (QA) is one of the ways to search the ground state of the problem Hamiltonian. Here, we propose the QA scheme to search arbitrary excited states of the problem Hamiltonian. In our scheme, an nnn-th excited state of the trivial Hamiltonian is initially prepared and is adiabatically changed into an nnn-th excited state of the target Hamiltonian. Although our scheme is general such that we can search any excited states, we especially discuss the first excited state search in this paper. As a comparison, we consider a non-adiabatic scheme to find the first excited state with non-adiabatic transitions from the ground state. By solving the Lindblad master equation, we evaluate the performance of each scheme under the influence of decoherence. Our conclusion is that the adiabatic scheme show better performance than the non-adiabatic scheme as long as the coherence time of qubits is sufficiently long. These results are important for applications in the area of quantum chemistry, quantum simulation, and post-quantum cryptography.