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

Performance enhancement of quantum annealing under the Lechner-Hauke-Zoller scheme by non-linear driving of the constraint term

友紀 須佐, Yuki Susa, 秀稔 西森, Hidetoshi Nishimori

Published Mar 1, 2020• 0 citations
OpenAlex

Related papers

Performance Enhancement of Quantum Annealing under the Lechner–Hauke–Zoller Scheme by Non-linear Driving of the Constraint Term

Yuki Susa, Hidetoshi Nishimori

We analyze the performance of quantum annealing as formulated by Lechner, Hauke, and Zoller (LHZ), by which a Hamiltonian with all-to-all two-body interactions is reduced to a corresponding Hamiltonian with local many-body interactions. Mean-field analyses show that problematic first-order quantum phase transitions that exist in the original LHZ formulation can be avoided, and thus an exponential speedup is achieved, if we drive the coefficient of the many-body term, which represents the constraint, non-linearly as a function of time. This result applies not only to a simple ferromagnetic model but also to the spin glass problem if a parameter in the spin glass model is chosen appropriately.

arXiv:1911.08116•Journal of the Physical Society of Japan•Mar 27, 2020•8 citations

Exponential enhancement of the efficiency of quantum annealing by non-stoquastic Hamiltonians

秀稔 西森, Hidetoshi Nishimori, 珠武己 高田 +1 more

•Feb 1, 2017•0 citations

Variational optimization of the quantum annealing schedule for the Lechner-Hauke-Zoller scheme

Yuki Susa, Hidetoshi Nishimori

The annealing schedule is optimized for a parameter in the Lechner-Hauke-Zoller (LHZ) scheme for quantum annealing designed for the all-to-all-interacting Ising model representing generic combinatorial optimization problems. We adapt the variational approach proposed by Matsuura et al. (arXiv:2003.09913) to the annealing schedule of a term representing a constraint for variables intrinsic to the LHZ scheme with the annealing schedule of other terms kept intact. Numerical results for a simple ferromagnetic model and the spin-glass problem show that nonmonotonic annealing schedules optimize the performance measured by the residual energy and the final ground-state fidelity. This improvement does not accompany a notable increase in the instantaneous energy gap, which suggests the importance of a dynamical viewpoint in addition to static analyses in the study of practically relevant diabatic processes in quantum annealing.

arXiv:2012.01694•Physical Review A•Feb 26, 2021•27 citations

Optimization algorithms for Quantum Annealing

E. Arvidsson

•Jan 1, 2020•0 citations

Relation between quantum fluctuations and the performance enhancement of quantum annealing in a non-stoquastic Hamiltonian

友紀 須佐, Yuki Susa, 秀稔 西森 +2 more

•Apr 1, 2017•0 citations

Improving success probability in Lechner-Hauke-Zoller parity embedding by computing with quantum walks

Jemma Bennett, Nicholas Chancellor, Viv M. Kendon +1 more

Lechner-Hauke-Zoller (LHZ) parity embedding is one of the front-running methods for implementing difficult-to-engineer long-range interactions in quantum optimization problems. Continuous-time quantum walks are a leading approach for solving quantum optimization problems. Because they populate excited states, quantum walks can avoid the exponential gap-closing problems seen in other continuous-time techniques such as quantum annealing and adiabatic quantum computation. An important question, therefore, is how continuous-time quantum walks perform in combination with the LHZ parity embedding. By numerically simulating continuous-time quantum walks on four-, five-, and six-logical-qubit Sherrington-Kirkpatrick Ising spin glass instances embedded onto the LHZ parity embedding, we are able to verify the continued efficacy of heuristics used to estimate the optimal hopping rate and the numerical agreement with the theory behind the location of the lower bound of the LHZ parity constraint strength. In addition, by comparing several different LHZ-based decoding methods, we identified postreadout error correction techniques which improve the success probability of the quantum walk.

arXiv:2502.18324•Physical Review A•Sep 17, 2025•0 citations
We analyze the performance of quantum annealing as formulated by Lechner, Hauke, and Zoller (LHZ), by which a Hamiltonian with all-to-all two-body interactions is reduced to a corresponding Hamiltonian with local many-body interactions. Mean-field analyses show that problematic first-order quantum phase transitions that exist in the original LHZ formulation can be avoided, and thus an exponential speedup is achieved, if we drive the coefficient of the many-body term, which represents the constraint, non-linearly as a function of time. This result applies not only to a simple ferromagnetic model but also to the spin glass problem if a parameter in the spin glass model is chosen appropriately.
The annealing schedule is optimized for a parameter in the Lechner-Hauke-Zoller (LHZ) scheme for quantum annealing designed for the all-to-all-interacting Ising model representing generic combinatorial optimization problems. We adapt the variational approach proposed by Matsuura et al. (arXiv:2003.09913) to the annealing schedule of a term representing a constraint for variables intrinsic to the LHZ scheme with the annealing schedule of other terms kept intact. Numerical results for a simple ferromagnetic model and the spin-glass problem show that nonmonotonic annealing schedules optimize the performance measured by the residual energy and the final ground-state fidelity. This improvement does not accompany a notable increase in the instantaneous energy gap, which suggests the importance of a dynamical viewpoint in addition to static analyses in the study of practically relevant diabatic processes in quantum annealing.
Lechner-Hauke-Zoller (LHZ) parity embedding is one of the front-running methods for implementing difficult-to-engineer long-range interactions in quantum optimization problems. Continuous-time quantum walks are a leading approach for solving quantum optimization problems. Because they populate excited states, quantum walks can avoid the exponential gap-closing problems seen in other continuous-time techniques such as quantum annealing and adiabatic quantum computation. An important question, therefore, is how continuous-time quantum walks perform in combination with the LHZ parity embedding. By numerically simulating continuous-time quantum walks on four-, five-, and six-logical-qubit Sherrington-Kirkpatrick Ising spin glass instances embedded onto the LHZ parity embedding, we are able to verify the continued efficacy of heuristics used to estimate the optimal hopping rate and the numerical agreement with the theory behind the location of the lower bound of the LHZ parity constraint strength. In addition, by comparing several different LHZ-based decoding methods, we identified postreadout error correction techniques which improve the success probability of the quantum walk.