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

Springer eBooks

Mean-Field Analysis of Sourlas Codes with Adiabatic Reverse Annealing

Shunta Arai

Published Oct 19, 2021• 0 citations
Publisher

Abstract

Abstract In this chapter, we analyze the typical performance of adiabatic reverse annealing (ARA) for Sourlas codes. Sourlas codes are representative error-correcting codes related to p-body spin-glass models and have a first-order phase transition for $$p>2$$ p > 2 , which degrades the estimation performance. In the ARA formulation, we introduce the initial Hamiltonian which incorporates the prior information of the solution into a vanilla quantum annealing (QA) formulation. The ground state of the initial Hamiltonian represents the initial candidate solution. To avoid the first-order phase transition, we apply ARA to Sourlas codes. We evaluate the typical ARA performance for Sourlas codes using the replica method. We show that ARA can avoid the first-order phase transition if we prepare for the proper initial candidate solution.

DOI
10.1007/978-981-16-4095-7_13

Related papers

Mean field analysis of reverse annealing for code-division multiple-access multiuser detection

Shunta Arai, Masayuki Ohzeki, Kazuyuki Tanaka

Code-division multiple-access (CDMA) multiuser detection is a kind of signal recovery problem. The main problem of CDMA multiuser detection is to estimate the original signal from the degraded information. In CDMA multiuser detection, the first-order phase transition happens. The first-order phase transition degrades the estimation performance. To avoid or mitigate the first-order phase transition, we apply adiabatic reverse annealing (ARA) to CDMA multiuser detection. In ARA, we introduce the initial Hamiltonian, which corresponds to the prior information of the original signal into quantum annealing (QA) formulation. The ground state of the initial Hamiltonian is the initial candidate solution. By using the prior information of the original signal, ARA enhances the performance of QA for CDMA multiuser detection. We evaluate the typical ARA performance of CDMA multiuser detection by means of statistical mechanics using the replica method. At first, we consider the oracle cases where the initial candidate solution is randomly generated with a fixed fraction of the original signal in the initial state. In the oracle cases, the first-order phase transition can be avoided or mitigated by ARA if we prepare for the proper initial candidate solution. We validate our theoretical analysis with quantum Monte Carlo simulations. The theoretical results to avoid the first-order phase transition are consistent with the numerical results. Next, we consider the practical cases where we prepare for the initial candidate solution obtained by commonly used algorithms. We show that the practical algorithms can exceed the threshold to avoid the first-order phase transition. Finally, we test the performance of ARA with the initial candidate solution obtained by the practical algorithm. In this case, ARA cannot avoid the first-order phase transition even if the initial candidate solution exceeds the threshold to avoid the first-order phase transition.

arXiv:2004.11066•Physical Review Research•Jul 2, 2021•36 citations

Adiabatic reverse annealing is robust to low-temperature decoherence

An Le, Christopher L. Baldwin

Adiabatic reverse annealing (ARA) is an improvement to conventional quantum annealing (QA) that uses an initial guess at the desired ground state to circumvent problematic phase transitions. Despite encouraging results in the closed-system setting, Ref. [1] has suggested on the basis of numerical simulations that ARA may lose its advantage in the presence of decoherence. Here, we revisit this problem from a more analytical perspective. Using the $p$-spin model as a solvable example, together with the adiabatic master equation to describe the effects of the environment (valid at weak coupling), we show that ARA can in fact succeed in open systems but that the temperature of the environment plays a key role. We first demonstrate that, in the adiabatic limit, the system will follow the instantaneous equilibrium state as long as the protocol does not pass through any (finite-temperature) phase transitions. Given this, there are two distinct mechanisms by which ARA can break down at high temperature: either there are no paths that avoid transitions, or the equilibrium state itself is disordered. When the temperature is sufficiently low that neither of these occur, then ARA succeeds. Remarkably, there are even situations in which the environment benefits ARA: we find parameter values for which no transition-avoiding paths exist at zero temperature but such paths appear at non-zero temperature.

quant-pharXiv:2511.16735•Nov 24, 2025•0 citations

Simulated outperforms quantum reverse annealing in mean-field models

Christopher L. Baldwin

Adiabatic reverse annealing (ARA) has been proposed as an improvement to conventional quantum annealing for solving optimization problems, in which one takes advantage of an initial guess at the solution to suppress problematic phase transitions. Here we interpret the performance of ARA through its effects on the free energy landscape, and use the intuition gained to introduce a classical analogue to ARA termed ``simulated reverse annealing'' (SRA). This makes it more difficult to claim that ARA provides a quantum advantage in solving a given problem, as not only must ARA succeed but the corresponding SRA must fail. As a solvable example, we analyze how both protocols behave in the infinite-range (non-disordered) $p$-spin model. Through both the thermodynamic phase diagrams and explicit dynamical behavior, we establish that the quantum algorithm has no advantage over its classical counterpart: SRA succeeds not only in every case where ARA does but even in a narrow range of parameters where ARA fails.

arXiv:2511.00150•Oct 31, 2025•0 citations

Standard quantum annealing outperforms adiabatic reverse annealing with decoherence

Gianluca Passarelli, Ka-Wa Yip, Daniel A. Lidar +1 more

We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic $p$-spin model with $p=3$ under independent and collective dephasing. For both models of decoherence, we show that the performance of open system ARA is far less sensitive to the choice of the initial state than its unitary counterpart, and, most significantly, that open system ARA by and large loses its time to solution advantage compared to standard quantum annealing. These results suggest that as a stand-alone strategy ARA is unlikely to experimentally outperform standard ``forward'' quantum annealing, and that error mitigation strategies will likely be required in order to realize the benefits of ARA in realistic, noisy settings.

arXiv:2201.11997•Physical Review A•Mar 18, 2022•14 citations

Reverse annealing for the fully connected p -spin model

Masaki Ohkuwa, Hidetoshi Nishimori, Daniel A. Lidar

Reverse annealing is a variant of quantum annealing that starts from a given classical configuration of spins (qubits). In contrast to the conventional formulation, where one starts from a uniform superposition of all possible states (classical configurations), quantum fluctuations are first increased and only then decreased. One then reads out the state as a proposed solution to the given combinatorial optimization problem. We formulate a mean-field theory of reverse annealing using the fully connected ferromagnetic $p$-spin model, with and without random longitudinal fields, and analyze it in order to understand how and when reverse annealing is effective at solving this problem. We find that the difficulty arising from the existence of a first-order quantum phase transition, which leads to an exponentially long computation time in conventional quantum annealing, is circumvented in the context of this particular problem by reverse annealing if the proximity of the initial state to the (known) solution exceeds a threshold. Even when a first-order transition is unavoidable, the difficulty is mitigated due to a smaller jump in the order parameter at a first-order transition, which implies a larger rate of quantum tunneling. Reverse annealing has not been studied analytically before, and this study paves the way toward a systematic understanding of this relatively unexplored protocol in a broader context.

arXiv:1806.02542•Physical Review A•Aug 13, 2018•112 citations

Dynamics of reverse annealing for the fully connected p-spin model

悠 山城, Yu Yamashiro, 秀稔 西森 +2 more

Reverse annealing is a relatively new variant of quantum annealing in which one starts from a classical state and increases and then decreases the amplitude of the transverse field, in the hope of finding a better classical state than the initial state for a given optimization problem.We numerically study the unitary quantum dynamics of reverse annealing for the mean-field-type p-spin model and show that the results are consistent with the predictions of equilibrium statistical mechanics.In particular, we corroborate the equilibrium analysis prediction that reverse annealing provides an exponential speedup over conventional quantum annealing in terms of solving the p-spin model.This lends support to the expectation that equilibrium analyses are effective at revealing essential aspects of the dynamics of quantum annealing.We also compare the results of quantum dynamics with the corresponding classical dynamics to reveal their similarities and differences.We distinguish between two reverse annealing protocols we call adiabatic and iterated reverse annealing.We further show that iterated reverse annealing, as has been realized in the D-Wave device, is ineffective in the case of the p-spin model but note that a recently introduced protocol ("h-gain"), which implements adiabatic reverse annealing, may lead to improved performance.

•Nov 1, 2019•0 citations
Abstract In this chapter, we analyze the typical performance of adiabatic reverse annealing (ARA) for Sourlas codes. Sourlas codes are representative error-correcting codes related to p-body spin-glass models and have a first-order phase transition for p>2p>2p>2 p > 2 , which degrades the estimation performance. In the ARA formulation, we introduce the initial Hamiltonian which incorporates the prior information of the solution into a vanilla quantum annealing (QA) formulation. The ground state of the initial Hamiltonian represents the initial candidate solution. To avoid the first-order phase transition, we apply ARA to Sourlas codes. We evaluate the typical ARA performance for Sourlas codes using the replica method. We show that ARA can avoid the first-order phase transition if we prepare for the proper initial candidate solution.
Code-division multiple-access (CDMA) multiuser detection is a kind of signal recovery problem. The main problem of CDMA multiuser detection is to estimate the original signal from the degraded information. In CDMA multiuser detection, the first-order phase transition happens. The first-order phase transition degrades the estimation performance. To avoid or mitigate the first-order phase transition, we apply adiabatic reverse annealing (ARA) to CDMA multiuser detection. In ARA, we introduce the initial Hamiltonian, which corresponds to the prior information of the original signal into quantum annealing (QA) formulation. The ground state of the initial Hamiltonian is the initial candidate solution. By using the prior information of the original signal, ARA enhances the performance of QA for CDMA multiuser detection. We evaluate the typical ARA performance of CDMA multiuser detection by means of statistical mechanics using the replica method. At first, we consider the oracle cases where the initial candidate solution is randomly generated with a fixed fraction of the original signal in the initial state. In the oracle cases, the first-order phase transition can be avoided or mitigated by ARA if we prepare for the proper initial candidate solution. We validate our theoretical analysis with quantum Monte Carlo simulations. The theoretical results to avoid the first-order phase transition are consistent with the numerical results. Next, we consider the practical cases where we prepare for the initial candidate solution obtained by commonly used algorithms. We show that the practical algorithms can exceed the threshold to avoid the first-order phase transition. Finally, we test the performance of ARA with the initial candidate solution obtained by the practical algorithm. In this case, ARA cannot avoid the first-order phase transition even if the initial candidate solution exceeds the threshold to avoid the first-order phase transition.
Adiabatic reverse annealing (ARA) is an improvement to conventional quantum annealing (QA) that uses an initial guess at the desired ground state to circumvent problematic phase transitions. Despite encouraging results in the closed-system setting, Ref. [1] has suggested on the basis of numerical simulations that ARA may lose its advantage in the presence of decoherence. Here, we revisit this problem from a more analytical perspective. Using the ppp-spin model as a solvable example, together with the adiabatic master equation to describe the effects of the environment (valid at weak coupling), we show that ARA can in fact succeed in open systems but that the temperature of the environment plays a key role. We first demonstrate that, in the adiabatic limit, the system will follow the instantaneous equilibrium state as long as the protocol does not pass through any (finite-temperature) phase transitions. Given this, there are two distinct mechanisms by which ARA can break down at high temperature: either there are no paths that avoid transitions, or the equilibrium state itself is disordered. When the temperature is sufficiently low that neither of these occur, then ARA succeeds. Remarkably, there are even situations in which the environment benefits ARA: we find parameter values for which no transition-avoiding paths exist at zero temperature but such paths appear at non-zero temperature.
Adiabatic reverse annealing (ARA) has been proposed as an improvement to conventional quantum annealing for solving optimization problems, in which one takes advantage of an initial guess at the solution to suppress problematic phase transitions. Here we interpret the performance of ARA through its effects on the free energy landscape, and use the intuition gained to introduce a classical analogue to ARA termed ``simulated reverse annealing'' (SRA). This makes it more difficult to claim that ARA provides a quantum advantage in solving a given problem, as not only must ARA succeed but the corresponding SRA must fail. As a solvable example, we analyze how both protocols behave in the infinite-range (non-disordered) ppp-spin model. Through both the thermodynamic phase diagrams and explicit dynamical behavior, we establish that the quantum algorithm has no advantage over its classical counterpart: SRA succeeds not only in every case where ARA does but even in a narrow range of parameters where ARA fails.
We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic ppp-spin model with p=3p=3p=3 under independent and collective dephasing. For both models of decoherence, we show that the performance of open system ARA is far less sensitive to the choice of the initial state than its unitary counterpart, and, most significantly, that open system ARA by and large loses its time to solution advantage compared to standard quantum annealing. These results suggest that as a stand-alone strategy ARA is unlikely to experimentally outperform standard ``forward'' quantum annealing, and that error mitigation strategies will likely be required in order to realize the benefits of ARA in realistic, noisy settings.
Reverse annealing is a variant of quantum annealing that starts from a given classical configuration of spins (qubits). In contrast to the conventional formulation, where one starts from a uniform superposition of all possible states (classical configurations), quantum fluctuations are first increased and only then decreased. One then reads out the state as a proposed solution to the given combinatorial optimization problem. We formulate a mean-field theory of reverse annealing using the fully connected ferromagnetic ppp-spin model, with and without random longitudinal fields, and analyze it in order to understand how and when reverse annealing is effective at solving this problem. We find that the difficulty arising from the existence of a first-order quantum phase transition, which leads to an exponentially long computation time in conventional quantum annealing, is circumvented in the context of this particular problem by reverse annealing if the proximity of the initial state to the (known) solution exceeds a threshold. Even when a first-order transition is unavoidable, the difficulty is mitigated due to a smaller jump in the order parameter at a first-order transition, which implies a larger rate of quantum tunneling. Reverse annealing has not been studied analytically before, and this study paves the way toward a systematic understanding of this relatively unexplored protocol in a broader context.
Reverse annealing is a relatively new variant of quantum annealing in which one starts from a classical state and increases and then decreases the amplitude of the transverse field, in the hope of finding a better classical state than the initial state for a given optimization problem.We numerically study the unitary quantum dynamics of reverse annealing for the mean-field-type p-spin model and show that the results are consistent with the predictions of equilibrium statistical mechanics.In particular, we corroborate the equilibrium analysis prediction that reverse annealing provides an exponential speedup over conventional quantum annealing in terms of solving the p-spin model.This lends support to the expectation that equilibrium analyses are effective at revealing essential aspects of the dynamics of quantum annealing.We also compare the results of quantum dynamics with the corresponding classical dynamics to reveal their similarities and differences.We distinguish between two reverse annealing protocols we call adiabatic and iterated reverse annealing.We further show that iterated reverse annealing, as has been realized in the D-Wave device, is ineffective in the case of the p-spin model but note that a recently introduced protocol ("h-gain"), which implements adiabatic reverse annealing, may lead to improved performance.