Masayuki Ohzeki - Academia.edu (original) (raw)

Papers by Masayuki Ohzeki

Research paper thumbnail of Measurement-Based Quantum Computation on Symmetry Breaking Thermal States

Physical Review Letters, 2013

We consider measurement-based quantum computation (MBQC) on thermal states of the interacting clu... more We consider measurement-based quantum computation (MBQC) on thermal states of the interacting cluster Hamiltonian containing interactions between the cluster stabilizers that undergoes thermal phase transitions. We show that the long-range order of the symmetry breaking thermal states below a critical temperature drastically enhance the robustness of MBQC against thermal excitations. Specifically, we show the enhancement in two-dimensional cases and prove that MBQC is topologically protected below the critical temperature in three-dimensional cases. The interacting cluster Hamiltonian allows us to perform MBQC even at a temperature an order of magnitude higher than that of the free cluster Hamiltonian.

Research paper thumbnail of Duality analysis on random planar lattices

Physical review. E, Statistical, nonlinear, and soft matter physics, 2012

The conventional duality analysis is employed to identify a location of a critical point on a uni... more The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the randomized structure based on the square lattice. We introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square. The random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure. A modern duality analysis fashion with real-space renormalization is found to be available for estimating the location of the critical points with a wide range of the randomness parameter. As a simple test bed, we demonstrate that our method indeed gives several critical points for the cases of the Ising and Potts models and the bond-percolation thresholds on the random planar lattice. Our method leads to not only such an extension of the duality analyses on the cl...

Research paper thumbnail of Multicritical points for spin-glass models on hierarchical lattices

Physical review. E, Statistical, nonlinear, and soft matter physics, 2008

The locations of multicritical points on many hierarchical lattices are numerically investigated ... more The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry, and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data. We propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one. This improvement is inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data.

Research paper thumbnail of Zero-temperature complex replica zeros of the ±J Ising spin glass on mean-field systems and beyond

Physica E Low-dimensional Systems and Nanostructures

Zeros of the moment of the partition function [Zn]J with respect to complex n are investigated in... more Zeros of the moment of the partition function [Zn]J with respect to complex n are investigated in the zero-temperature limit β→∞, n→0 keeping y=βn≈O(1). We numerically investigate the zeros of the ±J Ising spin-glass models on several Cayley trees and hierarchical lattices and compare those results. In both lattices, the calculations are carried out with feasible computational costs by using recursion relations originated from the structures of those lattices. The results for Cayley trees show that a sequence of the zeros approaches the real axis of y implying that a certain type of analyticity breaking actually occurs, although it is irrelevant for any known replica symmetry breaking. The result of hierarchical lattices also shows the presence of analyticity breaking, even in the two dimensional case in which there is no finite-temperature spin-glass transition, which implies the existence of the zero-temperature phase transition in the system. A notable tendency of hierarchical la...

Research paper thumbnail of Analytical evidence for the absence of spin glass transition on self-dual

We show strong evidence for the absence of a finite-temperature spin glass transition for the ran... more We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with ±J or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point.

Research paper thumbnail of Simple implementation of Langevin dynamics without detailed balance condition

Research paper thumbnail of Inverse Renormalization Group Transformation in Bayesian Image Segmentations

A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation w... more A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation with an inverse real space renormalization group transformation to reduce the computational time. In results of our experiment, we observe that the proposed method can reduce the computational time to less than one-tenth of that taken by conventional Bayesian approaches.

Research paper thumbnail of Violation of detailed balance accelerates relaxation

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo metho... more Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. Our result implies the existence of a kind of thermodynamic inequality that connects the nonequilibrium process relaxing toward steady state with the relaxation process which has the same probability distribution as its equilibrium state.

Research paper thumbnail of Analytical evidence for the absence of spin glass transition on self-dual lattices

We show strong evidence for the absence of a finite-temperature spin glass transition for the ran... more We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with ±J or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point.

Research paper thumbnail of Acceleration without Detailed Balance Condition from Perspective of Nonequilibrium Behavior

Monte-Carlo method is a major technique to investigate equilibrium properties governed by the wel... more Monte-Carlo method is a major technique to investigate equilibrium properties governed by the well-known Gibbs-Boltzmann distribution through an artificial relaxation process. The standard way is to realize the Gibbs-Boltzmann distribution under the detailed balance condition. Recent progress on a technique proposed by Suwa and Todo makes it possible to accelerate the relaxation process, while avoiding the detailed balance condition. Since the dynamical stochastic system implemented to perform the Monte-Carlo simulation does not possess an equilibrium state but a steady state, we must design the steady state to be equivalent to the desired distribution such as the Gibbs-Boltzmann one. In other words, we then exploit nonequilibrium behavior with some current to accelerate the relaxation to the desired distribution. Several evidence in the previous studies exists but we do not have an answer to a simple question how the absence of the detailed balance condition accelerates the converg...

Research paper thumbnail of Violation of detailed balance accelerates relaxation

Physical Review E, 2013

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo metho... more Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. Our result implies the existence of a kind of thermodynamic inequality that connects the nonequilibrium process relaxing toward steady state with the relaxation process which has the same probability distribution as its equilibrium state.

Research paper thumbnail of Duality analysis on random planar lattices

Physical Review E, 2012

The conventional duality analysis is employed to identify a location of a critical point on a uni... more The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the randomized structure based on the square lattice. We introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square. The random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure. The duality analysis in a modern fashion with real-space renormalization is found to be available for estimating the location of the critical points with wide range of the randomness parameter. As a simple testbed, we demonstrate that our method indeed gives several critical points for the cases of the Ising and Potts models, and the bond-percolation thresholds on the random planar lattice. Our method leads to not only such an extension of the duality analyses on the classical statistical mechanics but also a fascinating result associated with optimal error thresholds for a class of quantum error correction code, the surface code on the random planar lattice, which known as a skillful technique to protect the quantum state.

Research paper thumbnail of Analytical evidence for the absence of spin glass transition on self-dual lattices

Journal of Physics A: Mathematical and Theoretical, 2009

We show strong evidence for the absence of a finite-temperature spin glass transition for the ran... more We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with ±J or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point.

Research paper thumbnail of Quantum annealing with Jarzynski equality

Computer Physics Communications, 2011

We show a practical application of the Jarzynski equality in quantum computation. Its implementat... more We show a practical application of the Jarzynski equality in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many arguments. We consider to incorpolate the Jarzynski equality into quantum annealing, which is one of the generic algorithms to solve the combinatorial optimization problem. The ordinary quantum annealing suffers from non-adiabatic transitions whose rate is characterized by the minimum energy gap ∆ of the quantum system under consideration. The quantum sweep speed is therefore restricted to be extremely slow for the achievement to obtain a solution without relevant errors. However, in our strategy shown in the present study, we find that such a difficulty would not matter.

Research paper thumbnail of Scaling Law of the Residual Energy in Simulated Annealing

Research paper thumbnail of Internal Energy of the Potts model on the Triangular Lattice with Two-and Three-body Interactions

We calculate the internal energy of the Potts model on the triangular lattice with twoand three-b... more We calculate the internal energy of the Potts model on the triangular lattice with twoand three-body interactions at the transition point satisfying certain conditions for coupling constants. The method is a duality transformation. Therefore we have to make assumptions on uniqueness of the transition point and that the transition is of second order. These assumptions have been verified to hold by numerical simulations for q = 2, 3 and 4, and our results for the internal energy are expected to be exact in these cases.

Research paper thumbnail of Multicritical point of spin glasses

We present a theoretical framework to accurately calculate the location of the multicritical poin... more We present a theoretical framework to accurately calculate the location of the multicritical point in the phase diagram of spin glasses. The result shows excellent agreement with numerical estimates. The basic idea is a combination of the duality relation, the replica method, and the gauge symmetry. An additional element of the renormalization group, in particular in the context of hierarchical lattices, leads to impressive improvements of the predictions. * Dedicated to Prof. A. Nihat Berker on the occasion of his sixtieth birthday.

Research paper thumbnail of Nonequilibrium work distribution in quantum annealing

ABSTRACT Quantum annealing is a generic solver of classical optimization problems that makes full... more ABSTRACT Quantum annealing is a generic solver of classical optimization problems that makes full use of quantum fluctuations. We consider work statistics given by a repetition of quantum annealing processes by employing the Jarzynski equality proposed in nonequilibrium statistical physics. In particular, we analyze the distribution of the work performed by a transverse field. A special symmetry, gauge symmetry, leads to a non-trivial relationship between quantum annealing toward different targets in the theory of spin glasses. We believe that our results will be a step toward an alternative realization of efficient quantum computation as well as our better understanding of nonequilibrium behavior of systems under quantum control.

Research paper thumbnail of Nonequilibrium work performed in quantum annealing

Quantum annealing is a generic solver of classical optimization problems that makes full use of q... more Quantum annealing is a generic solver of classical optimization problems that makes full use of quantum fluctuations. We consider work statistics given by a repetition of quantum annealing processes by employing the Jarzynski equality proposed in nonequilibrium statistical physics. In particular, we analyze a nonequilibrium average of the exponentiated work performed by a transverse field. A special symmetry, gauge symmetry, leads to a non-trivial relationship between quantum annealing toward different targets in the theory of spin glasses. We believe that our results will be a step toward an alternative realization of efficient quantum computation as well as our better understanding of nonequilibrium behavior of systems under quantum control.

Research paper thumbnail of Jarzynski equality for spin glasses and its application

ABSTRACT We study an application of Jarzynski equality to spin glasses with gauge symmetry. It is... more ABSTRACT We study an application of Jarzynski equality to spin glasses with gauge symmetry. It is shown that the exponentiated free-energy difference appearing in the Jarzynski equality reduces to a simple analytic function written explicitly in terms of the initial and final temperatures if the temperature satisfies a certain condition related to gauge symmetry. This result can be used to derive a lower bound on the performed work during the nonequilibrium process by changing the external magnetic field as well as a pseudo work done during changing temperature. The latter case serves as useful information to implement the population annealing developed in numerical use of the Jarzynski equality to equilibrate the many-body system. We also prove several exact identities that relate equilibrium and nonequilibrium quantities. These identities show possibility of the population annealing to evaluate equilibrium quantities from nonequilibrium computations, which may be useful for avoiding the problem of slow relaxation in spin glasses.

Research paper thumbnail of Measurement-Based Quantum Computation on Symmetry Breaking Thermal States

Physical Review Letters, 2013

We consider measurement-based quantum computation (MBQC) on thermal states of the interacting clu... more We consider measurement-based quantum computation (MBQC) on thermal states of the interacting cluster Hamiltonian containing interactions between the cluster stabilizers that undergoes thermal phase transitions. We show that the long-range order of the symmetry breaking thermal states below a critical temperature drastically enhance the robustness of MBQC against thermal excitations. Specifically, we show the enhancement in two-dimensional cases and prove that MBQC is topologically protected below the critical temperature in three-dimensional cases. The interacting cluster Hamiltonian allows us to perform MBQC even at a temperature an order of magnitude higher than that of the free cluster Hamiltonian.

Research paper thumbnail of Duality analysis on random planar lattices

Physical review. E, Statistical, nonlinear, and soft matter physics, 2012

The conventional duality analysis is employed to identify a location of a critical point on a uni... more The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the randomized structure based on the square lattice. We introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square. The random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure. A modern duality analysis fashion with real-space renormalization is found to be available for estimating the location of the critical points with a wide range of the randomness parameter. As a simple test bed, we demonstrate that our method indeed gives several critical points for the cases of the Ising and Potts models and the bond-percolation thresholds on the random planar lattice. Our method leads to not only such an extension of the duality analyses on the cl...

Research paper thumbnail of Multicritical points for spin-glass models on hierarchical lattices

Physical review. E, Statistical, nonlinear, and soft matter physics, 2008

The locations of multicritical points on many hierarchical lattices are numerically investigated ... more The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry, and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data. We propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one. This improvement is inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data.

Research paper thumbnail of Zero-temperature complex replica zeros of the ±J Ising spin glass on mean-field systems and beyond

Physica E Low-dimensional Systems and Nanostructures

Zeros of the moment of the partition function [Zn]J with respect to complex n are investigated in... more Zeros of the moment of the partition function [Zn]J with respect to complex n are investigated in the zero-temperature limit β→∞, n→0 keeping y=βn≈O(1). We numerically investigate the zeros of the ±J Ising spin-glass models on several Cayley trees and hierarchical lattices and compare those results. In both lattices, the calculations are carried out with feasible computational costs by using recursion relations originated from the structures of those lattices. The results for Cayley trees show that a sequence of the zeros approaches the real axis of y implying that a certain type of analyticity breaking actually occurs, although it is irrelevant for any known replica symmetry breaking. The result of hierarchical lattices also shows the presence of analyticity breaking, even in the two dimensional case in which there is no finite-temperature spin-glass transition, which implies the existence of the zero-temperature phase transition in the system. A notable tendency of hierarchical la...

Research paper thumbnail of Analytical evidence for the absence of spin glass transition on self-dual

We show strong evidence for the absence of a finite-temperature spin glass transition for the ran... more We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with ±J or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point.

Research paper thumbnail of Simple implementation of Langevin dynamics without detailed balance condition

Research paper thumbnail of Inverse Renormalization Group Transformation in Bayesian Image Segmentations

A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation w... more A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation with an inverse real space renormalization group transformation to reduce the computational time. In results of our experiment, we observe that the proposed method can reduce the computational time to less than one-tenth of that taken by conventional Bayesian approaches.

Research paper thumbnail of Violation of detailed balance accelerates relaxation

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo metho... more Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. Our result implies the existence of a kind of thermodynamic inequality that connects the nonequilibrium process relaxing toward steady state with the relaxation process which has the same probability distribution as its equilibrium state.

Research paper thumbnail of Analytical evidence for the absence of spin glass transition on self-dual lattices

We show strong evidence for the absence of a finite-temperature spin glass transition for the ran... more We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with ±J or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point.

Research paper thumbnail of Acceleration without Detailed Balance Condition from Perspective of Nonequilibrium Behavior

Monte-Carlo method is a major technique to investigate equilibrium properties governed by the wel... more Monte-Carlo method is a major technique to investigate equilibrium properties governed by the well-known Gibbs-Boltzmann distribution through an artificial relaxation process. The standard way is to realize the Gibbs-Boltzmann distribution under the detailed balance condition. Recent progress on a technique proposed by Suwa and Todo makes it possible to accelerate the relaxation process, while avoiding the detailed balance condition. Since the dynamical stochastic system implemented to perform the Monte-Carlo simulation does not possess an equilibrium state but a steady state, we must design the steady state to be equivalent to the desired distribution such as the Gibbs-Boltzmann one. In other words, we then exploit nonequilibrium behavior with some current to accelerate the relaxation to the desired distribution. Several evidence in the previous studies exists but we do not have an answer to a simple question how the absence of the detailed balance condition accelerates the converg...

Research paper thumbnail of Violation of detailed balance accelerates relaxation

Physical Review E, 2013

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo metho... more Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. Our result implies the existence of a kind of thermodynamic inequality that connects the nonequilibrium process relaxing toward steady state with the relaxation process which has the same probability distribution as its equilibrium state.

Research paper thumbnail of Duality analysis on random planar lattices

Physical Review E, 2012

The conventional duality analysis is employed to identify a location of a critical point on a uni... more The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the randomized structure based on the square lattice. We introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square. The random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure. The duality analysis in a modern fashion with real-space renormalization is found to be available for estimating the location of the critical points with wide range of the randomness parameter. As a simple testbed, we demonstrate that our method indeed gives several critical points for the cases of the Ising and Potts models, and the bond-percolation thresholds on the random planar lattice. Our method leads to not only such an extension of the duality analyses on the classical statistical mechanics but also a fascinating result associated with optimal error thresholds for a class of quantum error correction code, the surface code on the random planar lattice, which known as a skillful technique to protect the quantum state.

Research paper thumbnail of Analytical evidence for the absence of spin glass transition on self-dual lattices

Journal of Physics A: Mathematical and Theoretical, 2009

We show strong evidence for the absence of a finite-temperature spin glass transition for the ran... more We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with ±J or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point.

Research paper thumbnail of Quantum annealing with Jarzynski equality

Computer Physics Communications, 2011

We show a practical application of the Jarzynski equality in quantum computation. Its implementat... more We show a practical application of the Jarzynski equality in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many arguments. We consider to incorpolate the Jarzynski equality into quantum annealing, which is one of the generic algorithms to solve the combinatorial optimization problem. The ordinary quantum annealing suffers from non-adiabatic transitions whose rate is characterized by the minimum energy gap ∆ of the quantum system under consideration. The quantum sweep speed is therefore restricted to be extremely slow for the achievement to obtain a solution without relevant errors. However, in our strategy shown in the present study, we find that such a difficulty would not matter.

Research paper thumbnail of Scaling Law of the Residual Energy in Simulated Annealing

Research paper thumbnail of Internal Energy of the Potts model on the Triangular Lattice with Two-and Three-body Interactions

We calculate the internal energy of the Potts model on the triangular lattice with twoand three-b... more We calculate the internal energy of the Potts model on the triangular lattice with twoand three-body interactions at the transition point satisfying certain conditions for coupling constants. The method is a duality transformation. Therefore we have to make assumptions on uniqueness of the transition point and that the transition is of second order. These assumptions have been verified to hold by numerical simulations for q = 2, 3 and 4, and our results for the internal energy are expected to be exact in these cases.

Research paper thumbnail of Multicritical point of spin glasses

We present a theoretical framework to accurately calculate the location of the multicritical poin... more We present a theoretical framework to accurately calculate the location of the multicritical point in the phase diagram of spin glasses. The result shows excellent agreement with numerical estimates. The basic idea is a combination of the duality relation, the replica method, and the gauge symmetry. An additional element of the renormalization group, in particular in the context of hierarchical lattices, leads to impressive improvements of the predictions. * Dedicated to Prof. A. Nihat Berker on the occasion of his sixtieth birthday.

Research paper thumbnail of Nonequilibrium work distribution in quantum annealing

ABSTRACT Quantum annealing is a generic solver of classical optimization problems that makes full... more ABSTRACT Quantum annealing is a generic solver of classical optimization problems that makes full use of quantum fluctuations. We consider work statistics given by a repetition of quantum annealing processes by employing the Jarzynski equality proposed in nonequilibrium statistical physics. In particular, we analyze the distribution of the work performed by a transverse field. A special symmetry, gauge symmetry, leads to a non-trivial relationship between quantum annealing toward different targets in the theory of spin glasses. We believe that our results will be a step toward an alternative realization of efficient quantum computation as well as our better understanding of nonequilibrium behavior of systems under quantum control.

Research paper thumbnail of Nonequilibrium work performed in quantum annealing

Quantum annealing is a generic solver of classical optimization problems that makes full use of q... more Quantum annealing is a generic solver of classical optimization problems that makes full use of quantum fluctuations. We consider work statistics given by a repetition of quantum annealing processes by employing the Jarzynski equality proposed in nonequilibrium statistical physics. In particular, we analyze a nonequilibrium average of the exponentiated work performed by a transverse field. A special symmetry, gauge symmetry, leads to a non-trivial relationship between quantum annealing toward different targets in the theory of spin glasses. We believe that our results will be a step toward an alternative realization of efficient quantum computation as well as our better understanding of nonequilibrium behavior of systems under quantum control.

Research paper thumbnail of Jarzynski equality for spin glasses and its application

ABSTRACT We study an application of Jarzynski equality to spin glasses with gauge symmetry. It is... more ABSTRACT We study an application of Jarzynski equality to spin glasses with gauge symmetry. It is shown that the exponentiated free-energy difference appearing in the Jarzynski equality reduces to a simple analytic function written explicitly in terms of the initial and final temperatures if the temperature satisfies a certain condition related to gauge symmetry. This result can be used to derive a lower bound on the performed work during the nonequilibrium process by changing the external magnetic field as well as a pseudo work done during changing temperature. The latter case serves as useful information to implement the population annealing developed in numerical use of the Jarzynski equality to equilibrate the many-body system. We also prove several exact identities that relate equilibrium and nonequilibrium quantities. These identities show possibility of the population annealing to evaluate equilibrium quantities from nonequilibrium computations, which may be useful for avoiding the problem of slow relaxation in spin glasses.