arXiv subjects

Masayuki Ohzeki

Publications and source records attributed to Masayuki Ohzeki.

At least 163 records · Page 9Linked to original sources

arXiv2013

Belief propagation with multipoint correlations and its application to Inverse problem

We give explicit formulas of the Bethe approximation with multipoint correlations for systems with magnetic field. The obtained formulas include the closed form of the magnetization and the correlations between adjacent degrees of freedom. On the basis of our results, we propose a new iterative algorithm of the improved Bethe approximation. We confirm that the proposed technique is available for the random spin systems and indeed gives more accurate locations of the critical points. We discuss the possibility of the application of our method to the Inverse Ising model by use of these equations.

cond-mat.dis-nn↗

arXiv2013

A challenge for critical point of spin glass in ground state

We show several calculations to identify the critical point in the ground state in random spin systems including spin glasses on the basis of the duality analysis. The duality analysis is a profound method to obtain the precise location of the critical point in finite temperature even for spin glasses. We propose a single equality for identifying the critical point in the ground state from several speculations. The equality can indeed give the exact location of the critical points for the bond-dilution Ising model on several lattices and provides insight on further analysis on the ground state in spin glasses.

cond-mat.dis-nn↗

arXiv2013

Nonequilibrium Work Relation in Macroscopic System

We reconsider a well-known relationship between the fluctuation theorem and the second law of thermodynamics by evaluating a probability measure-valued process. In order to establish a bridge between microscopic and macroscopic behaviors, we consider the thermodynamic limit of a stochastic dynamical system following the fundamental procedure often used in statistical mechanics. The thermodynamic path characterizing a macroscopic dynamical behavior can be formulated as an infimum of the action functional for the probability measure-valued process. In our formulation, the second law of thermodynamics can be derived by symmetry of the action functional, which is generated from the fluctuation theorem. We find that our formulation not only confirms that the ordinary Jarzynski equality in the thermodynamic limit can be rederived, but also enables us to establish a nontrivial nonequilibrium work relation for metastable states.

cond-mat.stat-mech↗

arXiv2013

Duality with real-space renormalization and its application to bond percolation

We obtain the exact solution of the bond-percolation thresholds with inhomogenous probabilities on the square lattice. Our method is based on the duality analysis with real-space renormalization, which is a profound technique invented in the spin-glass theory. Our formulation is a more straightforward way compared to the very recent study on the same problem [R. M. Ziff, et. al., J. Phys. A: Math. Theor. 45 (2012) 494005]. The resultant generic formulas from our derivation can give several estimations for the bond-percolation thresholds on other lattices rather than the square lattice.

cond-mat.dis-nn↗

arXiv2012

Fluctuation Theorems on Nishimori Line

The distribution of the performed work for spin glasses with gauge symmetry is considered. With the aid of the gauge symmetry, which leads to the exact/rigorous results in spin glasses, we find a fascinating relation of the performed work as the fluctuation theorem. The integral form of the resultant relation reproduces the Jarzynski-type equation for spin glasses we have obtained. We show that similar relations can be established not only for the distribution of the performed work but also that of the free energy of spin glasses with gauge symmetry, which provides another interpretation of the phase transition in spin glasses.

cond-mat.dis-nn↗

arXiv2012

Duality analysis on random planar lattice

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.

cond-mat.dis-nn↗

arXiv2012

Measurement-Based Quantum Computation on Symmetry Breaking Thermal States

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.

quant-ph↗

arXiv2012

Error threshold estimates for surface code with loss of qubits

We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a finite-dimensional spin glass, which is disordered magnetic material. We compare our estimations to the heuristic numerical results reported in earlier studies. Further application of our method to the depolarizing channel, a natural generalization of the noise model, unveils its wider robustness even with loss of qubits.

quant-ph↗

arXiv2012

Strong Resilience of Topological Codes to Depolarization

The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by mapping the quantum problem onto a classical disordered eight-vertex Ising model. By studying the stability of the related ferromagnetic phase both via large-scale Monte Carlo simulations and via the duality method, we are able to demonstrate an increased error threshold of 18.9(3)% when noise correlations are taken into account. Remarkably, this agrees within error bars with the result for a different class of codes-topological color codes-where the mapping yields interesting new types of interacting eight-vertex models.

quant-ph↗

arXiv2012

Spin Glass: A Bridge between quantum computation and statistical mechanics

We show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Second, we show another interesting technique to employ quantum nature, quantum annealing. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

quant-ph↗

arXiv2011

Nonequilibrium work on spin glasses in longitudinal and transverse fields

We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is established for the work done on the system in nonequilibrium processes, and identities are proven to relate equilibrium and nonequilibrium quantities. In the case of uniform transverse fields, identities are proven between physical quantities and exponentiated work done to the system at different parts of the phase diagram with the context of quantum annealing in mind. Additional relations are given, which relate the exponentiated work in quantum and simulated (classical) annealing. It is also suggested that the Jarzynski equality may serve as a guide to develop a method to perform quantum annealing under non-adiabatic conditions.

cond-mat.dis-nn↗

arXiv2011

Nonequilibrium work performed in quantum annealing

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.

cond-mat.dis-nn↗

arXiv2011

Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices

Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted. We study the topological color codes on the hexagonal lattice and on the square-octagonal lattice by the use of mapping into the spin glass systems. The analysis for the corresponding spin glass systems consists of the duality, and the gauge symmetry, which has succeeded in deriving locations of special points, which are deeply related with the accuracy thresholds of topological error correcting codes. We predict that the accuracy thresholds for the topological color codes would be $1-p_c = 0.1096-8 $ for the hexagonal lattice and $1-p_c = 0.1092-3$ for the square-octagonal lattice, where $1-p$ denotes the error probability on each qubit. Hence both of them are expected to be slightly lower than the probability $1-p_c = 0.110028$ for the quantum Gilbert-Varshamov bound with a zero encoding rate.

cond-mat.dis-nn↗

arXiv2011

Jarzynski Equality for an Energy-Controlled System (Proceedings of nanoPHYS'11)

We extend the Jarzynski equality, which is an exact identity between the equilibrium and nonequilibrium averages, to be useful to compute the value of the entropy difference by changing the Hamiltonian. To derive our result, we introduce artificial dynamics where the instantaneous value of the energy can be arbitrarily controlled during a nonequilibrium process. We establish an exact identity on such a process corresponding to the so-called Jarzynski equality. It is suggested that our formulation is valuable in a practical application as in optimization problems.

cond-mat.stat-mech↗

arXiv2011

Universality in phase boundary slopes for spin glasses on self dual lattices

We study the effects of disorder on the slope of the disorder--temperature phase boundary near the Onsager point (Tc = 2.269...) in spin-glass models. So far, studies have focused on marginal or irrelevant cases of disorder. Using duality arguments, as well as exact Pfaffian techniques we reproduce these analytical estimates. In addition, we obtain different estimates for spin-glass models on hierarchical lattices where the effects of disorder are relevant. We show that the phase-boundary slope near the Onsager point can be used to probe for the relevance of disorder effects.

cond-mat.dis-nn↗

arXiv2011

Jarzynski Equality for an Energy-Controlled System

The Jarzynski equality (JE) is known as an exact identity for nonequillibrium systems. The JE was originally formulated for isolated and isothermal systems, while Adib reported an JE extended to an isoenergetic process. In this paper, we extend the JE to an energy-controlled system. We make it possible to control the instantaneous value of the energy arbitrarily in a nonequilibrium process. Under our extension, the new JE is more practical and useful to calculate the number of states and the entropy than the isoenergetic one. We also show application of our JE to a kind of optimization problems.

cond-mat.stat-mech↗

arXiv2010

Quantum annealing with Jarzynski equality

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 $Δ_{\rm min.}$ 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.

quant-ph↗

arXiv2010

Quantum Annealing with Jarzynski Equality (CCP2009)

We show a practical application of an well-known nonequilibrium relation, 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. It has been disclosed that the ordinary quantum computational algorithm to solve a kind of hard optimization problems, has a bottleneck that its computational time is restricted to be extremely slow without relevant errors. However, by our novel strategy shown in the present study, we might overcome such a difficulty.

quant-ph↗