arXiv subjects

Hirotaka Irie

Publications and source records attributed to Hirotaka Irie.

17 recordsLinked to original sources

arXiv2025

Impact of Fixing Spins in a Quantum Annealer with Energy Rescaling

Quantum annealing is a promising algorithm for solving combinatorial optimization problems. However, various hardware restrictions significantly impede its efficient performance. Size-reduction methods provide an effective approach for addressing large-scale problems but often introduce additional challenges. A notable hardware restriction is the limited number of decision variables quantum annealing can handle compared to the size of the problem. Moreover, when employing size-reduction methods, the interactions and local magnetic fields in the Ising model--used to represent the combinatorial optimization problem--can become excessively large, making them difficult to implement on hardware. Although prior studies suggest that energy rescaling impacts the performance of quantum annealing, its interplay with size-reduction methods remains unexplored. This study examines the relationship between fixing spins, a promising size-reduction method, and the effects of energy rescaling. Numerical simulations and experiments conducted on a quantum annealer demonstrate that the fixing spins method enhances quantum annealing performance while preserving the spin-chain embedding for a homogeneous, fully connected ferromagnetic Ising model.

cond-mat.stat-mech↗

arXiv2024

Advantages of fixing spins in quantum annealing

Quantum annealing can efficiently obtain solutions to combinatorial optimization problems. Size-reduction methods are used to treat large-scale combinatorial optimization problems that cannot be input directly into a quantum annealer because of its size limitation. Various size-reduction methods using fixing spins have been proposed as quantum-classical hybrid methods to obtain solutions. However, the high performance of these hybrid methods is yet to be clearly elucidated. In this study, we adopted a parameterized fixing spins method to verify the effects of fixing spins. The results revealed that setting the appropriate number of spins of the subproblem is crucial for obtaining a satisfactory solution, and the energy gap expansion is confirmed after fixing spins.

cond-mat.stat-mech↗

arXiv2021

Hybrid Quantum Annealing via Molecular Dynamics

A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transverse-field Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen and ambivalent spins for quantum annealers. The performance and accuracy of our smooth hybridization in comparison to the standard classical algorithms (the tabu search and the simulated annealing) are demonstrated by employing the MAX-CUT and Ising spin-glass problems.

quant-ph↗

arXiv2019

Quantum Annealing of Vehicle Routing Problem with Time, State and Capacity

We propose a brand-new formulation of capacitated vehicle routing problem (CVRP) as quadratic unconstrained binary optimization (QUBO). The formulated CVRP is equipped with time-table which describes time-evolution of each vehicle. Therefore, various constraints associated with time are successfully realized. With a similar method, constraints of capacities are also introduced, where capacitated quantities are allowed to increase and decrease according to the cities which vehicles arrive. As a bonus of capacity-qubits, one also obtains a description of state, which allows us to set a variety of traveling rules, depending on each state of vehicles. As a consistency check, the proposed QUBO formulation is also evaluated by quantum annealing with D-Wave 2000Q.

quant-ph↗

arXiv2016

Wronskians, dualities and FZZT-Cardy branes

The resolvent operator plays a central role in matrix models. For instance, with utilizing the loop equation, all of the perturbative amplitudes including correlators, the free-energy and those of instanton corrections can be obtained from the spectral curve of the resolvent operator. However, at the level of non-perturbative completion, the resolvent operator is generally not sufficient to recover all the information from the loop equations. Therefore it is necessary to find a sufficient set of operators which provide the missing non-perturbative information. In this paper, we study generalized Wronskians of the Baker-Akhiezer systems as a manifestation of these new degrees of freedom. In particular, we derive their isomonodromy systems and then extend several spectral dualities to these systems. In addition, we discuss how these Wronskian operators are naturally aligned on the Kac table. Since they are consistent with the Seiberg-Shih relation, we propose that these new degrees of freedom can be identified as FZZT-Cardy branes in Liouville theory. This means that FZZT-Cardy branes are the bound states of elemental FZZT branes (i.e. the twisted fermions) rather than the bound states of principal FZZT-brane (i.e. the resolvent operator).

hep-th↗

arXiv2014

Duality Constraints on String Theory: Instantons and spectral networks

We study an implication of $p-q$ duality (spectral duality or T-duality) on non-perturbative completion of $(p,q)$ minimal string theory. According to the Eynard-Orantin topological recursion, spectral $p-q$ duality was already checked for all-order perturbative analysis including instanton/soliton amplitudes. Non-perturbative realization of this duality, on the other hand, causes a new fundamental issue. In fact, we find that not all the non-perturbative completions are consistent with non-perturbative $p-q$ duality; Non-perturbative duality rather provides a constraint on non-perturbative contour ambiguity (equivalently, of D-instanton fugacity) in matrix models. In particular, it prohibits some of meta-stability caused by ghost D-instantons, since there is no non-perturbative realization on the dual side in the matrix-model description. Our result is the first quantitative observation that a missing piece of our understanding in non-perturbative string theory is provided by the principle of non-perturbative string duality. To this end, we study Stokes phenomena of $(p,q)$ minimal strings with spectral networks and improve the Deift-Zhou's method to describe meta-stable vacua. By analyzing the instanton profile on spectral networks, we argue the duality constraints on string theory.

hep-th↗

arXiv2012

Analytic Study for the String Theory Landscapes via Matrix Models

We demonstrate a first-principle analysis of the string theory landscapes in the framework of non-critical string/matrix models. In particular, we discuss non-perturbative instability, decay rate and the true vacuum of perturbative string theories. As a simple example, we argue that the perturbative string vacuum of pure gravity is stable; but that of Yang-Lee edge singularity is inescapably a false vacuum. Surprisingly, most of perturbative minimal string vacua are unstable, and their true vacuum mostly does not suffer from non-perturbative ambiguity. Importantly, we observe that the instability of these tachyon-less closed string theories is caused by ghost D-instantons (or ghost ZZ-branes), the existence of which is determined only by non-perturbative completion of string theory.

hep-th↗

arXiv2011

Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory

We study Stokes phenomena of the k \times k isomonodromy systems with an arbitrary Poincaré index r, especially which correspond to the fractional-superstring (or parafermionic-string) multi-critical points (\hat p,\hat q)=(1,r-1) in the k-cut two-matrix models. Investigation of this system is important for the purpose of figuring out the non-critical version of M theory which was proposed to be the strong-coupling dual of fractional superstring theory as a two-matrix model with an infinite number of cuts. Surprisingly the multi-cut boundary-condition recursion equations have a universal form among the various multi-cut critical points, and this enables us to show explicit solutions of Stokes multipliers in quite wide classes of (k,r). Although these critical points almost break the intrinsic Z_k symmetry of the multi-cut two-matrix models, this feature makes manifest a connection between the multi-cut boundary-condition recursion equations and the structures of quantum integrable systems. In particular, it is uncovered that the Stokes multipliers satisfy multiple Hirota equations (i.e. multiple T-systems). Therefore our result provides a large extension of the ODE/IM correspondence to the general isomonodromy ODE systems endowed with the multi-cut boundary conditions. We also comment about a possibility that N=2 QFT of Cecotti-Vafa would be "topological series" in non-critical M theory equipped with a single quantum integrability.

hep-th↗

arXiv2011

Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models

The Stokes multipliers in the matrix models are invariants in the string-theory moduli space and related to the D-instanton chemical potentials. They not only represent non-perturbative information but also play an important role in connecting various perturbative string theories in the moduli space. They are a key concept to the non-perturbative completion of string theory and also expected to imply some remnant of strong coupling dynamics in M theory. In this paper, we investigate the non-perturbative completion problem consisting of two constraints on the Stokes multipliers. As the first constraint, Stokes phenomena which realize the multi-cut geometry are studied in the Z_k symmetric critical points of the multi-cut two-matrix models. Sequence of solutions to the constraints are obtained in general k-cut critical points. A discrete set of solutions and a continuum set of solutions are explicitly shown, and they can be classified by several constrained configurations of the Young diagram. As the second constraint, we discuss non-perturbative stability of backgrounds in terms of the Riemann-Hilbert problem. In particular, our procedure in the 2-cut (1,2) case (pure-supergravity case) completely fixes the D-instanton chemical potentials and results in the Hastings-McLeod solution to the Painlevé II equation. It is also stressed that the Riemann-Hilbert approach realizes an off-shell background independent formulation of non-critical string theory.

hep-th↗

arXiv2010

Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory

Multi-cut two-matrix models are studied in the Z_k symmetry breaking k-cut (\hat p,\hat q) critical points which should correspond to (\hat p,\hat q) minimal k-fractional superstring theory. FZZT-brane or macroscopic loop amplitudes are obtained in all of these critical points and found to have two kinds of solutions in general. Each of these solutions is expressed by hyperbolic cosine or sine functions with proper phase shifts. The algebraic geometries and ZZ-brane disk amplitudes (instanton actions) of these solutions are also studied. In particular, our results suggest that minimal \infty-fractional superstring theory can be viewed as a mother theory which includes all the minimal k-fractional superstring theories (k=1,2,...) as its perturbative vacua in the weak-coupling string landscape. Our results also indicate that, in the strong coupling regime of this fractional superstring theory, there is a three-dimensional theory which would be understood as the non-critical version of M theory in the sense proposed by P. Horava and C. A. Keeler.

hep-th↗

arXiv2009

Macroscopic loop amplitudes in the multi-cut two-matrix models

Multi-cut critical points and their macroscopic loop amplitudes are studied in the multi-cut two-matrix models, based on an extension of the prescription developed by Daul, Kazakov and Kostov. After identifying possible critical points and potentials in the multi-cut matrix models, we calculate the macroscopic loop amplitudes in the Z_k symmetric background. With a natural large N ansatz for the matrix Lax operators, a sequence of new solutions for the amplitudes in the Z_k symmetric k-cut two-matrix models are obtained, which are realized by the Jacobi polynomials.

hep-th↗

arXiv2009

Fractional supersymmetric Liouville theory and the multi-cut matrix models

We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p,q) minimal fractional superstring theories appear in the Z_k-symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.

hep-th↗

arXiv2008

Notes on D-branes and dualities in (p,q) minimal superstring theory

We study boundary states in (p,q) minimal superstring theory, combining the explicit form of matter wave functions. Within the modular bootstrap framework, Cardy states of (p,q) minimal superconformal field theory are completely determined in both cases of the different supercharge combinations, and the remaining consistency checks in the super-Liouville case are also performed. Using these boundary states, we determine the explicit form of FZZT- and ZZ-brane boundary states both in type 0A and 0B GSO projections. Annulus mplitudes of FZZT branes are evaluated and principal FZZT branes are identified. In particular, we found that these principal FZZT branes do not satisfy Cardy's consistency conditions for each other and play a role of order/disorder parameters of the Kramers-Wannier duality in spacetime of this superstring theory.

hep-th↗

arXiv2007

A string field theoretical description of (p,q) minimal superstrings

A string field theory of (p,q) minimal superstrings is constructed with the free-fermion realization of 2-component KP (2cKP) hierarchy, starting from 2-cut ansatz of two-matrix models. Differential operators of 2cKP hierarchy are identified with operators in super Liouville theory, and we obtain algebraic curves for the disk amplitudes of η=-1 FZZT-branes and the partition functions of neutral/charged η=-1 ZZ branes, which correctly reproduce those of type 0B (p,q) minimal superstrings in conformal backgrounds. In the course of study, some subtle points are clarified, including a difference of (p,q) even/odd models and quantization of flux, and we show that the Virasoro constraints naturally incorporate quantized fluxes without ambiguity. We also argue within this string field framework that type 0A minimal superstrings can be obtained by orbifolding the type 0B strings with a Z_2 symmetry existing when special backgrounds are taken.

hep-th↗

arXiv2007

Supermatrix models and multi ZZ-brane partition functions in minimal superstring theories

We study (p,q)=(2,4k) minimal superstrings within the minimal superstring field theory constructed in hep-th/0611045. We explicitly give a solution to the W_{1+\infty} constraints by using charged D-instanton operators, and show that the (m,n)-instanton sector with m positive-charged and n negative-charged ZZ-branes is described by an (m+n)\times (m+n) supermatrix model. We argue that the supermatrix model can be regarded as an open string field theory on the multi ZZ-brane system.

hep-th↗

arXiv2006

Notes on the algebraic curves in (p,q) minimal string theory

Loop amplitudes in (p,q) minimal string theory are studied in terms of the continuum string field theory based on the free fermion realization of the KP hierarchy. We derive the Schwinger-Dyson equations for FZZT disk amplitudes directly from the W_{1+\infty} constraints in the string field formulation and give explicitly the algebraic curves of disk amplitudes for general backgrounds. We further give annulus amplitudes of FZZT-FZZT, FZZT-ZZ and ZZ-ZZ branes, generalizing our previous D-instanton calculus from the minimal unitary series (p,p+1) to general (p,q) series. We also give a detailed explanation on the equivalence between the Douglas equation and the string field theory based on the KP hierarchy under the W_{1+\infty} constraints.

hep-th↗

arXiv2005

Comments on the D-instanton calculus in (p,p+1) minimal string theory

The FZZT and ZZ branes in (p,p+1) minimal string theory are studied in terms of continuum loop equations. We show that systems in the presence of ZZ branes (D-instantons) can be easily investigated within the framework of the continuum string field theory developed by Yahikozawa and one of the present authors (hep-th/9609210). We explicitly calculate the partition function of a single ZZ brane for arbitrary p. We also show that the annulus amplitudes of ZZ branes are correctly reproduced.

hep-th↗