arXiv subjects

Tadashi Kadowaki

Publications and source records attributed to Tadashi Kadowaki.

26 records · Page 2Linked to original sources

arXiv2022

Application of QUBO solver using black-box optimization to structural design for resonance avoidance

Quadratic unconstrained binary optimization (QUBO) solvers can be applied to design an optimal structure to avoid resonance. QUBO algorithms that work on a classical or quantum device have succeeded in some industrial applications. However, their applications are still limited due to the difficulty of transforming from the original optimization problem to QUBO. Recently, black-box optimization (BBO) methods have been proposed to tackle this issue using a machine learning technique and a Bayesian treatment for combinatorial optimization. We employed the BBO methods to design a printed circuit board for resonance avoidance. This design problem is formulated to maximize natural frequency and simultaneously minimize the number of mounting points. The natural frequency, which is the bottleneck for the QUBO formulation, is approximated to a quadratic model in the BBO method. We demonstrated that BBO using a factorization machine shows good performance in both the calculation time and the success probability of finding the optimal solution. Our results can open up QUBO solvers' potential for other applications in structural designs.

cond-mat.mes-hall↗

arXiv2021

Benchmark test of Black-box optimization using D-Wave quantum annealer

In solving optimization problems, objective functions generally need to be minimized or maximized. However, objective functions cannot always be formulated explicitly in a mathematical form for complicated problem settings. Although several regression techniques infer the approximate forms of objective functions, they are at times expensive to evaluate. Optimal points of "black-box" objective functions are computed in such scenarios, while effectively using a small number of clues. Recently, an efficient method by use of inference by sparse prior for a black-box objective function with binary variables has been proposed. In this method, a surrogate model was proposed in the form of a quadratic unconstrained binary optimization (QUBO) problem, and was iteratively solved to obtain the optimal solution of the black-box objective function. In the present study, we employ the D-Wave 2000Q quantum annealer, which can solve QUBO by driving the binary variables by quantum fluctuations. The D-Wave 2000Q quantum annealer does not necessarily output the ground state at the end of the protocol due to freezing effect during the process. We investigate effects from the output of the D-Wave quantum annealer in performing black-box optimization. We demonstrate a benchmark test by employing the sparse Sherrington-Kirkpatrick (SK) model as the black-box objective function, by introducing a parameter controlling the sparseness of the interaction coefficients. Comparing the results of the D-Wave quantum annealer to those of the simulated annealing (SA) and semidefinite programming (SDP), our results by the D-Wave quantum annealer and SA exhibit superiority in black-box optimization with SDP. On the other hand, we did not find any advantage of the D-Wave quantum annealer over the simulated annealing. As far as in our case, any effects by quantum fluctuation are not found.

cond-mat.stat-mech↗

arXiv2019

Experimental and Theoretical Study of Thermodynamic Effects in a Quantum Annealer

Quantum devices are affected by intrinsic and environmental noises. An in-depth characterization of noise effects is essential for exploiting noisy quantum computing. To this end, we studied the energy dissipative behavior of a quantum annealer via experiments and numerical simulations. Our investigation adopts a recently proposed technique that interpolates between pure quantum dynamics and pure thermodynamics. Experiments were conducted on a quantum annealer with an anneal pause function, which inserts a thermal relaxation period into the annealing schedule by pausing the transverse field, which is a source of quantum fluctuation. After investigating the special Hamiltonian that characterizes the quantum thermodynamics of the system, we then observed enhancement of thermodynamic signature depending on the anneal pause parameter. The time development of the state vector, observed in the open quantum simulation, provides rich information for investigating phenomena beyond energy-gap analysis. We identified a special eigenstate bridges ground states far-separated in Hilbert space and the transfer probabilities from one ground state to another. This finding can improve the sampling uniformity by reducing the sampling bias in finding the classical ground states in the quantum annealer. Our study does not only characterize the open quantum phenomenon of the specific Hamiltonian but also demonstrates the usefulness of the method in investigating noisy quantum devices.

quant-ph↗

arXiv2018

Dynamics of open quantum systems by interpolation of von Neumann and classical master equations, and its application to quantum annealing

We propose a method to interpolate dynamics of von Neumann and classical master equations with an arbitrary mixing parameter to investigate the thermal effects in quantum dynamics. The two dynamics are mixed by intervening to continuously modify their solutions, thus coupling them indirectly instead of directly introducing a coupling term. This maintains the quantum system in a pure state even after the introduction of thermal effects and obtains not only a density matrix but also a state vector representation. Further, we demonstrate that the dynamics of a two-level system can be rewritten as a set of standard differential equations, resulting in quantum dynamics that includes thermal relaxation. These equations are equivalent to the optical Bloch equations at the weak coupling and asymptotic limits, implying that the dynamics cause thermal effects naturally. Numerical simulations of ferromagnetic and frustrated systems support this idea. Finally, we use this method to study thermal effects in quantum annealing, revealing nontrivial performance improvements for a spin glass model over a certain range of annealing time. This result may enable us to optimize the annealing time of real annealing machines.

quant-ph↗

arXiv2002

Study of Optimization Problems by Quantum Annealing

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. The idea is tested by the two models, the transverse Ising model and the traveling salesman problem (TSP). Adding the transverse field to the Ising model is a simple way to introduce quantum fluctuations. The strength of the transverse field is controlled as a function of time similarly to the temperature in the conventional method. TSP can be described by the Ising spin, so that we also apply the same technique to TSP. We directory solve the time-dependent Schrödinger equation for small-size systems and perform the quantum Monte Carlo simulation for large-size systems. Comparison with the results of the corresponding classical (thermal) method reveals that the quantum method leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule of the control parameters. We also find that the relaxation time is quite short for quantum systems by numerical simulations. We consider this is one of the reasons why the annealing in quantum systems have a better performance of finding the optimal state in comparison with classical systems.

quant-ph↗

arXiv1998

Quantum Annealing in the Transverse Ising Model

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach. The idea is tested by the transverse Ising model, in which the transverse field is a function of time similar to the temperature in the conventional method. The goal is to find the ground state of the diagonal part of the Hamiltonian with high accuracy as quickly as possible. We have solved the time-dependent Schrödinger equation numerically for small size systems with various exchange interactions. Comparison with the results of the corresponding classical (thermal) method reveals that the quantum annealing leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule.

cond-mat.stat-mech↗

arXiv1997

High-Temperature Dynamics of Spin Glasses

We develop a systematic expansion method of physical quantities for the SK model and the finite-dimensional $\pm J$ model of spin glasses in non-equilibrium states. The dynamical probability distribution function is derived from the master equation using a high temperature expansion. We calculate the expectation values of physical quantities from the dynamical probability distribution function. The theoretical curves show satisfactory agreement with Monte Carlo simulation results in the appropriate temperature and time regions. A comparison is made with the results of a dynamics theory by Coolen, Laughton and Sherrington.

cond-mat.dis-nn↗

arXiv1996

Exact Ground-State Energy of the Ising Spin Glass on Strips

We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for complex values of the probability describing quenched randomness. We study the $\pm J$ and the site-random models using this method for strips of various sizes up to $5\times\infty$. The ground-state energy of these models is found to have singular points in the complex-probability plane, reminiscent of Lee-Yang zeros in the complex-field plane for the Ising ferromagnet. The $\pm J$ Ising model has a series of singularities which may approach a limiting point around $p \sim 0.9$ on the real axis in the limit of infinite width.

cond-mat↗