Un modelo cuántico para máquinas Ising coherentes: formulación de retroalimentación de medición de tiempo discreto

Recientemente las máquinas Ising coherentes como redes de osciladores paramétricos ópticos degenerados, han sido investigados para resolver problemas de optimización cobinatoria Ising. Ellos formularon un modelo teórico para máquinas Ising coherentes con procesos de retroalimentación de medición con tiempo discreto y llevaron a cabo simulaciones numéricas para una red simple, compuesto por dos pulsos de osciladores paramétricos ópticos degenerados con acomplamiento mútuo antiferromagnético. Ellos evaluaron la extención en la cual la coherencia cuántica existe durante el proceso de optimización.

Les cito la introducción:

A Quantum Model for Coherent Ising Machines: Discrete-time Measurement Feedback Formulation

There is significant interest in finding alternatives to modern von-Neuman computers, in particular for solving combinatorial optimization problems in NP-hard and NP-complete classes. Artificial neural networks can implement NP-hard Ising problems [1] and NP-complete k-SAT problems [2]. Other efforts include adiabatic quantum computation [3], and quantum annealing [4] with superconducting quantum circuits. However, providing dense connectivity between qubits in such physical systems remains a major challenge in achieving a satisfying efficiency with these alternative approaches [5].Recently, many types of Coherent Ising machines (CIM) have been studied to solve Ising-type combinatorial optimization problems [6-8]. Among these systems, the CIMs using denegerate optical parametric oscillator (DOPO) networks are also being discussed [9-11]. The first generation of this CIM implements spin-spin coupling through optical delay lines [12-16].

This type of direct coupling Ising machine can implement O(N2) spin-spin connections with N-1 optical delay lines, which remains still a technical challenge for a large spin size (N≫1). Recently, the DOPO networks with the measurement feedback circuit were implemented at Stanford University [17] and NTT [18]. In these machines, the oscillators are coupled indirectly with the discrete-time quantum measurement and feedback processes, which can generate classical correlations between oscillators. In this paper, we formulate a quantum model with completely positive trace preserving (CPTP) maps of themeasurement feedback process for the first time, and numerically evaluate the extent to which quantum coherence exists during the optimization process. This paper is organized as follows. In Section II, we introduce our theoretical model of the DOPO network with the discrete-time measurement feedback processes. In Section III, we present numerical simulation results for a simple DOPO network. Finally, in Section IV we conclude with a brief summary.

Atsushi Yamamura, 1, 2, * Kazuyuki Aihara, 1, 2, 3 and Yoshihisa Yamamoto 4
1 Department of Electrical Engineering and Information System, the University of Tokyo, Japan
2 Institute of Industrial Science, The University of Tokyo, Japan
3 Department of Mathematical Informatics, the University of Tokyo, Japan
4 E.L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
September 29, 2017

Miguel Angel Vargas Cruz
2017-12-03 09:25:27 Post #2271