Day 2 Dec-3 2021

Session 3 9:00-9:45

Recent Progress in Coherent Ising Machines

Yamamoto, Y.

yoshihisa.yamamoto@ntt-research.com

PHI (Physics & Informatics) Laboratories, NTT Research, Inc., U.S.A.

In this talk we will discuss various recent results on coherent Ising machines (CIM): the quantum principles and application as heuristic algorithms on current digital platform.

1. Quantum principles of CIMs

A coherent Ising machine (CIM) is an analog neural network consisting of optical parametric oscillators (OPO) and capable of finding optimum or sub-optimum solutions for combinatorial optimization problems.[1,2] An optical delay line (ODL-)CIM implements a target (Ising) Hamiltonian directly in optical domain.[3-5] Quantum correlation is formed among OPOs at below threshold, which induces a collective symmetry breaking at above threshold toward an optimum solution. The degree of entanglement in OPO network reaches a maximum at threshold [6], when a decision is induced by the formed quantum correlation (collective pitchfork bifurcation). A measurement feedback (MFB-)CIM implements a target Hamiltonian indirectly using digital electronic circuits.[7-9] In this case, the quantum correlation between internal and external (measurement) fields is converted to classical correlation among OPOs via measurement induced state reduction.

2. CIM as a digital algorithm

Although CIM has been studied as a computing hardware platform in the past, the quantum model in its simplest version can be implemented as a heuristic algorithm on current digital platform such as GPU and FPGA. This cyber-CIM is one of the quantum inspired optimization (QIO) approaches. One advantage of QIO is that we can create an ideal quantum machine with arbitrary precision and controlled (optimized) noise. The CIM with chaotic amplitude control (CAC) [10] and discrete simulated bifurcation machine (dSBM) [11] are representative examples of QIO. CIM-CAC and dSBM are very similar in their principles, so the difference between the two algorithms is very subtle. In general, dSBM is a faster solver for easy instances but constantly struggles for harder instances.

**Reference:**

[1] Y. Yamamoto et al., npj Quantum Information 3, 49 (2017).

[2] Y. Yamamoto et al., Appl. Phys. Lett. 117, 160501 (2020).

[3] A. Marandi et al., Nature Photonics 8, 937 (2014).

[4] K. Takata et al., Scientific Reports 6, 34089 (2016).

[5] T. Inagaki et al., Nature Photonics 10, 415 (2016).

[6] Y. Inui and Y. Yamamoto, Phys. Rev. A 102, 062419 (2020).

[7] P. L. McMahon, et al., Science 354, 614 (2016).

[8] T. Inagaki et al., Science 354, 603 (2016).

[9] R. Hamerly et al., Science Advances 5, eaau0823 (2019).

[10] T. Leleu et al., Phys. Rev. Lett. 122, 040607 (2019).

[11] K. Tatsumura et al., Nature Electron. 4. 208 (2021).

Yoshihisa Yamamoto is the Director of PHI (Physics & Informatics) Laboratories, NTT Research, Inc. He received B.S. degree from Tokyo Institute of Technology and Ph.D. degree from the University of Tokyo in 1973 and 1978, respectively, and joined NTT Basic Research Laboratories in 1978. He became a Professor of Applied Physics and Electrical Engineering at Stanford University in 1992 and also a Professor at National Institute of Informatics (NII) in 2003. He is currently a Professor (emeritus) of Stanford University and NII. His past research areas are coherent communications, squeezed states, quantum non-demolition measurements, exciton-polariton BEC, single photon and spin-photon entanglement generation and mesoscopic transport noise. He has received many distinctions for his past work, including Carl Zeiss Award (1992), Nishina Memorial Prize (1992), IEEE/LEOS Quantum Electronics Award (2000), Medal with Purple Ribbon (2005), Hermann A. Haus Lecturer of MIT (2010), and Okawa Prize (2011). His current research interest focuses on quantum information processing, physics of quantum-to-classical transition and coherent Ising machines.