High-accuracy Ising machine using Kerr-nonlinear parametric oscillators with local four-body interactions

Abstract

A two-dimensional array of Kerr-nonlinear parametric oscillators (KPOs) with local four-body interactions is a promising candidate for realizing an Ising machine with all-to-all spin couplings, based on adiabatic quantum computation in the Lechner–Hauke–Zoller (LHZ) scheme. However, its performance has been evaluated only for a symmetric network of three KPOs, and thus it has been unclear whether such an Ising machine works in general cases with asymmetric networks. By numerically simulating an asymmetric network of more KPOs in the LHZ scheme, we find that the asymmetry in the four-body interactions causes inhomogeneity in photon numbers and hence degrades the performance. We then propose a method for reducing the inhomogeneity, where the discrepancies of the photon numbers are corrected by tuning the detunings of KPOs depending on their positions, without monitoring their states during adiabatic time evolution. Our simulation results show that the performance can be dramatically improved by this method. The proposed method, which is based on the understanding of the asymmetry, is expected to be useful for general networks of KPOs in the LHZ scheme and thus for their large-scale implementation.

Two-qubit gate using conditional driving for highly detuned Kerr-nonlinear parametric oscillators

“…KPOs have been implemented experimentally with superconducting quantum interference devices (SQUIDs) [24,25] or by a superconducting nonlinear asymmetric inductive element (SNAIL) transmon [26]. Remarkably, KPOs can be used for both quantum annealing [18,21,[27][28][29][30][31][32] and gate-based quantum compu- * hiroomi1.chono@toshiba.co.jp tation [19-23, 33, 34]. For universal quantum computing using KPOs, three kinds of gates are required: R x gate (X rotation), R z gate (Z rotation), and R zz gate (ZZ rotation) [19,20,35].…”

Autonomous Quantum Error Correction in a Four-Photon Kerr Parametric Oscillator

“…Since this fourphoton pump cannot be achieved by simple linear driving and must be achieved by parametric modulation of the Josephson junction energy [27,28] (see Supplementary Note 1), we term this system a four-photon Kerr parametric oscillator (KPO). Although a KPO has received much attention very recently because of its use for the generation and stabilization of the cat states [29-36, 38, 72], gate-based quantum computation [30,34,[38][39][40][41][42], measurement-based error correction [43,44], quantum annealing [45][46][47][48][49][50][51], and other physically interesting topics [52][53][54][55][56][57][58][59], little attention has been paid to its applicability to AQEC. Our study reveals that a KPO can be a suitable system for AQEC.…”

Simulated bifurcation assisted by thermal fluctuation

“…Among such algorithms, simulated bifurcation (SB) is a recently proposed heuristic algorithm [34]. SB originates from numerical simulations of Hamiltonian dynamics with bifurcation that is a classical counterpart of quantum adiabatic bifurcation in nonlinear oscillators [39,40], which itself has been studied actively [41][42][43][44][45][46][47][48][49]. Simulation-based approaches such as SB allow one to deal with dense spinspin interactions with high precision, which might be challenging for physical implementations.…”