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arXiv:1808.10609 · Journal of the Physical Society of Japan

Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators

Hayato Goto

Published Mar 1, 2019• 113 citations
arXivHTMLPDF

Abstract

Quantum computers with Kerr-nonlinear parametric oscillators (KPOs) have recently been proposed by the author and others. Quantum computation using KPOs is based on quantum adiabatic bifurcations of the KPOs, which lead to quantum superpositions of coherent states, such as Schrodinger cat states. Therefore, these quantum computers are referred to as "quantum bifurcation machines (QbMs)." QbMs can be used for qauntum adiabatic optimization and universal quantum computation. Superconducting circuits with Josephson junctions, Josephson parametric oscillators (JPOs) in particular, are promising for physical implementation of KPOs. Thus, KPOs and QbMs offer not only a new path toward the realization of quantum bits (qubits) and quantum computers, but also a new application of JPOs. Here we theoretically explain the physics of KPOs and QbMs, comparing them with their dissipative counterparts. Their physical implementations with superconducting circuits are also presented.

DOI
10.7566/jpsj.88.061015

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Quantum computers with Kerr-nonlinear parametric oscillators (KPOs) have recently been proposed by the author and others. Quantum computation using KPOs is based on quantum adiabatic bifurcations of the KPOs, which lead to quantum superpositions of coherent states, such as Schrodinger cat states. Therefore, these quantum computers are referred to as "quantum bifurcation machines (QbMs)." QbMs can be used for qauntum adiabatic optimization and universal quantum computation. Superconducting circuits with Josephson junctions, Josephson parametric oscillators (JPOs) in particular, are promising for physical implementation of KPOs. Thus, KPOs and QbMs offer not only a new path toward the realization of quantum bits (qubits) and quantum computers, but also a new application of JPOs. Here we theoretically explain the physics of KPOs and QbMs, comparing them with their dissipative counterparts. Their physical implementations with superconducting circuits are also presented.
Kerr parametric oscillators (KPOs) can stabilize the superpositions of coherent states, which can be utilized as qubits, and are promising candidates for realizing hardware-efficient quantum computers. Although elementary gates for universal quantum computation with KPO qubits have been proposed, these gates are usually based on adiabatic operations and thus need long gate times, which result in errors caused by photon loss in KPOs realized by, e.g., superconducting circuits. In this work we accelerate the elementary gates by experimentally feasible control methods, which are based on numerical optimization of pulse shapes for shortcuts to adiabaticity. By numerical simulations, we show that the proposed methods can achieve speedups compared to adiabatic ones by up to six times with high gate fidelities of 99.9%. These methods are thus expected to be useful for quantum computers with KPOs.
A Kerr-nonlinear parametric oscillator (KPO) can generate a quantum superposition of two oscillating states, known as a Schr\"odinger cat state, via quantum adiabatic evolution and can be used as a qubit for gate-based quantum computing and quantum annealing. In this work, we investigate complex dynamics, i.e., chaos, in two coupled nondissipative KPOs at a few-photon level. After showing that a classical model for this system is nonintegrable and consequently exhibits chaotic behavior, we provide quantum counterparts for the classical results, which are quantum versions of the Poincar\'e surface of section and its lower-dimensional version defined with time integrals of the Wigner and Husimi functions and also the initial and long-term behavior of out-of-time-ordered correlators. We conclude that some of them can be regarded as quantum signatures of chaos, together with energy-level spacing statistics (conventional signature). Thus, the system of coupled KPOs is expected to offer not only an alternative approach to quantum computing but also a promising platform for the study on quantum chaos.
Kerr parametric oscillators (KPOs), which can be implemented with superconducting parametrons possessing large Kerr nonlinearity, have been attracting much attention in terms of their applications to quantum annealing, universal quantum computation, and studies of quantum many-body systems. It is of practical importance for these studies to realize fast and accurate tunable coupling between KPOs in a simple manner. We develop a simple scheme of fast tunable coupling of KPOs with high tunability in speed and amplitude using the fast transitionless rotation of a KPO in the phase space based on the shortcuts to adiabaticity. Our scheme enables rapid switching of the effective coupling between KPOs, and can be implemented with always-on linear coupling between KPOs, by controlling the phase of the pump field and the resonance frequency of the KPO without controlling the amplitude of the pump field nor using additional drive fields and couplers. We apply the coupling scheme to a two-qubit gate, and show that our scheme realizes high gate fidelity compared with a purely adiabatic one, by mitigating undesired nonadiabatic transitions.
A Kerr nonlinear parametric oscillator (KPO) is one of the promising devices used to realize qubits for universal quantum computing. The KPO can stabilize two coherent states with opposite phases, yielding a quantum superposition called a Schr\"odinger cat state. Universal quantum computing with KPOs requires three kinds of quantum gates: Rz,Rx{R}_{z},{R}_{x}Rz​,Rx​, and Rzz{R}_{zz}Rzz​ gates. We theoretically propose a two-qubit gate Rzz{R}_{zz}Rzz​ for highly detuned KPOs. In the proposed scheme, we add a parametric drive for the first KPO. This leads to the Rzz{R}_{zz}Rzz​ gate based on the driving of the second KPO depending on the first-KPO state, which we call ``conditional driving.'' First, we perform simulations using a conventional KPO Hamiltonian derived from a superconducting-circuit model under some approximations and evaluate the gate fidelity. Next, we also perform numerical simulations of the two-qubit gate using the superconducting-circuit model without the approximations. The simulation results indicate that the conditional-driving gates can be implemented with high fidelity (>99.9>99.9%>99.9) for rotation angles required for universality.
A Josephson parametric oscillator (JPO) is an interesting system from the viewpoint of quantum optics because it has two stable self-oscillating states and can deterministically generate quantum cat states. A theoretical proposal has been made to operate a network of multiple JPOs as a quantum annealer, which can solve adiabatically combinatorial optimization problems at high speed. Proof-of-concept experiments have been actively conducted for application to quantum computations. This article provides a review of the mechanism of JPOs and their application as a quantum annealer.
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrodinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.