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

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.

14 pages, 7 figures

References in corpus (22)

• Charge insensitive qubit design derived from the Cooper pair box
• Coupling Superconducting Qubits via a Cavity Bus
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Resolving photon number states in a superconducting circuit
• Reconstruction of non-classical cavity field states with snapshots of their decoherence
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
• Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System
• Generating Single Microwave Photons in a Circuit
• Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
• Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
• Josephson junction-embedded transmission-line resonators: from Kerr medium to in-line transmon
• Quantum annealing versus classical machine learning applied to a simplified computational biology problem
• Fault-tolerant detection of a quantum error
• Switching via quantum activation: A parametrically modulated oscillator
• On the construction of model Hamiltonians for adiabatic quantum computation and its application to finding low energy conformations of lattice protein models
• Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting qubits
• A Quantum Model for Coherent Ising Machines: Discrete-time Measurement Feedback Formulation
• Performance evaluation of coherent Ising machines against classical neural networks
• A Quantum Model for Coherent Ising Machine: Stochastic Differential Equations with Replicator Dynamics
• Universal controlled-phase gate with cat-state qubits in circuit QED
• Binary phase oscillation of two mutually coupled semiconductor lasers

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• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
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