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.
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.
Abstract Josephson parametric oscillators (JPOs) have potential as fundamental building blocks for large-scale quantum annealing systems. To scale up such systems, both readout and control circuits need to be implemented at cryogenic temperatures. Adiabatic quantum flux parametron (AQFP) circuits are well suited for such environments due to their ultra-low power consumption. This paper proposes a phase-state readout scheme for JPOs based on AQFP circuits, which enables real-time digitization of oscillation phases. A JPO was fabricated, and the concept was experimentally validated at 4.2 K. After confirming stable oscillations in the JPO, a digital readout method using AQFP circuits was demonstrated. Analysis of the probability of obtaining a logical ‘1’ at the output revealed a clear phase-dependent behavior. Furthermore, our simulations predicted a readout fidelity of nearly 100% at millikelvin temperatures, demonstrating the feasibility of AQFP-based phase-state readout for future large-scale quantum annealing systems.
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.
Parametric oscillations are well studied phenomena, with applications in amplification, quantum optics, and quantum information processing. They can occur as a parameter of a system, such as the resonant frequency, is being modulated or “pumped” by an external field. A nonlinearity of the system can then transfer power from the pumping frequency to two frequencies called signal and idler. When the signal falls within a resonance, and when the pump amplitude exceeds an instability threshold, parametric oscillations occur. When signal and idler fall within the same resonance, the pumping is called degenerate.Due to somewhat different implementations, in combination with rich nonlinear physics, the details of the parametric oscillations can differ in different systems. In this work, we expand on the research done on parametric oscillations using a superconducting microwave resonator with a tunable boundary condition. Previously, a degenerate Josephson parametric oscillator (JPO) has been demonstrated by modulation of this boundary condition at twice the resonator's resonant frequency. We further use the JPO to implement a novel read-out method for a superconducting qubit. Moreover, we demonstrate a different, nondegenerate regime of the JPO, which we denote the NJPO, by modulating the frequency at the sum of two resonant frequencies of a multimode resonator.Both the JPO qubit read-out and the NJPO have applications within quantum information processing. The perhaps most promising platform for quantum information processing is represented by the circuit-QED architecture with superconducting resonators and artificial atoms, where the two lowest atomic levels represent the qubit. We make these circuits using lithographic techniques, and control and measure them at low temperature using microwaves. The qubit's state is fragile and difficult to read out with high fidelity. To this end, we have developed a method based on the JPO, in which the qubit state is mapped onto a zero-amplitude or a large-amplitude state of the JPO. We achieved a large contrast (185±15 photons), therefore eliminating the need for a following quantum-limited parametric amplifier. Our readout fidelity was 81.5 %, and by carefully modeling we can distinguish fidelity loss from the qubit and the readout, respectively. This analysis displays an actual readout fidelity of 98.7 %.An alternative model for quantum computing is based on continuous variables, and uses harmonic oscillators instead of qubits. Entangled states, which can be used as quantum resources, can then be created, for example, by two-mode squeezing of the oscillator ground state. The state of the NJPO produces correlated oscillations in its two modes, which might be useful for continuous-variable quantum computing. In this work we fully characterize the classical properties of the NJPO, and show good quantitative agreement with a theoretical model.
Ising machines (IMs) have emerged as a promising solution for rapidly solving NP-complete combinatorial optimization problems, surpassing the capabilities of traditional computing methods. By efficiently determining the ground state of the Hamiltonian during the annealing process, IMs can effectively complement CPUs in tackling optimization challenges. To realize these IMs, a bistable oscillator is essential to emulate the atomic spins and interactions of the Ising model. This study introduces a Josephson parametric oscillator (JPO) based tile structure, serving as a fundamental unit for scalable superconductor-based IMs. Leveraging the bistable nature of JPOs, which are superconductor-based oscillators, the proposed machine can operate at frequencies of $\ensuremath{\sim}7.5$ GHz while consuming significantly less power (by three orders of magnitude) than complementary metal-oxide semiconductor based systems. Furthermore, the compatibility of the proposed tile structure with the Lechner-Hauke-Zoller architecture ensures its viability for large-scale integration. We conducted simulations of the tile in a noisy environment to validate its functionality. We verified its operational characteristics by comparing the results with the analytical solution of its Hamiltonian model. This verification demonstrates the feasibility and effectiveness of the JPO-based tile in implementing IMs, opening new avenues for efficient and scalable combinatorial optimization in quantum computing.
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.
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 Schrödinger 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.