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arXiv:2301.13666 · Physical Review A

Coherent-cluster-state generation in networks of degenerate optical parametric oscillators

Zhengyang Zhou, Clemens Gneiting, J. Q. You, Franco Nori

Published Aug 7, 2023• 7 citations

Abstract

Cluster states are versatile quantum resources and an essential building block for measurement-based quantum computing. The possibility to generate cluster states in specific systems may thus serve as an indicator regarding if and to what extent these systems can be harnessed for quantum technologies and quantum information processing in particular. Here, we apply this analysis to networks of degenerate optical parametric oscillators (DOPOs), also called coherent Ising machines (CIMs). CIMs are distinguished by their highly flexible coupling capabilities, which makes it possible to use them, e.g., to emulate large spin systems. As CIMs typically operate with coherent states (and superpositions thereof), it is natural to consider cluster states formed by superpositions of coherent states, i.e., coherent cluster states. As we show, such coherent cluster states can, under ideal conditions, be generated in DOPO networks with the help of beam splitters and classical pumps. Our subsequent numerical analysis provides the minimum requirements for the generation of coherent cluster states under realistic conditions. Moreover, we discuss how nonequilibrium pumps can improve the generation of coherent cluster states. In order to assess the quality of the cluster-state generation, we map the generated states to an effective spin space using modular variables, which allows us to apply entanglement criteria tailored for spin-based cluster states.

DOI: 10.1103/physreva.108.023704

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Recently, the coherent Ising machine (CIM) as a degenerate optical parametric oscillator (DOPO) network has been researched to solve Ising combinatorial optimization problems. We formulate a theoretical model for the CIM with discrete-time measurement feedback processes, and perform numerical simulations for the simplest network, composed of two degenerate optical parametric oscillator pulses with the antiferromagnetic mutual coupling. We evaluate the extent to which quantum coherence exists during the optimization process.

Abstract We present the quantum theory of coherent Ising machines based on networks of degenerate optical parametric oscillators (DOPOs). In a simple model consisting of two coupled DOPOs, both positive- P representation and truncated Wigner representation predict quantum correlation and inseparability between the two DOPOs in spite of the open-dissipative nature of the system. Here, we apply the truncated Wigner representation method to coherent Ising machines with thermal, vacuum, and squeezed reservoir fields. We find that the probability of finding the ground state of a one-dimensional Ising model increases substantially as a result of reducing excess thermal noise and squeezing the incident vacuum fluctuation on the out-coupling port.

We report a coherent Ising machine (CIM), which is a network of degenerate optical parametric oscillators for simulating the Ising model. Using a long-distance fiber cavity that includes a telecom-band phase sensitive amplifier, we generated large number of degenerate optical parametric oscillator (DOPO) pulses multiplexed in time domain, which represent the Ising spins. By using a measurement and feedback scheme, we could implement all-to-all coupling among 2048 DOPOs. We experimentally confirmed that the CIM could find solutions to maximum cut problems for graphs with as many as 2000 nodes.

In this work, we study the detection of quantum phase transitions (QPTs) in coherent Ising machines (CIMs) through a spectral mapping between the one-dimensional XY spin model and a network of degenerate optical parametric oscillators (DOPOs). This exact correspondence reveals that the DOPO spectrum faithfully encodes the critical behavior of anisotropic and isotropic XY chains, while a strongly anisotropic regime provides a controlled near-transverse-field-Ising realization, with the energy gap closing precisely at the critical point. The ground-state energy density and its derivatives are analyzed, and the resulting singularities in magnetic susceptibility accurately pinpoint the quantum critical points of the corresponding spin model. These results show that CIMs not only serve as powerful platforms for solving combinatorial optimization problems but also provide a versatile tool for probing universal quantum critical phenomena, bridging quantum-spin models and photonic quantum systems.

We introduce the recent progress of coherent Ising machine (CIM), which finds solutions to complex combinatorial optimization problems using a network of degenerate optical parametric oscillators (DOPO). We describe our effort to generate time-multiplexed DOPOs using long-distance fiber cavities including telecom-band phase sensitive amplifiers [1-4]. We then present our experiments where we found solutions to complex combinatorial optimization problems using a CIM with measurement-feedback scheme [5]. Finally, a future perspective of the CIM project will briefly described.