All-optical coherent Ising machine

Brief description of the context of the research including potential impact: An important class of computational problems is combinatorial optimisation: finding an optimal solution among a discrete set. Combinatorial optimisation problems are NP hard, meaning that they rapidly become intractable with the increasing problem sizes. Yet they have an enormous range of application, ranging from logistics and investment portfolio optimization to the modelling of protein molecule folding and quantum condensed matter physics.

In view of its complexity and practical significance, it is natural to attempt tackling combinatorial optimisation using quantum technology. A promising approach is represented by the coherent Ising machine (CIM). An optoelectronic version of CIM, capable of solving fully-connected quadratic unconstrained binary optimisation (QUBO) problems, has been demonstrated in 2016.

The primary element of the CIM architecture is an optical parametric oscillator (OPO) made up of a fibre loop and a degenerate parametric amplifier (single-mode squeezer). In the OPO, a sequence of pulsed modes is circulating. The QUBO nodes are encoded in the phases of these pulses, which, due to the phase-sensitive nature of the squeezer, are bistable while their amplitudes approach the OP saturation level.

In the original optoelectronic CIM, the pulsed modes are coupled in a measurement-feedback scheme, with each mode subjected to a measurement of the quadrature during each round-trip, and then displaced in the phase space by an amplitude corresponding to a linear combination of the measurement results on all other modes.. The original version of CIM contained up to 2000 modes, and this number has recently been in- creased to 100,000.

CIM was demonstrated to outperform not only classical simulated annealing algorithms, but also (arguably) the D-Wave annealer. This advantage arises thanks to fully-connected nature of CIM, in contrast to D-Wave in which each qubit is connected to only a few neighbors. However, a major disadvantage of this scheme is that it prevents any entanglement the modes units because their coupling is through a classical measurement and feedback.

This precludes any quantum speedup. Indeed, the most computationally expensive operation in the CIM - multiplication of the QUBO matrix by the quadrature vector - is performed via a classical digital device. These limitations were demonstrated, by our group and others, by developing classical simulation algorithms, executed on a classical computer with a GPU and capable of outperforming the physical CIM in terms of both the processing speed and optimisation quality.

Aims and objectives: The main objective of the project is to construct a coherent Ising machine (CIM) - a network of quantum optical parametric oscillators that are based on optical nonlinearity in atomic vapour and are coupled by means of a spatial light modulator. When launched, this system "anneals" itself to a phase state encoding the solution to a given quadratic unconstrained binary optimization problem.

Novelty of the research methodology. To eliminate the aforementioned shortcomings of optoelectronic CIMs, the CIM should be all-optical : the interaction between modes must occur not via a classical measurement and optoelectronic feedback, but via interference. Systems of interferometrically coupled OPOs have been proven theoretically to solve QUBO and related problems, but not yet implemented in practice.

While attempts at implementing all-optical version of the CIM have been reported, they either involved very few oscillators or had the coupling limited to nearest neighbours.

Alignment to EPSRC's strategies and research areas. This project falls within the EPSRC research area "Quantum optics and information".