Objective 1:
Experimental implementation of a photonic XY annealer

The primary HEISINGBERG objective is the first experimental realisation of a novel optical spatial ΧΥ spin simulator utilising coherent free-space light illumination and intensity detection. The device will accommodate programmable spin couplings via various methods: (i) coherent optical vector-matrix multiplication schemes, and (ii) an alternative coupling scheme based on holography and ancillary spin variables. This allows us to select the more efficient coupling strategy when the annealer is driven with quantum light. Moreover, we will incorporate an effective magnetic field by additional light modulation, which will augment the computational capabilities of our platform, enabling us to solve a plethora of optimization problems with various heuristic strategies including annealing and adiabatic algorithms. The device aims to operate with up to 100,000 spin elements surpassing current state-of-the-art devices in terms of scale, versatility, and fidelity.

Achievement Indicators:

  • Demonstrate annealing of an XY Hamiltonian for fully programmable spin coupling aiming for 100,000 spins.
  • Implement an all-optical Vector Matrix multiplication scheme
  • Incorporation of an effective magnetic field, enabling the solution of a range of optimization problems

Objective 2:
Development of annealing algorithms, complexity class mapping and practical applications for HEISINGBERG

Objective 2 aims to develop custom-tailored algorithms to optimise the annealing process employed by the software part of the machine. Furthermore, we will develop HEISINGBERG solvers inspired by the principle of operation that are compatible with a hybrid quantum/classical implementation of the system. This will allow us to finetune the regime of operation of the machine and benchmark algorithmic performance using NP-hard real-life problems for which no efficient conventional algorithm exists. These developments will enhance the search for high-quality ground state solutions. The annealing time crucially depends on the number of elements (i.e., qubits), the type of interactions between them and how precisely the interactions can be controlled. These requirements depend on the optimal mapping of the original problem onto the HEISINGBERG architecture. We will thus develop such optimal representation for a range of problems: phase retrieval, quadratic binary combinatorial optimization that typically requires O(N2) dynamical equations for problem embedding, where N characterises the problem size, and higher order binary optimization, having in mind different operational modes of the HEISINGBERG machine and which Hamiltonian models it emulates (XY, Ising, and k-local spin Hamiltonians).

Achievement Indicators:

  • Deployment of annealing algorithms based on HEISINGBERG mode of operation.
  • Development of optimal phase-retrieval and quadratic binary representations and algorithms.
  • Development of higher order binary optimization algorithms.

Objective 3:
Theory and operation of the SPIM with non-classical light states.

Harnessing the quantum potential of the HEISINGBERG platform requires significant extensions of the theoretical model, as the algorithmic complexity increases, and an upgrade of the experimental setup. From the theory side, the existing model will be generalised to account for the quantum degrees of freedom of light. The developed theory will then be used to identify optimal quantum operation techniques for the system and to gauge its potential. Experimentally, expertise will be developed to produce the required quantum input, to process it through the iterative feedback loop, and to measure the output of the simulator operating in the quantum regime. We will focus on readily available sources of nonclassical squeezed light, which reduce fluctuations of certain observables. The first step will be to extend the classical XY simulator model beyond the mean-field approximation, which will provide a more accurate description of the experimental setups by considering quantum fluctuations. At the next stage we will study the effect of squeezing of the phase and amplitude of the light source on the simulator performance. Finally, we will

supplement intensity measurements with nonclassical observables such as many-photon correlations to exploit the system’s Hilbert space in the entanglement regime, available from the collapse of interfering squeezed light states by photon measurement.

Achievement Indicators:

  • Theoretical model describing the simulator beyond the mean-field approximation using squeezed light states
  • Determination of potential limitations and optimal parameters of the simulator operating with quantum light
  • Proof-of-principle experimental showcase of the Quantum HEISINGBERG annealer with a 3×3 lattice

Objective 4:
HEISINGBERG Machine graphical control interface and online server for open access

Efficient uptake of any new technology crucially depends on the operability as well as accessibility of the system by the broader scientific community that can effectively reveal novel use case applications as well as potential limitations. To this end, HEISINGBERG will create the necessary dedicated control software to handle the operation of the hardware components of the device, the implementation of the recurrent algorithms that will be developed for the different machine configurations and the live visual tracking of the monitoring and convergence variables of the system. As a first step towards making the system available to the wider scientific and technological community, the developed device control software will be ported to a server portal. To enable this development additional machine safety attestation and integrity checks will be implemented to safeguard the smooth operation of the underlying hardware. This service aims to be designed and developed in parallel with the hardware and algorithmic development, incorporating the mature scientific and technological advances implemented in the system. The portal will offer the opportunity of an actual and on demand experience of the operation of an optical annealing machine. This objective also aims to inform the next round of development and prototyping by enabling the assessment of crucial parameters such as the scientific and commercial interest for the device.

Achievements Indicators:

  • Development of a dedicated graphical control software for the Heisinberg platform
  • Deployment of the system control software through a dedicated online server