A Binary Optimisation Algorithm for Near-Term Photonic Quantum Processors

TL;DR

The paper addresses discrete binary optimisation on near-term photonic quantum processors by introducing the Bosonic Binary Solver (BBS), a variational hybrid quantum-classical algorithm that uses a photonic circuit to generate samples and train per-mode bit-flip probabilities via gradient-based updates. It achieves full solution-space coverage with a single circuit configuration through trainable classical post-processing, and scales to larger problems using a tiling strategy. Evaluations on Knapsack, Tactical Deconfliction, and TSP show that BBS yields high-quality solutions in simulation and on hardware, with competitive performance relative to classical heuristics and clear potential for scalability on photonic platforms. The work demonstrates a practical path to leveraging photonic hardware for large-scale real-world optimisation, while outlining avenues for theoretical and algorithmic enhancements to further improve performance.

Abstract

Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem sizes. Here, we propose a new algorithm for binary optimisation, the Bosonic Binary Solver, designed for near-term photonic quantum processors. This variational algorithm uses samples from a quantum optical circuit, which are post-processed using trainable classical bit-flip probabilities, to propose candidate solutions. A gradient-based training loop finds progressively better solutions until convergence. We perform ablation tests that validate the structure of the algorithm. We then evaluate its performance on an illustrative range of binary optimisation problems, using both simulators and real hardware, and perform comparisons to classical algorithms. We find that this algorithm produces high-quality solutions to these problems. As such, this algorithm is a promising method for leveraging the scalable nature of photonic quantum processors to solve large-scale real-world optimisation problems.

Figures (5)

• Figure 1: a) In this work, our experiments focus on quantum photonic processors that use a time-bin architecture. In such an architecture, single photons are sequentially sent into a network of optical delay lines with programmable coupling coefficients. This creates an entangled state between different time-bins which can be measured by a photon number resolving detector. b) Photonic circuit implemented by the time-bin architecture shown above, where the length of the first delay line is such that sequential photons interfere with each other, and the second delay line is twice as long. Each operation is a beamsplitter between two modes with a programmable coupling parameter. This example interferes 3 photons in 5 modes.
• Figure 2: Schematic diagram of the BBS algorithm architecture. A single run of the quantum optical circuit with click detectors produces a binary measurement pattern. In a classical post-processing step, trainable probabilistic bit-flips are applied, returning a new bit string. A collection of bit strings produced using this process is used to estimate the average cost of generated solutions, and the parameters of the quantum circuit and the bit-flips are updated accordingly. This process continues with the circuit iteratively improving the average quality of solutions generated.
• Figure 3: Schematic diagram of a tiled BBS algorithm architecture. To allow a smaller-sized photonic quantum processor to solve a larger problem, we use the quantum processor to implement multiple 'tiles', each of which represents a disjoint set of trainable variables.
• Figure 4: We plot the evolution of loss and an arbitrary selection of bit-flip probabilities and beamsplitter angles during a typical run of the BBS algorithm. The algorithm is run on a size 30 tactical deconfliction cost function, with the same hyperparameters as previously defined.
• Figure 5: Violin plots for dimension 30 ablation tests across different optimisation problem types. Each parameter training subroutine of the BBS algorithm improves performance. The magnitude of this improvement is problem dependent.