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arXiv:2606.04548

Distributed Variational Quantum Optimisation by Entanglement-Selective Transport

Edric Matwiejew, Pascal Elahi, Ugo Varetto

quant-phSubmitted Jun 3, 2026• Announced Jun 4, 2026• 0 citations
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Abstract

Distributed quantum optimisation is challenging because computing the problem cost function across multiple quantum processors requires non-local gates, which can incur overhead in latency and fidelity. Here we introduce QESTO, a distributed variational ansatz for graph-based discrete optimisation that requires only persistent pre-shared Bell pairs for remote operations. Using local operations, it encodes local constraint information in the Bell pairs that is leveraged to produce amplitude transfer towards globally valid distributed solution states. QESTO requires one Bell pair per distributed edge of the problem graph and, after initialisation of the Bell states, uses no non-local gates. On two bounded weighted Wang tile-matching problem ensembles, QESTO achieves stronger convergence to low-cost tilings than equivalently partitioned QAOA with no distributed gates at ansatz depths of two or higher, and exceeds the mean performance of monolithic QAOA at the deepest studied depth in both ensembles. These results suggest that persistent entanglement can support useful variational communication while reducing per-layer non-local gate overhead.

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Distributed quantum optimisation is challenging because computing the problem cost function across multiple quantum processors requires non-local gates, which can incur overhead in latency and fidelity. Here we introduce QESTO, a distributed variational ansatz for graph-based discrete optimisation that requires only persistent pre-shared Bell pairs for remote operations. Using local operations, it encodes local constraint information in the Bell pairs that is leveraged to produce amplitude transfer towards globally valid distributed solution states. QESTO requires one Bell pair per distributed edge of the problem graph and, after initialisation of the Bell states, uses no non-local gates. On two bounded weighted Wang tile-matching problem ensembles, QESTO achieves stronger convergence to low-cost tilings than equivalently partitioned QAOA with no distributed gates at ansatz depths of two or higher, and exceeds the mean performance of monolithic QAOA at the deepest studied depth in both ensembles. These results suggest that persistent entanglement can support useful variational communication while reducing per-layer non-local gate overhead.
Distributed quantum computing offers a scalable route to quantum information processing by entangling spatially separated processors. Although gate teleportation enables universal computation across distributed nodes, it requires repeated consumption of high-fidelity Bell pairs, ancillary qubits, and real-time feedforward, which imposes significant overhead and reduces fidelity. However, many variational quantum algorithms do not demand full universality; rather, they rely on sufficient expressibility to explore solution spaces effectively. Building on this, we propose a distributed variational quantum computing protocol based on deterministic entanglement tuning. In contrast to probabilistic filtering, our approach deterministically modulates pre-shared entanglement using only local operations and classical communication. We validate the protocol through a proof-of-principle experiment by estimating ground-state energies of the He-H+^++ molecule and the Schwinger model, showing that diverse entanglement levels can be engineered to match problem-specific requirements. Our results suggest a practical alternative for near-term distributed quantum applications.
Distributed quantum computing relies on coordinated operations between remote quantum processing units (QPUs), yet most existing work either assumes full connectivity, unrealistic for large networks, or relies on entanglement swapping. To mitigate the overhead of communication, we propose a scheme for the distribution of collective quantum operations among remote quantum processing units by exploiting distributed fan-out operations to a central node in network architectures similar to those used for high-performance computing, which requires only pre-shared entanglement, local operations and classical communication. We show that a general diagonal gate can be distributed among any number of nodes and provide the ebit cost bounds. For a single distributed multicontrolled gate, this amounts to a single additional Bell pair over the theoretically optimal calculation with all-to-all pre-shared entanglement, demonstrating better scalability when compared to current proposals based on entanglement swapping through a network. We provide a recipe for the lumped distribution of gates such as arbitrarily-sized Toffoli and multicontrolled Z, andRzz(θ)R_{zz}(\theta)Rzz​(θ)gates. Finally, we provide an exact implementation of a distributed Grover's search algorithm using this protocol to partition the circuit, with Bell pair cost growing linearly with the number of Grover iterations and the number of partitions, and show how these techniques can be applied to other algorithms such as QAOA. Our results show that alternative approaches to entanglement swapping can provide major benefits in distributed quantum computing, pointing to promising avenues for future research.
As distributed quantum architectures begin to emerge, understanding the interaction between quantum circuit optimisation and circuit partitioning becomes increasingly important. In this work, we study how circuit optimisation influences distributed quantum workloads under system-level trade-offs. We compare three compilation strategies (global optimisation, local optimisation, and a hybrid approach) across a large benchmark suite of quantum algorithms. Using telegate-based partitioning, we evaluate the resulting distributed circuits in terms of gate counts, circuit depth, the number of induced non-local gates, and compilation overhead, thereby approximating computational, communication, and classical preprocessing costs. Our results show that circuit optimisation does not uniformly benefit distributed execution. Global optimisation minimises computational resources and achieves the lowest compilation overhead. Local optimisation can reduce communication cost even though it is not explicitly communication-aware. The hybrid strategy can simultaneously reduce both computational and communication overhead, but at the expense of significantly increased compilation time.
We investigate the problem of compiling the generation of graph states to arbitrarily many distributed homogeneous quantum processing units (QPUs), providing a scalable partitioning algorithm and graph state generation protocol to minimize the number of Bell pairs required. Current approaches focus on the naive metric of cut edges to estimate the quantum communication cost. We show that the problem of balanced k graph partitioning, with the objective of minimizing the sizes of the maximum matchings between the partitions, leads to lower entanglement requirements across partitions. Our heuristic algorithm, BURY, partitions graph states to require fewer Bell pairs for generation than state-of-the-art k partition algorithms. Furthermore, we show that BURY reduces the cut-rank of the partitions, demonstrating that the partitioning found by our algorithm is likely to minimize the Bell pair utilization of any future improved distributed graph state generation protocol. We also discuss how our methods apply to the dynamic case where the graph state generation and measurement are performed concurrently. Our compilation approach provides a scalable foundation for reducing quantum network overhead for distributed measurement-based quantum computation (MBQC), as well as any scheme where distributed graph state generation is desired.
As distributed quantum architectures begin to emerge, understanding the interaction between quantum circuit optimisation and circuit partitioning becomes increasingly important. In this work, we study how circuit optimisation influences distributed quantum workloads under system-level trade-offs. We compare three compilation strategies (global optimisation, local optimisation, and a hybrid approach) across a large benchmark suite of quantum algorithms. Using telegate-based partitioning, we evaluate the resulting distributed circuits in terms of gate counts, circuit depth, the number of induced non-local gates, and compilation overhead, thereby approximating computational, communication, and classical preprocessing costs. Our results show that circuit optimisation does not uniformly benefit distributed execution. Global optimisation minimises computational resources and achieves the lowest compilation overhead. Local optimisation can reduce communication cost even though it is not explicitly communication-aware. The hybrid strategy can simultaneously reduce both computational and communication overhead, but at the expense of significantly increased compilation time.
Distributed quantum computing (DQC) is a new paradigm aimed at scaling up quantum computing via the interconnection of smaller quantum processing units (QPUs). Shared entanglement allows teleportation of both states and gates between QPUs. This leads to an attractive horizontal scaling of quantum processing power that comes at the expense of the additional time and noise introduced by entanglement sharing protocols. Consequently, protocols for partitioning quantum circuits should aim to minimise the amount of entanglement-based communication required between distributed QPUs. Existing protocols tend to focus primarily on optimising entanglement costs for gate teleportation or state teleportation to cover operations between QPUs, rather than both at the same time. The most general form of the problem should treat gate and state teleportation on the same footing, allowing minimal cost circuit partitions through a combination of the two. This work introduces a graph-based formulation that allows joint optimisation of gate and state teleportation cost. The formulation permits lowe-bit cost for a variety of circuit types. Using a genetic algorithm, improved performance over state-of-the-art methods is obtained in terms of both average e-bit cost and time scaling.