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arXiv:2212.12688 · Quantum

Entanglement-efficient bipartite-distributed quantum computing

Jun-Yi Wu, Kosuke Matsui, Tim Forrer, Akihito Soeda, Pablo Andrés-Martínez, Daniel Mills, Luciana Henaut, Mio Murao

Published Dec 5, 2023• 32 citations

Abstract

In noisy intermediate-scale quantum computing, the limited scalability of a single quantum processing unit (QPU) can be extended through distributed quantum computing (DQC), in which one can implement global operations over two QPUs by entanglement-assisted local operations and classical communication. To facilitate this type of DQC in experiments, we need an entanglement-efficient protocol. To this end, we extend the protocol in [Eisert et. al., PRA, 62:052317(2000)] implementing each nonlocal controlled-unitary gate locally with one maximally entangled pair to a packing protocol, which can pack multiple nonlocal controlled-unitary gates locally using one maximally entangled pair. In particular, two types of packing processes are introduced as the building blocks, namely the distributing processes and embedding processes. Each distributing process distributes corresponding gates locally with one entangled pair. The efficiency of entanglement is then enhanced by embedding processes, which merge two non-sequential distributing processes and hence save the entanglement cost. We show that the structure of distributability and embeddability of a quantum circuit can be fully represented by the corresponding packing graphs and conflict graphs. Based on these graphs, we derive heuristic algorithms for finding an entanglement-efficient packing of distributing processes for a given quantum circuit to be implemented by two parties. These algorithms can determine the required number of local auxiliary qubits in the DQC. We apply these algorithms for bipartite DQC of unitary coupled-cluster circuits and find a significant reduction of entanglement cost through embeddings. This method can determine a constructive upper bound on the entanglement cost for the DQC of quantum circuits.

DOI: 10.22331/q-2023-12-05-1196

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In noisy intermediate-scale quantum computing, the limited scalability of a single quantum processing unit (QPU) can be extended through distributed quantum computing (DQC), in which one can implement global operations over two QPUs by entanglement-assisted local operations and classical communication. To facilitate this type of DQC in experiments, we need an entanglement-efficient protocol. To this end, we extend the protocol in [Eisert et. al., PRA, 62:052317(2000)] implementing each nonlocal controlled-unitary gate locally with one maximally entangled pair to a packing protocol, which can pack multiple nonlocal controlled-unitary gates locally using one maximally entangled pair. In particular, two types of packing processes are introduced as the building blocks, namely the distributing processes and embedding processes. Each distributing process distributes corresponding gates locally with one entangled pair. The efficiency of entanglement is then enhanced by embedding processes, which merge two non-sequential distributing processes and hence save the entanglement cost. We show that the structure of distributability and embeddability of a quantum circuit can be fully represented by the corresponding packing graphs and conflict graphs. Based on these graphs, we derive heuristic algorithms for finding an entanglement-efficient packing of distributing processes for a given quantum circuit to be implemented by two parties. These algorithms can determine the required number of local auxiliary qubits in the DQC. We apply these algorithms for bipartite DQC of unitary coupled-cluster circuits and find a significant reduction of entanglement cost through embeddings. This method can determine a constructive upper bound on the entanglement cost for the DQC of quantum circuits.

Distributed quantum computation connects multiple quantum processing units (QPUs) through quantum communication to jointly perform large-scale quantum computations. Since the number of qubits available at each QPU is limited, it is important to reduce quantum communication while keeping the qubit overhead small. To this end, we study an entanglement-assisted model, in which entanglement consumption serves as a measure of quantum communication cost. For exact deterministic implementations in this model, the operator Schmidt rank of the target bipartite unitary provides a general lower bound on entanglement cost when qubit overhead is unrestricted. However, it has remained unclear how closely this bound can be approached with constant qubit overhead. In this work, we show that this lower bound is attainable for every bipartite Clifford unitary using at most two auxiliary qubits per QPU. In addition, for non-Clifford unitaries specified by exact Clifford+

T

decompositions with

T

-count

t

, we construct implementations with the same qubit overhead whose entanglement cost is at most

2t

Bell pairs above this lower bound.

Scaling quantum computers, i.e., quantum processing units (QPUs) to enable the execution of large quantum circuits is a major challenge, especially for applications that should provide a quantum advantage over classical algorithms. One approach to scale QPUs is to connect multiple machines through quantum and classical channels to form clusters or even quantum networks. Using this paradigm, several smaller QPUs can collectively execute circuits that each would not be able on its own. However, communication between QPUs is costly as it requires generating and maintaining entanglement, and hence it should be used wisely. In this paper, we evaluate the architectures, and in particular the entanglement patterns, of variational quantum circuits in a distributed quantum computing (DQC) setting. That is, using Qiskit, we simulate the execution of an eight qubit circuit using four QPUs each with two computational and two communication qubits where non-local CX-gates are performed using the remote-CX protocol. We compare the performance of various circuits on a binary classification task where training is executed under ideal and testing under noisy conditions. The study provides initial results on suitable VQC architectures for the DQC paradigm, and indicates that a standard VQC baseline is not always the best choice, and alternative architectures that use entanglement between QPUs sparingly deliver better results under noise.

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.

Quantum computing is a promising paradigm for problems that are challenging for classical machines, but realizing that promise requires far more qubits than a single processor can offer. Distributed quantum computing (DQC) scales out by connecting multiple quantum processing units (QPUs), at the cost of making entanglement the scarce resource: every remote gate consumes a Bell pair, and inter-QPU links generate Bell pairs at finite rates orders of magnitude slower than local gates. Since quantum programs are executed repeatedly, this rate bounds how fast shots complete and thus how fast results are obtained. Existing DQC compilers emit a single implementation per circuit, so throughput is capped by its busiest link while other links stay idle. We observe that alternative compilations of the same circuit are logically equivalent yet stress different links; executing them concurrently and pooling their samples converts idle Bell pairs into additional shots. We formulate the joint selection of compilations and allocation of shots under per-link Bell-pair capacities as Candidate-Constrained Max-Shot Allocation (CMA), prove it NP-hard, and solve it with a dynamic program and its approximate variant AppDP, a compact MILP, and a greedy heuristic Effi. In simulation on six-QPU networks, multi-compilation raises throughput by 2-4.5* over the single compilation and correspondingly improves output fidelity under equal Bell-pair budgets. On hardware, it increases measured fidelity by up to 93% and reaches the single-compilation fidelity in up to 10* less time. Scaling to 36 QPUs and 144-qubit circuits, MILP improves throughput over the single compilation by 76.8% on average across 48 configurations while Effi allocates in milliseconds.

Distributed quantum computing (DQC) is widely regarded as a promising approach to overcome quantum hardware limitations. A major challenge in DQC lies in reducing the communication cost introduced by remote CNOT gates, which are significantly slower and more resource-consuming than local operations. Existing DQC approaches treat the three essential components (qubit allocation, entanglement management, and network scheduling) as independent stages, optimizing each in isolation. However, we observe that these components are inherently interdependent, and therefore adopting a unified optimization strategy can be more efficient to achieve the global optimal solutions. Consequently, we propose UNIQ, a novel DQC optimization framework that integrates all three components into a non-linear integer programming (NIP) model. UNIQ aims to reduce the circuit runtime by maximizing parallel Einstein-Podolsky-Rosen (EPR) pair generation through the use of idle communication qubits, while simultaneously minimizing the communication cost of remote gates. To solve this NP-hard formulated problem, we adopt two key strategies: a greedy algorithm for efficiently mapping logical qubits to different QPUs, and a JIT (Just-In-Time) approach that builds EPR pairs in parallel within each time slot. Extensive simulation results demonstrate that our approach is widely applicable to diverse quantum circuits and QPU topologies, while substantially reducing communication cost and runtime over existing methods.