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Review of Distributed Quantum Computing. From single QPU to High Performance Quantum Computing

David Barral, F. Javier Cardama, Guillermo Díaz, Daniel Faílde, Iago F. Llovo, Mariamo Mussa Juane, Jorge Vázquez-Pérez, Juan Villasuso, César Piñeiro, Natalia Costas, Juan C. Pichel, Tomás F. Pena, Andrés Gómez

arXiv:2404.01265v1quant-phcs.ET

TL;DR

Distributed quantum computing is proposed as a way to increase the computational power of current quantum systems, but important physical and algorithmic constraints remain. This review surveys the field across its full stack, organizing its principles, achievements, challenges, and future directions through a four-layer model.

  • Problem

    Individual quantum systems have shown impressive capabilities, motivating distributed quantum computing as an approach that could vastly increase computational power.

  • Method

    The review analyzes distributed quantum computing across communications, distributed applications, physical devices, and interconnection networks using a four-layered physical, network, development, and application model.

  • Results

    The survey presents the current state of the art in distributed quantum computing, covering its foundational principles, achievements, challenges, and promising directions for further research.

  • Takeaways & Limitations

    Distributed quantum computing emerges as a clear pathway to enhance the computational capabilities of current quantum systems.

  • Takeaways & Limitations

    Circuit cutting has a strictly exponential sampling overhead that cannot be reduced to a polynomial increase in circuit executions.

Abstract

from arXiv · show

The emerging field of quantum computing has shown it might change how we process information by using the unique principles of quantum mechanics. As researchers continue to push the boundaries of quantum technologies to unprecedented levels, distributed quantum computing raises as an obvious path to explore with the aim of boosting the computational power of current quantum systems. This paper presents a comprehensive survey of the current state of the art in the distributed quantum computing field, exploring its foundational principles, landscape of achievements, challenges, and promising directions for further research. From quantum communication protocols to entanglement-based distributed algorithms, each aspect contributes to the mosaic of distributed quantum computing, making it an attractive approach to address the limitations of classical computing. Our objective is to provide an exhaustive overview for experienced researchers and field newcomers.

1. Introduction

Distributed quantum computing is presented as a way to overcome the physical and practical limits of scaling a standalone QPU by connecting modular processors. The review uses a layered, full-stack structure to survey devices, networks, development tools, applications, achievements, challenges, and future directions.

  • Standalone QPUs face decoherence, dissipation, crosstalk, topology, cabling, connectors, and control-electronics constraints that hinder ultra-large devices.
  • DQC instead connects clusters of small quantum chips through classical and/or quantum communications within quantum-centric HPC infrastructures.
  • DQC research spans early theoretical studies, experimental proposals, distributed Grover and Shor algorithms, and taxonomies distinguishing entangled from classically connected nodes.
  • The review updates earlier work by covering the DQC full stack, from communications and physical devices through networks, distributed tools, algorithms, and applications.
  • Its layered model organizes the discussion into physical, network, development, and application layers, paralleling a full-stack architecture.

2. Physical layer for distributed quantum computing

The physical layer supplies the quantum resources and communication mechanisms needed to perform computation between distant QPUs. Entanglement and teleportation protocols support state transfer, remote correlations, and operations across distributed nodes.

  • DQC networks coordinate information across devices, but the no-cloning theorem prevents arbitrary quantum states from being perfectly copied and broadly distributed.
  • Entanglement is the fragile physical resource enabling non-local computation and the distribution of quantum states between distant nodes.
  • Quantum teleportation supports one-way state transfer, entanglement swapping supports bidirectional communication, and gate teleportation enables operations at a distance.
  • These two-node protocols can extend to multiparticipant networks, including assisted teleportation and imperfect quantum telecloning.

2.1. Quantum entanglement

Quantum entanglement describes nonclassical correlations that prevent a composite system from being reduced to independent descriptions of its parts. Bell states provide a central two-qubit example and underpin quantum communication protocols.

  • The EPR thought experiment helped motivate the concept of quantum entanglement and its study as a primary form of quantum correlation.
  • Entanglement prevents a composite quantum system from being described solely through its individual components because of nonclassical subsystem correlations.
  • Bell states are two-qubit entangled states shared by Alice and Bob, with measurement outcomes exhibiting perfect non-local correlations.
  • Bell-state correlations allow a symmetric gate applied to one qubit to have the same effect as applying it to the other qubit.
  • Entangled states form the basis of quantum teleportation and many other quantum-information protocols.

2.2. Quantum teleportation or teledata

Quantum teleportation reconstructs an unknown quantum state at a distant location without transmitting the physical system itself. The review describes its entanglement and classical-communication requirements, protocol mechanics, performance measures, and demonstrations across increasingly practical settings.

  • Quantum teleportation reconstructs an unknown state at another location without physically transmitting the system, using entanglement and classical communication.
  • Teleportation networks, entanglement swapping, and quantum repeaters distribute entanglement over long distances, while gate teleportation supports remote operations.
  • Demonstrations have progressed from diverse laboratory substrates to metropolitan two-node links, hybrid memory platforms, and multinode entanglement networks.
  • In teledata, Alice and Bob share a Bell state, Charlie supplies an unknown qubit, and Alice performs a Bell-state measurement before classical correction at Bob.
  • Teleportation milestones are evaluated using Bell-state-measurement efficiency, fidelity, distance, and quantum memory.
  • For discrete-variable photonic qubits, Bell-state measurement efficiency reaches 50% at maximum, while teleportation fidelity is benchmarked against Fclass = 2/3.

2.3. Variants of quantum teleportation

Quantum teleportation provides several primitives for distributed quantum computing, including entanglement swapping, telegate, and multipartite teleportation. These variants distribute entanglement, quantum states, or gate operations across separated parties and nodes.

  • Entanglement swapping: Entanglement swapping transfers quantum entanglement between distant users who do not directly share a quantum resource.A relay performs Bell measurements, broadcasts the outcomes classically, and enables the end users to share an entangled state conditioned on those outcomes.
  • Entanglement swapping: Entanglement swapping has connected spatially separated solid-state memories and entangled non-neighboring NV qubits in multinode networks.These demonstrations followed the original polarization-entangled-photon experiment.
  • Circuit variants: Figure 3 contrasts teledata, which teleports a remote state to another QPU, with telegate, which uses cat-entangler and cat-disentangler primitives for remote control.Both circuits support CZ gates across qubits located in different QPUs.
  • Quantum gate teleportation: Quantum gate teleportation, or telegate, replaces non-local two-qubit gates with entangled states, local measurements, single-qubit operations, and classical corrections.The procedure implements a controlled gate on unknown states held by noninteracting parties.
  • Measurement-based quantum computing: Measurement-based quantum computing uses multipartite entanglement and measurements to teleport unitary-transformed states across network nodes.The network topology and measurement choice determine how the transformed state is distributed.
  • Multipartite teleportation: Multipartite teleportation extends teleportation beyond two parties using GHZ states, with assisted and unassisted variants including quantum telecloning.Examples include open-destination teleportation, shared-quantum-secret teleportation, partial teleportation, entanglement cloning, and copy distribution.

2.4. Quantum devices for entanglement distribution

Distributed quantum computing combines heterogeneous QPUs with transducers, memories, repeaters, and networking hardware to distribute entanglement across platforms and distances. The main engineering challenges are interoperability, photon coupling, transmission loss, memory scalability, and the need for hierarchical networking as systems grow.

  • Quantum platforms and modular devices: Quantum platforms offer different strengths, so modular architectures use specialized hardware to support scalable distributed quantum computing.Superconducting systems provide short gates, while NV centers, atomic qubits, and photonic systems offer coherence or mobility advantages.
  • Quantum transducers: Quantum transduction converts local qubit states into flying qubits that can be delivered between QPUs, memories, or repeaters.Photons are a natural long-distance carrier, while pitch-and-catch protocols couple flying qubits to local quantum systems.
  • Entanglement generation: Entanglement swapping generates deterministic remote entanglement by entangling flying and local qubits, then performing Bell-state measurements on the photons.Photon sources, quantum dots, trapped ions, neutral atoms, and NV centers support different implementations of this process.
  • Entanglement generation: Up to 88% Bell-state fidelity at 230 m has been demonstrated in trapped-ion systems, alongside deterministic state transfer between NV-center nodes.These results illustrate experimentally demonstrated long-distance entanglement and inter-node transfer capabilities.
  • Interoperability: Frequency conversion can transcode photons between incompatible platforms, but current quantum efficiency remains low and efforts target unity efficiency.Demonstrated directions include infrared-to-visible, visible-to-infrared, and microwave-to-infrared transduction.
  • Quantum memories: Photonic memories store and retrieve photons, whereas alternative memories address high-fidelity retrieval and scalability limitations in photonic implementations.Trapped-ion, neutral-atom, and NV-center memories have demonstrated long coherence times and error-correction-relevant gates.
  • Quantum repeaters: Fiber attenuation of approximately 0.14–0.4 dB/km and the inability of EDFAs to amplify arbitrary quantum states make quantum repeaters essential for long-distance entanglement distribution.Repeaters address transmission loss without violating the no-cloning theorem.
  • Entanglement routers and switches: Hierarchical networks become necessary at tens or hundreds of QPUs, improving scalability and interoperability while offloading entanglement distribution to dedicated hardware.Entanglement switches and routers operate as single-purpose QPUs that establish entanglement among compute nodes.

3. Networks for distributed quantum computing

Distributed quantum computing depends on quantum and classical networks that connect QPUs and distribute entanglement, but these networks face distinctive reliability, synchronization, and architectural challenges. The reviewed architectures span layered designs for bipartite or multipartite entanglement, resource reservation, and classical coordination.

  • Challenges: Practical constraints include decoherence-limited qubit and memory lifetimes, probabilistic entanglement generation and swapping, fidelity improvement, and the need for both quantum and classical channels.Additional design choices concern sequential versus parallel link operations and bipartite versus multipartite resources.
  • Network role: Quantum networks distribute entanglement between nearby or geographically separated QPUs for distributed computing and other quantum applications.The same entanglement resources can support sensing and encryption in addition to DQC.
  • Network architectures: Entanglement distribution requires specialized mechanisms because classical network architectures and protocols cannot be directly extrapolated to quantum networks.The literature addresses architectures, protocols, and protocol stacks for local and wide-area entanglement distribution.
  • Network architectures: Quantum-network architectures differ in their layering and entanglement model, including recursive bipartite designs and stacks supporting multipartite GHZ graph states.Examples assign distinct responsibilities to physical, link, connectivity, network, transport, and higher layers.
  • Resource management: Network design must address entanglement-resource reservation, including path selection and resource allocation across all links between communicating endpoints.Reservation can follow connection-oriented or connection-less strategies analogous to classical networking.
  • Challenges: The field still has few proposals covering network architecture, technology implementation, offered services, and fault-tolerant error-correction mechanisms.Existing approaches vary across optical and hybrid technologies, discrete- and continuous-variable systems, and entanglement resources.
  • Classical communications: A proposed short-distance DQC architecture gives each QPU qubit, FPGA, and CPU layers, with a synchronized classical management network connecting nodes to a centralized controller.The design supports scheduled circuit-layer execution and can use LAN technologies with TCP/IP or industrial messaging protocols.

4. Development layer

Quantum compilation retains the classical analysis-and-synthesis structure because compilation is primarily classical, but distributed execution adds steps and restrictions. The resulting development process uses intermediate representations and must account for distribution-specific compiler concerns.

  • Classical compilation: The classical compiler process has analysis and synthesis phases, with analysis checking code and producing an intermediate representation for later optimization.Analysis includes lexical, syntactic, and semantic checks before translation into the IR.
  • Quantum compilation: Quantum compilation generally follows the classical scheme because compilation is a classical task, while quantum workloads are executed after compilation.Many quantum development tools therefore build on classical programming languages and reuse existing analysis implementations.
  • Distributed compilation: Adding distribution leaves the compilation scheme largely unchanged but introduces additional steps and restrictions.The distributed compilation discussion separates circuit-distribution methods from compilation under distribution constraints.

4.1. Types of distribution

Distributed quantum computing uses circuit distribution, circuit cutting, and embarrassingly parallel execution to overcome single-QPU limits, with model choice governed by communication resources and task requirements. These approaches share execution, measurement, and post-processing stages but differ in partitioning, communication, and reconstruction costs.

  • Overview: Three distribution categories are identified: circuit distribution, circuit cutting, and embarrassingly parallel execution.Their applicable use depends on network communication mechanisms and quantum-task resources.
  • Circuit distribution: Circuit distribution uses a quantum communication network to execute one circuit requiring more qubits than a single QPU provides.Its stages include finding a partition and distributing EPR pairs.
  • Circuit cutting: Circuit cutting partitions oversized circuits without quantum communication, using quasi-probabilistic decomposition and classical post-processing to reconstruct outcomes.The number of subcircuits grows exponentially with the quantum communication being simulated.
  • Embarrassingly parallel: When quantum communication is unavailable and a circuit fits on one QPU, embarrassingly parallel execution distributes workloads or offloads quantum tasks before mapping circuits to QPUs.Quantum compilers typically select one distribution option, although hybrid combinations have been proposed.
  • Circuit cutting: Circuit-cutting overhead is strictly exponential and cannot be reduced to a polynomial increase in circuit executions.Minimizing this overhead remains an active research topic.
  • Embarrassingly parallel: Embarrassingly parallel methods distribute Pauli-string measurements or optimizer individuals across QPUs, while commuting-group formation reduces repeated circuit executions.General commutativity can reduce groups more efficiently but requires finding suitable joint-measurement unitaries.

4.2. Compilation

The review frames distributed quantum compilation using a structure analogous to classical compilation. It separates analysis, Quantum Intermediate Representation, and synthesis while emphasizing differences between classical and quantum compilation.

  • Compilation: Distributed quantum compilation is organized into analysis, Quantum Intermediate Representation, and synthesis phases.This structure is used to examine compilation and distinguish distributed quantum computing from classical computing.

4.2.1. Analysis phase

The analysis phase of distributed quantum compilation resembles monolithic compilation but is constrained by limited distributed-specific languages, software, and formal tooling. QMPI extends MPI conceptually with classical and quantum nodes plus EPR-pair support, while a dedicated distributed quantum language remains needed.

  • Distributed quantum compilation follows a similar analysis phase to monolithic compilation but has less literature and software support.
  • Qiskit, Cirq, and Qulacs are widely adopted because they use familiar classical languages, whereas standalone distributed quantum languages remain scarce.
  • QMPI extends MPI for distributed quantum systems by distinguishing classical nodes from quantum nodes that can handle both quantum and classical calls.
  • QMPI includes EPR pairs as a resource for quantum communication protocols.
  • A proper distributed quantum programming language is needed to exploit distributed structures through advanced computational techniques.

4.2.2. Distributed quantum Intermediate Representation

Distributed quantum intermediate representations extend compiler abstractions to express quantum instructions, classical and quantum communication, and entanglement across processing units. InQuIR translates remote-gate programs into node-specific code and automatically inserts the directives required for telegate execution.

  • Intermediate representations decouple compiler front ends from back ends and support abstract optimizations for target machines.
  • Quantum IRs must represent operations from different high-level languages and support compilation into different machine codes.
  • Distributed quantum IRs add classical and quantum communication instructions between processing units; InQuIR is designed for this purpose.
  • InQuIR compiles an OpenQASM remote CNOT between nodes connected by a Bell pair into node-specific code with automatically added telegate directives.
  • InQuIR code initializes communication channels, local qubits, and an EPR pair before applying gates and measurements across nodes.

4.2.3. Synthesis phase

The synthesis phase covers optimization, verification, and qubit mapping, with distributed compilation adding partitioning, communication, and network constraints. Verification is especially important because quantum measurement destructively collapses states, while mapping remains computationally difficult.

  • Synthesis comprises optimization, verification, and qubit mapping, with optimization targeting circuit complexity and error susceptibility.
  • Distributed optimization adds circuit distribution or cutting to monolithic objectives, except when embarrassingly parallel execution preserves the monolithic problem.
  • Circuit-cutting optimization primarily reduces sampling overhead, while fewer subcircuits can also simplify scheduling and post-processing.
  • Quantum-program verification is necessary because measurement irreversibly collapses states and prevents observing successive states without alteration.
  • Qubit mapping: Qubit mapping assigns logical qubits to physical qubits under connectivity and error constraints, and the problem is NP-hard.
  • Qubit mapping: Gate decomposition converts circuit gates into native processor gates, while allocation and routing assign qubits and find efficient communication paths.
  • Qubit mapping: Ring and one-way architectures can require equivalent circuit transformations when logical gates do not match available physical connections.
  • Qubit mapping: QA-DQC addresses distributed qubit allocation with a heuristic local search algorithm and a multistage hybrid simulated annealing algorithm.

4.2.4. Available compilers

Distributed quantum compiler development remains immature: available systems are mainly conceptual designs and prototypes rather than usable full-stack tools. Existing approaches target circuit distribution, circuit cutting, embarrassingly parallel workloads, scheduling, routing, or hybrid combinations of these strategies.

  • No usable full-stack distributed quantum compiler is identified; existing tools are conceptual designs and prototypes classified by distribution strategy.
  • Compiler designs for circuit distribution include partitioning and depth-minimization strategies based on data-qubit swapping or entanglement swapping.
  • An integer-linear-programming approach models compilation as a generalized quickest multi-commodity flow problem and incorporates quasi-parallelism.
  • Qurzon combines CutQC circuit partitioning with scheduling and optimal qubit routing for circuit-cutting execution.
  • Embarrassingly parallel workloads can distribute shots across QPUs, allowing existing quantum compilers or frameworks to be adapted without a dedicated compiler.
  • Palloq extends mapping mechanisms with layout synthesis for multiple circuits and job scheduling in a multiprogramming setting.
  • QDCA combines graph-based input partitioning, variational circuits, distributed execution, and quantum circuit cutting for hybrid computation.

5. Application layer

The application layer distributes quantum algorithms through circuit distribution, circuit cutting, and embarrassingly parallel execution. Reviewed examples reduce QPU size, divide workloads, or shorten circuit depth, while exposing communication, sequentiality, and noise-related constraints.

  • Application modes: DQC applications use circuit distribution, circuit cutting, and embarrassingly parallel execution as three communication-based distribution categories.Circuit-cutting approaches use classical communication to combine results, while embarrassingly parallel applications execute smaller circuits independently before classical combination.
  • Circuit-distribution based applications: Shor’s algorithm can parallelize the QFT and modular exponentiation, reducing each QPU’s size despite O((log2N)2) communication complexity and increased total qubits.The distributed proposal replaces controlled operations with remote-controlled operations and divides modular exponentiation across QPUs.
  • Circuit-distribution based applications: 2048-bit factoring is estimated at 8 hours with 20 million noisy qubits, while distributing across 2 or 8 QPUs reduces each-QPU requirements to 11 million or 4 million qubits.The estimate assumes nanosecond-scale operations and requires a quantum network bandwidth of 150 qb/s.
  • Circuit-distribution based applications: Teledata outperforms telegate for the studied arithmetic operations, and a linear architecture is identified as the best topology.The comparison covers different distributed topologies and teledata/telegate methods.
  • Circuit-distribution based applications: Distributed Deutsch-Jozsa algorithms remain sequential, while QMPI demonstrations of phase estimation and Trotter evolution omit real quantum communications.These results leave global depth and time reduction unresolved and limit the demonstration’s physical scope.
  • Circuit knitting: Distributed Bernstein-Vazirani, Grover, Deutsch-Jozsa, and Simon algorithms retain advantages over classical solutions, but Grover’s construction assumes one solution and the advantage falls against fault-tolerant versions.The shallow circuits may make these approaches relevant to current NISQ devices.
  • Circuit knitting: Circuit cutting divides larger problems into smaller circuits, including VQE, combinatorial optimization, and QML workloads, then combines their results classically.Automatic cutting can skip subcircuits with negligible contributions and achieve classification results close to classical neural networks.
  • Embarrassingly parallel applications: Embarrassingly parallel applications execute smaller circuits in parallel without reducing required qubits, but reduce depth, execution time, and rotation-angle-related errors.Partial diffusion operators for Grover’s search illustrate this trade-off.

6. Conclusions

The review presents distributed quantum computing as a four-layer route toward greater computational capability, but practical deployment still depends on quantum networking, auxiliary protocols, and managing circuit-cutting costs and heterogeneous noise.

  • Conclusions: The review organizes DQC into physical, network, development, and application layers to survey its principles, achievements, challenges, and research directions.This four-layer model spans the underlying devices and networks through tools and applications.
  • Physical layer: Quantum teleportation transmits quantum states across physical separation and supports interconnected processors through telegate and teledata protocols.The review identifies teleportation as the basic physical-layer mechanism for distributed algorithms.
  • Physical layer: Initial results show teledata can outperform telegate, but the advantage depends on the problem and teleoperation techniques and requires further confirmation.Single-qubit transport could also simplify the network architecture compared with protocols using an EPR pair.
  • Network layer: Datacenter-scale QPUs require networks that distribute entanglement between nodes using devices such as repeaters, switches, routers, and transducers.These components support pre-establishing entangled qubits for communication.
  • Network layer: Current networking solutions are costly and lack the performance, fidelity, and robustness required for practical deployment.Networking protocols, connectivity, scalability, and robustness remain early-stage concerns.
  • Development layer: Circuit cutting can address large problems with small noisy QPUs without a fully realized quantum network, but its cost scales exponentially with cut entanglement.Usefulness is most promising for clustered circuits with limited connectivity and requires handling different QPU noise profiles and execution times.
  • Development layer: General-purpose agnostic compilers for partitioning can scale poorly, favoring problems or ansatzes designed to be easy to cut.The review connects this limitation to classical auto-parallelism and modular-architecture-aware problem design.
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