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Distributed Quantum Computing: a Survey

Marcello Caleffi, Michele Amoretti, Davide Ferrari, Daniele Cuomo, Jessica Illiano, Antonio Manzalini, Angela Sara Cacciapuoti

arXiv:2212.10609v1quant-phcs.NI

TL;DR

Current quantum processors do not yet provide the qubit resources needed by many practical algorithms, motivating distributed quantum computing across multiple processors. This survey synthesizes the field from a computer and communications engineering perspective, covering algorithms, networking, compiling, simulation, and future directions. It highlights networking mechanisms and open problems while identifying missing general frameworks for algorithm distributability and resource-aware execution.

  • Problem

    Many practical quantum algorithms require more qubits than current NISQ processors provide, while a general framework for ranking algorithm distributability remains missing.

  • Method

    The survey organizes distributed quantum computing across algorithms, networking, compiling, and simulation, including relevant execution, simulation, industrial, and development perspectives.

  • Results

    The survey reviews distributed-execution approaches, quantum-networking mechanisms, compilation methods, simulation tools, and prominent challenges and open problems.

  • Takeaways & Limitations

    Distributed quantum computing uses cooperating limited-qubit processors, with teleportation enabling quantum-information exchange for remote quantum operations.

  • Takeaways & Limitations

    A general theory of distributable quantum algorithms and a quantitative definition of quantum-circuit distributability are still missing.

Abstract

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Nowadays, quantum computing has reached the engineering phase, with fully-functional quantum processors integrating hundred of noisy qubits available. Yet -- to fully unveil the potential of quantum computing out of the labs and into business reality -- the challenge ahead is to substantially scale the qubit number, reaching orders of magnitude exceeding the thousands (if not millions) of noise-free qubits. To this aim, there exists a broad consensus among both academic and industry communities about considering the distributed computing paradigm as the key solution for achieving such a scaling, by envision multiple moderate-to-small-scale quantum processors communicating and cooperating to execute computational tasks exceeding the computational resources available within a single processing device. The aim of this survey is to provide the reader with an overview about the main challenges and open problems arising with distributed quantum computing, and with an easy access and guide towards the relevant literature and the prominent results from a computer/communications engineering perspective.

1 INTRODUCTION

Distributed quantum computing connects limited quantum processors to execute tasks beyond one device's resources, while quantum networking provides the broader infrastructure for this paradigm. This survey bridges fragmented literature by organizing distributed quantum computing across algorithms, networking, compiling, and simulation, and by reviewing its challenges and development perspectives.

  • Quantum Internet context: The Quantum Internet is envisioned to connect quantum processors and devices, enabling communication and computing capabilities impossible with classical communication alone.
  • Motivation: A linear increase in interconnected quantum processors can unlock an exponential increase in quantum computational power.Distributed processors cooperate on tasks exceeding the resources available within a single limited-qubit device.
  • Survey rationale: The survey addresses a fundamental gap caused by distributed quantum-computing literature being spread across physics, communications and computer engineering, and computer science.
  • Survey objectives: The survey compares distributed classical and quantum computing and examines the challenges arising from the shift from monolithic to distributed quantum computing.
  • Intended contribution: The survey aims to provide accessible guidance to relevant literature and prominent results for computer science and communications/computer engineering communities.
  • Survey organization: The survey organizes its treatment around algorithms, networking, compiling, and simulation, then adds an industrial perspective and possible development stages.

2 DQC: DISTRIBUTED QUANTUM COMPUTING

Distributed quantum computing addresses single-chip qubit limitations by clustering modular quantum processors and coordinating them through quantum networks. The survey organizes its analysis around algorithms, networking, compiling, and simulation, with compiling incorporating network constraints into circuit partitioning.

  • Current quantum technologies face hard limits on the number of qubits that can be embedded in a single chip.
  • Distributed quantum computing clusters modular quantum chips so computations can be split across interconnected processors.IBM’s planned Kookaburra illustrates this modular direction with interconnected multi-chip systems.
  • The survey examines DQC through four perspectives: algorithms, networking, compiling, and simulation.These perspectives cover algorithm partitioning and execution management, processor internetworking, compilation, and simulation.
  • Algorithms: DQC algorithms require partitioning and execution management challenges that differ from monolithic quantum computing.
  • Compiling: DQC compiling must account for network constraints when splitting a quantum circuit into portions executed concurrently on individual QPUs.

3 QUANTUM PRELIMINARIES

This section introduces qubits, their state representations, quantum gates, circuits, entanglement, and measurement. It establishes the circuit model as a reversible framework whose measurements extract classical information while altering quantum states.

  • 3.1 Qubits in a Nutshell: A qubit is a vector in a two-dimensional complex Hilbert space and can be expressed as a normalized superposition of basis states |0⟩ and |1⟩.The amplitudes are complex and satisfy |α|^2 + |β|^2 = 1.
  • 3.1 Qubits in a Nutshell: The Bloch sphere represents pure single-qubit states as points on a sphere surface parameterized by spherical coordinates θ and ϕ.The relative phase ϕ is crucial for interference patterns used by quantum algorithms.
  • 3.1 Qubits in a Nutshell: An n-qubit system has a 2^n-dimensional Hilbert space and may occupy a superposition of all 2^n basis states; entangled states cannot generally be factored into single-qubit states.Entanglement is identified as a key ingredient in quantum computing, with Bell states providing a two-qubit example.
  • 3.2 Quantum Circuits: Quantum circuits sequentially connect gates to model quantum-information processing, while unitary gates make quantum computation reversible.Different gate arrangements or orderings can represent the same computation.
  • 3.2 Quantum Circuits: Single-qubit unitaries can be expressed using rotations and a global phase, while controlled-U gates apply an operation to a target conditioned on a control qubit.Two arbitrary rotation operators suffice to obtain the third rotation type, and CNOT is a controlled Pauli-X gate.
  • 3.2 Quantum Circuits: Starting from |00⟩, applying a Hadamard gate to the first qubit followed by CNOT produces the Bell state, whereas measurement outputs a classical bit and collapses the measured qubit.Measurement irreversibly alters the original quantum state.

Gate Synthesis and Circuit Compilation

Quantum compilation adapts abstract circuits to hardware by mapping logical qubits onto physical qubits and replacing unsupported interactions with equivalent gate sequences. Hardware gate sets and coupling constraints therefore shape the compiled circuit and its optimization.

  • Circuit Compilation: A processor coupling map specifies which physical-qubit pairs can directly execute two-qubit gates such as CNOT.In the IBM Yorktown example, q0–q1 is directly connected whereas q0–q2 is not.
  • Gate Synthesis: Quantum processors support limited gate sets determined by their underlying qubit technology, so unsupported gates require synthesis from allowed operations.For IBM superconducting processors, the native set includes CNOT, I, R_Z, SX, and X gates.
  • Circuit Compilation: Compilation maps each logical qubit onto physical qubits and transforms non-adjacent two-qubit gates into equivalent sequences over adjacent qubits.The mapping and gate transformation steps are inter-dependent.
  • Circuit Compilation: Equivalent circuits can implement an unavailable CNOT by inserting operations such as swaps and an available intermediate CNOT.The example routes a CNOT from q0 to q4 through q2 using quantum state transfer.
  • Circuit Compilation: The compiled circuit is optimized against processor constraints, typically by minimizing its circuit depth.The target circuit must satisfy the processor coupling map while preserving computational equivalence.
  • Gate Synthesis: Universal hardware gate sets can implement arbitrary gates to arbitrary accuracy through finite sequences, allowing abstract circuits to be executed after compilation.This relies on the available gate set being universal.

4 QUANTUM ALGORITHMS

Quantum algorithms often exceed the qubit resources of current processors, motivating distributed execution across multiple QPUs. This section distinguishes naturally partitionable algorithms from monolithic circuits and surveys partitioning, compilation, scheduling, and networking requirements.

  • 4 QUANTUM ALGORITHMS: Most practical quantum applications require more qubits than current NISQ processors provide; IBM Quantum Osprey’s 433 qubits are insufficient for practical Shor implementations.The resource gap is framed in terms of qubit number.
  • 4 QUANTUM ALGORITHMS: Distributed quantum computing increases available computational resources by coordinating limited quantum processors on tasks exceeding a single device’s capacity.The surveyed paradigm connects individual processors to work together on larger computations.
  • 4.1 Partitioning of Quantum Algorithms: Perfectly distributable algorithms can be split into autonomous or weakly interacting parts assigned to separate processors without communication overhead for interactions.The criterion concerns the interaction structure of the quantum circuit.
  • 4.1 Partitioning of Quantum Algorithms: QFT is a monolithic algorithm because each qubit strongly interacts with all others through controlled R_n gates.Its circuit combines a Hadamard gate with controlled phase operations involving higher-order qubits.
  • 4.1 Partitioning of Quantum Algorithms: Distributing monolithic algorithms requires compiler-selected breakdowns that minimize gates applied between qubits stored on different devices.Algorithm-specific partitioning studies include quantum phase estimation and VQE.
  • 4.2 Execution Management: Distributed execution management partitions circuit instances into subsets and schedules those subsets across available QPUs in successive rounds.Each schedule maps selected instances to the quantum network, with classical outputs accumulated into an output vector.
  • 4.2 Execution Management: Scheduling should remain orthogonal to partitioning, while the network must support entangled-state creation across any QPU pair whose combined capacity fits the circuit width.The scheduling and networking planes are treated as separate services.
  • 4.3 Open Issues and Research Directions: A general theory ranking algorithms by distributability is still missing, and efficient concurrent execution requires strategies specific to quantum parallelism, no-cloning, and entanglement.Future work also includes the trade-off between distributed circuit complexity and processor distance.

5 QUANTUM NETWORKING

Distributed quantum networking connects smaller processors so remote qubits can interact through teleportation-based communication. The section presents teleportation, remote-operation strategies, entanglement swapping, and resource trade-offs governing performance.

  • Quantum networking foundations: Remote qubits require communication primitives because classical protocols cannot directly perform gates across separate quantum processors.Quantum communication differs fundamentally because quantum information cannot be freely copied or measured without alteration.
  • Quantum teleportation: Quantum teleportation transmits an unknown qubit without physically transferring its carrier, using a pre-shared entangled pair and two classical bits.The destination applies conditional operations based on the source measurements to reconstruct the original state.
  • Entanglement swapping: The number of additional interactions from entanglement swapping scales linearly with processor count using two communication qubits per intermediate processor, and more than linearly when that constraint is relaxed.The resulting augmented connectivity increases possible remote interactions within the virtual processor.
  • Entanglement swapping: Entanglement swapping creates virtual quantum links, allowing remote processors to share Bell states without a direct quantum connection.Intermediate processors perform Bell-state measurements and local corrections to establish the remote entanglement.
  • Remote operations: TeleData and TeleGate each consume one EPR pair and two classical bits, but their performance depends on circuit operation patterns, network characteristics, and data-to-communication-qubit ratio.The two strategies therefore have equal stated communication-resource consumption but can behave differently in context.
  • Open issues: Choosing communication qubits creates an augmented-connectivity-versus-EPR-cost trade-off because swapping consumes Bell states, especially across longer processor paths.Communication-qubit allocation also trades parallel remote operations against the data qubits available for computation.

6 QUANTUM COMPILING

Distributed quantum compiling translates hardware-independent circuits into feasible executions across constrained quantum processors. Its central challenges are assigning logical qubits, handling non-local gates, and minimizing operation, noise, and communication overhead.

  • Compilation overview: Quantum compilation translates an input circuit into an equivalent circuit that accounts for device characteristics and minimizes multi-qubit gates.For distributed execution, compilation must also account for communication costs.
  • Open issues: Compiler design is NP-hard even for a single processor, while DQC additionally requires minimizing communication, operation, and noise overhead.The literature contains many proposed strategies, which may be combined into multi-layer optimizers.
  • Compilation overview: DQC compilers primarily perform qubit assignment and non-local gate handling.These steps are compared across programming languages, network topologies, assignment strategies, gate-handling strategies, and software availability.
  • Qubit assignment: Qubit assignment partitions logical qubits across processors to minimize interactions among different subsets.Assignments may be static or dynamic, with dynamic approaches changing partitions during execution.
  • Non-local gate handling: Non-local gates arise when a circuit requires operations between qubits assigned to different QPUs.Ebit optimization and circuit transformations can reduce the number of non-local gates and communication costs.
  • Open issues: Noise-aware compilation for DQC remains an open problem because the appropriate scope of noise knowledge across processors and quantum links is unsettled.Possible approaches range from complete knowledge of the target execution platform to more limited information.

7 SIMULATION TOOLS

Simulation tools support the design and evaluation of distributed quantum computing by modeling hardware, protocols, or applications. They differ in physical realism, scalability, noise support, and ease of use.

  • Simulation roles: Simulation tools help define hardware requirements from applications and protocols and support quantum-network sizing.They enable high-level KPI-driven design rather than trial-and-error hardware development.
  • Simulation roles: The survey classifies DQC simulation tools as hardware-oriented, protocol-oriented, or application-oriented.The classification organizes tools according to their primary design and evaluation focus.
  • Hardware-oriented tools: Hardware-oriented tools model physical entities and noise, enabling evaluation of how hardware technologies affect distributed-program execution quality.SQUANCH and NetSquid are presented as prominent examples.
  • Protocol-oriented tools: Protocol-oriented tools support hardware-agnostic quantum-network protocol design, generally with limited or missing noise modeling.Examples include SimulaQron, SeQUeNCe, QuiSP, and QuNetSim.
  • Protocol-oriented tools: QuiSP targets large-scale heterogeneous-network protocol simulation while tracking errors rather than full quantum states.Its declared long-term goal is an internetwork with 100 networks of 100 nodes each.
  • Protocol-oriented tools: QuNetSim works well for five to ten hosts separated by few hops but reaches limits with many entangled qubits and parallel operations.This illustrates the scalability trade-off in protocol-oriented simulation.
  • Application-oriented tools: Application-oriented tools rapidly assess quantum-circuit splits, while NetQASM SDK and QNE-ADK simplify DQC simulation configuration.DQC Executor further automates network construction and simulation setup from network and algorithm descriptions.

8 CONCLUSIONS AND FUTURE PERSPECTIVES

The survey concludes that practical distributed quantum computing requires hardware abstraction, infrastructure integration, standardization, and multidisciplinary development. It sketches a progression from processors within one computer to geographically distributed quantum farms, with increasing heterogeneity and communication demands.

  • Industrial perspective: Distributed quantum computing still requires significant work on enabling components and systems despite substantial worldwide public and private investment.The survey frames industrial opportunities as a motivation for continued development.
  • Industrial perspective: Hardware fragmentation is a major obstacle because industry has not consolidated around one quantum technology.The survey proposes a Quantum-HAL to abstract across computing and networking hardware.
  • Industrial perspective: A Quantum-HAL would provide unified northbound APIs and decouple higher layers from technologies such as trapped ions, superconducting qubits, and silicon photonic qubits.This abstraction is intended to simplify and speed development of platforms, services, and applications.
  • Industrial perspective: Increasing DQC readiness requires management and control architectures and APIs that interwork with current Telecom and ICT infrastructures.The survey identifies coordinated standardization efforts involving bodies such as ITU-T, ETSI, IETF, and IEEE.
  • Development stages: The proposed development path has three stages: processors within one computer, quantum computers within one farm, and geographically distributed quantum farms.Later stages introduce greater hardware, network, timing, and interoperability challenges.
  • Development stages: Geographically distributed farms face spread heterogeneity across operators and quantum links, while distance-induced delays complicate coordination.Relevant links may be optical, free-space, or satellite.
  • Development stages: Deployment evolution depends strongly on technological advances and experimental implementations across the DQC ecosystem.The survey gives no definite timetable and emphasizes collaboration between academia and industry.
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