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Classification of Hybrid Quantum-Classical Computing

Frank Phillipson, Niels Neumann, Robert Wezeman

arXiv:2210.15314v1quant-ph

TL;DR

Because “hybrid” is used for different settings, the paper develops a workflow-based classification of hybrid quantum-classical computing. It distinguishes vertical and horizontal classes, names further types, and presents the framework as a way to make the scope of research contributions clearer.

  • Problem

    “Hybrid quantum-classical computing” has diffuse, multi-interpretable uses, making it difficult to identify the scope of contributions described with the term.

    Source: §I · pp. 1–2

  • Method

    The paper connects workflow terminology and classical computer science concepts to classify hybrid computing as vertical or horizontal and subdivide both classes.

    Source: §I · p. 2, §III · pp. 3–4

  • Results

    The paper distinguishes vertical, application-agnostic control and operation activities from horizontal, application-dependent algorithm activities, and names further types within both classes.

    Source: §III · p. 4, §V · p. 6

  • Takeaways & Limitations

    The classification can help researchers and practitioners clarify what they mean by hybrid quantum-classical computing and support more concise tools.

    Source: §V · p. 6

Abstract

from arXiv · show

As quantum computers mature, the applicability in practice becomes more important. Many uses of quantum computers will be hybrid, with classical computers still playing an important role in operating and using the quantum computer. The term hybrid is however diffuse and multi-interpretable. In this work we define two classes of hybrid quantum-classical computing: vertical and horizontal. The first is application-agnostic and concerns using quantum computers. The second is application-specific and concerns running an algorithm. For both, we give a further subdivision in different types of hybrid quantum-classical computing and we coin terms for them.

I. INTRODUCTION

The paper frames hybrid quantum-classical computing as increasingly relevant to practical quantum use, but notes that the term is used for different settings. It proposes a classification framework to clarify those meanings and name the approaches.

I. INTRODUCTION

  • Quantum computers remain in the NISQ era, with limited qubit counts and noise constraining their ability to solve real-world problems.The paper notes that other practical factors include operation parallelism and qubit topology.Source: §I · p. 1
  • The term “hybrid quantum-classical computing” is used for different settings, creating confusion for researchers and practitioners.The paper proposes a classification framework so authors can make the scope of their contributions clearer.Source: §I · pp. 1–2
  • The paper connects quantum research with classical computer science and workflow terminology to classify hybrid approaches and name them clearly.It presents this as a framework for clarifying the scope of contributions.Source: §I · p. 2

II. LITERATURE

Prior literature uses hybrid quantum-classical computing for a range of architectures and algorithms. The paper gives a non-exhaustive overview of these meanings as context for its classification.

II. LITERATURE

  • The overview is explicitly non-exhaustive and focuses on examples illustrating the different meanings of hybrid quantum-classical computing.It excludes hybrid forms involving discrete and continuous variables and hybrid quantum-classical molecular models.Source: §II · p. 2
  • Prior work includes integrated quantum-classical resources for measurement-based computing and quantum co-processors that accelerate subroutines of larger tasks.The cited examples include a system-level software infrastructure for hybrid quantum-classical computing.Source: §II · p. 2
  • Hybrid algorithm examples include variational quantum algorithms, classical pre- or post-processing, and iterative quantum-classical computation.Other described approaches partition large circuits or problems into smaller pieces evaluated by quantum processors or classical simulators, or use classical and quantum solvers in parallel.Source: §II · pp. 2–3

III. TYPES OF HYBRID COMPUTING

The classification uses workflows to distinguish vertical hybrid computing, concerned with operating quantum circuits, from horizontal hybrid computing, concerned with using quantum and classical computers in algorithms. The two categories are not mutually exclusive.

III. TYPES OF HYBRID COMPUTING

  • The framework builds on workflows that specify activity order and dependencies, with activities expandable into sub-workflows.The authors extend the workflow and software-architecture perspective into further subcategories.Source: §III · p. 3
  • Vertical hybrid quantum computing covers application-agnostic control and operation of a quantum circuit, while horizontal hybrid quantum computing covers application-dependent algorithm activities.The paper associates the vertical category mainly with the computing stack and the horizontal category mainly with algorithms.Source: §III · p. 4
  • The vertical and horizontal categories are not mutually exclusive, and a use case may show signs of more than one type.The paper further subdivides both categories.Source: §III · p. 4

A. Vertical hybrid quantum computing

Vertical hybrid types describe classical steps needed to run a quantum routine. The paper distinguishes steps by whether they are topology- and technology-agnostic.

A. Vertical hybrid quantum computing

1) Decomposition hybrid:

Decomposition hybrid divides a higher-level algorithm into classical and quantum instructions, then lowers quantum routines into hardware-agnostic instructions. The high-level description may use a common classical language with classical routines or a dedicated quantum routine.

1) Decomposition hybrid:

  • A high-level quantum routine is broken down into low-level, hardware-agnostic quantum instructions.Source: 1) Decomposition hybrid · p. 4, Figure 4 · p. 4
  • The instruction set can include single-qubit rotations and two-qubit gates such as CNOT and controlled-phase gates.Source: 1) Decomposition hybrid · p. 4
  • Decomposition can split algorithmic instructions into classical and quantum instructions, with classical routines helping lower instructions toward hardware mapping.The higher-level description can use a commonly used classical language enhanced with classical routines, or a dedicated quantum routine.Source: 1) Decomposition hybrid · p. 4

2) Implementation hybrid:

Implementation hybrid maps hardware-agnostic instructions to hardware-specific instructions; controlling hybrid covers operating and controlling the quantum computer. These workflows include hardware-aware mapping and calibration, and implementation may use optimized approximations.

2) Implementation hybrid:

  • Implementation hybrid maps low-level, hardware-agnostic instructions to hardware-specific instructions, including classical and quantum instructions.The mapping assigns operations to qubits, accounts for backend topology, and produces a time-schedule; error-correcting routines and their classical feedback loop may also be added.Source: 2) Implementation hybrid · p. 4, Figure 5 · p. 5

3) Controlling hybrid:

  • Controlling hybrid covers operating the quantum computer, including hardware-instruction mapping and qubit calibration.Because operations may behave differently over time than intended, continuous effort is needed to keep the computer behaving as expected.Source: 3) Controlling hybrid · p. 4, Figure 6 · p. 5
  • Optimized approximation methods can yield better-performing implementations than exact full implementations.Source: 3) Controlling hybrid · pp. 4–5

B. Horizontal hybrid quantum computing

Horizontal hybrid computing distinguishes algorithm types by the ordering of quantum and conventional computing steps. Processing hybrid uses one quantum block with classical preprocessing and postprocessing.

B. Horizontal hybrid quantum computing

1) Processing hybrid:

  • Processing hybrid combines a single quantum block with classical preprocessing and postprocessing.Source: 1) Processing hybrid · p. 5, Figure 7 · p. 5
  • In a distance-based classifier, data standardization and normalization are preprocessing, while translating measurements into the desired kernel classifier is postprocessing.Shor's and Simon's algorithms are also given as processing-hybrid examples.Source: 1) Processing hybrid · p. 5

2) Micro hybrid split:

A micro hybrid split concerns one activity within a larger workflow, where classical and quantum operations may occur, potentially in an iterative fashion.

2) Micro hybrid split:

  • A micro hybrid split places classical and quantum operations within one activity of a larger workflow, potentially iteratively.Source: 2) Micro hybrid split · p. 5, Figure 8 · p. 5
  • Variational algorithms are examples of micro hybrid splits, and measurement-based quantum computing is a special case in which later measurements and operations depend on earlier measurements and classical operations.Source: 2) Micro hybrid split · p. 5

3) Macro hybrid split:

Macro hybrid split describes tasks within a larger algorithm, while parallel hybrid uses independent branches to solve a problem. The workflows can combine different levels of quantum-classical work and multiple solvers.

3) Macro hybrid split:

  • Macro hybrid split divides a larger algorithm into tasks that may each contain quantum and classical operations.Tasks can iterate, and the granularity of observation distinguishes macro from micro splits.Source: 3) Macro hybrid split · p. 5, Figure 9 · p. 5
  • A micro hybrid split can form part of a macro hybrid split, and a macro task can itself be subdivided into a micro workflow.The distinction depends mainly on the workflow's granularity.Source: 3) Macro hybrid split · p. 5, Figure 10 · p. 5

4) Parallel hybrid:

  • Parallel hybrid runs independent branches on a problem and returns the first or best solution found.Branches may use different solvers; the schematic also gives the first-finishing branch as one possible return criterion.Source: 4) Parallel hybrid · p. 5, Figure 11 · p. 6
  • The D-Wave-hybrid framework is an example of parallel hybrid, with samples parsed to four parallel solvers.A classical tabu-search branch may return an answer with certainty or be interrupted by another finished branch,.Source: 4) Parallel hybrid · pp. 5–6

5) Breakdown hybrid:

Breakdown hybrid divides a problem too large to solve directly into smaller parts, runs each part sequentially on a quantum computer, and reconstructs an answer from partial answers.

5) Breakdown hybrid:

  • Breakdown hybrid splits a problem too large to solve directly into smaller parts, runs each part sequentially on a quantum computer, then reconstructs the final answer.The workflow reconstructs the answer from the partial answers.Source: 5) Breakdown hybrid · p. 6, Figure 12 · p. 6
  • Examples include separately evaluating smaller sub-circuits and dividing problems among classical or quantum annealing approaches.The cited examples are a gate-based approach and options within D-Wave hybrid solvers.Source: 5) Breakdown hybrid · p. 6
  • Breakdown and parallel hybrid are not disjoint; a breakdown part may run classically in parallel with quantum tasks.Such a workflow combines breakdown hybrid with parallel hybrid.Source: 5) Breakdown hybrid · p. 6

IV. APPLICATION

The authors use selected 2022 papers to illustrate their classification, finding that most fall within micro and macro hybrid split. They present the framework as a way to clarify what researchers mean by hybrid quantum-classical computing, while acknowledging the categorization is not complete.

IV. APPLICATION

  • Most papers in the classification fall within the micro and macro hybrid split classes, while none found in processing hybrid use the term hybrid quantum-classical.The authors selected examples from 2022 with the relevant terms in their title or keywords, rather than attempting an exhaustive overview.Source: §IV · p. 6

V. CONCLUSIONS

  • The framework distinguishes horizontal and vertical hybrid quantum computing and names specific types within those classes to clarify the term's varied uses.The authors connect quantum research with workflow terminology and classical computer science.Source: §V · p. 6
  • The authors do not claim the overview and categorization are complete, and encourage future researchers and practitioners to complement the framework.Source: §V · p. 6

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