Foreword

Introduction

1Scope

2Normative references

3Terms and definitions

3.1Background

3.1.1model

3.1.2parametermodel parameter

3.2Quantum physics background

3.2.1Hilbert space

3.2.2operator

3.2.3quantum physicsquantum mechanics

3.2.4quantum, adjective

3.2.5quantum, noun

3.2.6quantum system

3.2.7quantum state

3.2.8quantum entanglement

3.2.9quantum operator

3.2.10Hamiltonian

3.2.11quantum measurement

3.2.12quantum coherence

3.2.13decoherence

3.2.14quantum noise

3.3Quantum Information

3.3.1quantum encoding

3.3.2qubit

3.3.3physical qubit

3.3.4logical qubit

3.3.5logical operator

3.3.6state fidelity

3.3.7fidelity

3.3.8process fidelity

3.4Quantum processing

3.4.1quantum information processingquantum processing

3.4.2quantum gate

3.4.3gate fidelity

3.4.4quantum circuit

3.4.5quantum error correction

3.4.6quantum error mitigation

3.4.7quantum processor

3.4.8quantum algorithm

3.4.9quantum computer

3.4.10quantum computing

3.4.11fault-tolerant quantum computing

3.4.12circuit-based quantum computinggate-based quantum computing

3.4.13adiabatic quantum computing

3.4.14quantum computing stack

3.4.15calibration

3.4.16quantum tomographyquantum state tomography

3.4.17quantum memory

3.4.18quantum annealer

3.5Quantum programming

3.5.1quantum simulatorquantum emulator

4Symbols

5Benchmarking methodology

5.1Assessment criteria

5.1.1General

5.1.2Relevance

5.1.3Reproducibility

5.1.4Fairness

5.1.5Verifiability

5.1.6Scalability

5.1.7Usability

5.2Benchmarking Setup

5.3Categorization

6Benchmarking Frameworks

6.1Volumetric Benchmarking

6.2Mirror Benchmarking

7High-Level Benchmarks

7.1Application Benchmarks

7.1.1Q-score

7.1.2Algorithmic Qubit Benchmark

7.1.3Variational Quantum Eigensolver (VQE)

7.1.4Generative Quantum Machine Learning

7.1.5Quantum phase estimation

7.1.6Linear Systems of Equations

7.2Algorithmic Building Blocks

7.2.1General

7.2.2Distribution Initialization

7.2.3Quantum Fourier Transform

7.2.4Grover Diffusion Operator

7.2.5Multiqubit-Operators for Error Correction

7.2.6Multiqubit-Operators for Quantum Optimization

7.2.7Post-circuit/Pre-measurement basis transformation

7.2.8Mid-circuit measurement

7.2.9Multi-Controlled X Gates

8Low-level benchmarks

8.1Randomized Benchmarking (gate error characterization):

8.2Coherence time characterization

8.3Entanglement Characterization

9Outlook: Paving the way to standardized KPIs for quantum computing benchmarking

Bibliography