Theory of quantum system certification: a tutorial

Abstract

The precise control of complex quantum systems promises numerous technological applications including digital quantum computing. The complexity of such devices renders the certification of their correct functioning a challenge. To address this challenge, numerous methods were developed in the last decade. In this tutorial, we explain prominent protocols for certifying the physical layer of quantum devices described by quantum states and processes. Such protocols are particularly important in the development of near-term devices. Specifically, we discuss methods of direct quantum state certification, direct fidelity estimation, shadow fidelity estimation, direct quantum process certification, randomized benchmarking and cross-entropy benchmarking. Moreover, we provide an introduction to powerful mathematical methods, which are widely used in quantum information theory, in order to derive theoretical guarantees for the protocols.

47 pages, 4 figures, 62 Theorems, Propositions, Lemma, Protocols, Definitions and Examples; v2: published version with numerous small improvements; v3: the argument leading to the diamond norm normalization of quantum channels has been corrected

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• Nonstabilizerness determining the hardness of direct fidelity estimation
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• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
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• Performance analysis of multi-shot shadow estimation
• Distributed quantum inner product estimation
• Estimating gate-set properties from random sequences
• Synthesis of and compilation with time-optimal multi-qubit gates
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• Inferring Nonlinear Many-Body Bell Inequalities From Average Two-Body Correlations: Systematic Approach for Arbitrary Spin-j Ensembles
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• Robust and efficient verification of graph states in blind measurement-based quantum computation
• Classification of four-qubit entangled states via Machine Learning
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• Model predictive control for robust quantum state preparation
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• Qibolab: an open-source hybrid quantum operating system
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• Learning logical Pauli noise in quantum error correction
• Engineering unsteerable quantum states with active feedback
• No-Go Theorems for Universal Entanglement Purification
• Experimental sample-efficient quantum state tomography via parallel measurements
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Benchmarking universal quantum gates via channel spectrum
• Learning fermionic correlations by evolving with random translationally invariant Hamiltonians
• Enhancing quantum state tomography via resource-efficient attention-based neural networks
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Efficient quantum interpolation of natural data
• Unitarity estimation for quantum channels
• High-accuracy Hamiltonian learning via delocalized quantum state evolutions
• Synergies Between Operations Research and Quantum Information Science
• Certifying dimension of quantum systems by sequential projective measurements
• Quantum reservoir computing for photonic entanglement witnessing
• Variational certification of quantum devices
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• Cross-Platform Verification in Quantum Networks
• Operational Markovianization in Randomized Benchmarking
• Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate
• Optimal parent Hamiltonians for time-dependent states
• Optimal trace-distance bounds for free-fermionic states: Testing and improved tomography
• Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
• Universal algorithms for quantum data learning
• Inherent quantum resources in stationary spin chains
• Robust ultra-shallow shadows
• Coherent randomized benchmarking
• Approximate inverse measurement channel for shallow shadows
• Cross-Platform Comparison of Arbitrary Quantum Processes
• Nondestructive Verification of Entangled States via Fidelity Witnessing
• Decoding general error correcting codes and the role of complementarity
• Interferometric detection of continuous-variable entanglement using two states
• Sampling Groups of Pauli Operators to Enhance Direct Fidelity Estimation
• PAC-learning of free-fermionic states is NP-hard
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification
• Classical certification of quantum gates under the dimension assumption
• Lindblad-like quantum tomography for non-Markovian quantum dynamical maps
• Low variance estimations of many observables with tensor networks and informationally-complete measurements
• Tomography of parametrized quantum states
• Bosonic randomized benchmarking with passive transformations
• Nearly query-optimal classical shadow estimation of unitary channels
• Error metric for non-trace-preserving quantum operations
• Excluding false negative error in certification of quantum channels
• Robust one-sided self-testing of two-qubit states via quantum steering
• Quantum subspace verification for error correction codes
• Generalized Cross-Entropy Benchmarking for Random Circuits with Ergodicity
• Shot-noise reduction for lattice Hamiltonians
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Experimental measurement and a physical interpretation of quantum shadow enumerators
• Short-time simulation of quantum dynamics by Pauli measurements
• Experimental Verification of Entangled States in the Adversarial Scenario
• The tightness of multipartite coherence from spectrum estimation
• Testing identity of collections of quantum states: sample complexity analysis
• Optimal randomized measurements for a family of non-linear quantum properties
• Prescriptive preparation and verification of nonstabilizer states
• The abelian state hidden subgroup problem: Learning stabilizer groups and beyond
• Optimizing Measurements Sequences for Quantum State Verification
• On the query complexity of unitary channel certification
• Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning
• Topology-Aware Block Coordinate Descent for Qubit Frequency Allocation of Superconducting Quantum Processors
• Detecting entanglement from few partial transpose moments and their decay via weight enumerators
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