Predicting Many Properties of a Quantum System from Very Few Measurements

Abstract

Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order $\log M$ measurements suffice to accurately predict $M$ different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.

arXiv comment10 pages, 9 figures + 30 page appendix; supersedes arXiv:1908.08909; open source code available at https://github.com/momohuang/predicting-quantum-properties

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• Quantum contextual bandits and recommender systems for quantum data
• Characterization of coherent errors in gate layers with robustness to Pauli noise
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Learning topological states from randomized measurements using variational tensor network tomography
• The 7 faces of quantum NP
• Learning quantum states prepared by shallow circuits in polynomial time
• A quantum computing approach to fixed-node Monte Carlo using classical shadows
• Single-copy stabilizer testing
• Quantum Local Differential Privacy and Quantum Statistical Query Model
• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Expanding variational quantum eigensolvers to larger systems by dividing the calculations between classical and quantum hardware
• Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions
• Operation fidelity explored by numerical range of Kraus operators
• Random Projection using Random Quantum Circuits
• Universal framework for simultaneous tomography of quantum states and SPAM noise
• A New World in the Depths of Microcrypt: Separating OWSGs and Quantum Money from QEFID
• Quantum Property Preservation
• Resource-efficient Generalized Quantum Subspace Expansion
• Quantum Circuit Cutting for Classical Shadows
• A learning theory for quantum photonic processors and beyond
• On the connection between least squares, regularization, and classical shadows
• Learning Quantum Processes with Quantum Statistical Queries
• Retrieving maximum information of symmetric states from their corrupted copies
• Many-Body Entanglement in Solid-State Emitters
• Pitfalls when tackling the exponential concentration of parameterized quantum models
• Fast algorithms for classical specifications of stabiliser states and Clifford gates
• Hacking Cryptographic Protocols with Advanced Variational Quantum Attacks
• Completeness Stability of Quantum Measurements
• Detecting genuine multipartite entanglement using moments of positive maps
• Robust Estimation of Nonlinear Properties of Quantum Processes
• Entanglement dynamics and Page curves in random permutation circuits
• Estimating many properties of a quantum state via quantum reservoir processing
• Clifford circuit based heuristic optimization of fermion-to-qubit mappings
• On relating one-way classical and quantum communication complexities
• Randomized measurements for multi-parameter quantum metrology
• Sampling Groups of Pauli Operators to Enhance Direct Fidelity Estimation
• Boson sampling enhanced quantum chemistry
• Quantum-enhanced mean value estimation via adaptive measurement
• Real randomized measurements for analyzing properties of quantum states
• Perturbative gadgets for gate-based quantum computing: Non-recursive constructions without subspace restrictions
• Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
• Visualization of all two-qubit states via partial-transpose-moments
• Unsupervised Detection of Topological Phase Transitions with a Quantum Reservoir
• Optimisation of time-ordered processes in the finite and asymptotic regime
• Information theoretic approach to readout error mitigation for quantum computers
• Robust one-sided self-testing of two-qubit states via quantum steering
• A quantum tug of war between randomness and symmetries on homogeneous spaces
• Purity-Assisted Zero-Noise Extrapolation for Quantum Error Mitigation
• Adaptive measurement strategy for quantum subspace methods
• Efficient Learning of Long-Range and Equivariant Quantum Systems
• Local measurement strategies for multipartite entanglement quantification
• Biased Estimator Channels for Classical Shadows
• PAC-learning of free-fermionic states is NP-hard
• Dual-unitary shadow tomography
• Learning quantum graph states with product measurements
• Efficient and robust estimation of many-qubit Hamiltonians
• Detection of entanglement via moments of positive maps
• Approximating dynamical correlation functions with constant depth quantum circuits
• Clifford Circuits can be Properly PAC Learned if and only if $\text{RP}=\text{NP}$
• Holographic Classical Shadow Tomography
• Low variance estimations of many observables with tensor networks and informationally-complete measurements
• Tomography of parametrized quantum states
• Single-shot quantum measurements sketch quantum many-body states
• Error threshold in active steering protocols for few-qubit systems
• Benchmarking the performance of a high-Q cavity qudit using random unitaries
• Measuring temporal entropies in experiments
• Learning Density Functionals from Noisy Quantum Data
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Exploring entanglement in finite-size quantum systems with degenerate ground state
• Pseudochaotic Many-Body Dynamics as a Pseudorandom State Generator
• Quantum Computational Insurance and Actuarial Science
• Agnostic Process Tomography
• Nearly query-optimal classical shadow estimation of unitary channels
• Universal graph representation of stabilizer codes
• Continuous-variable designs and design-based shadow tomography from random lattices
• Quantum implicit representation of vortex filaments in turbulence
• Mitigation of correlated readout errors without randomized measurements
• Adaptive Lattice Gas Algorithm: Classical and Quantum implementations
• Experimental verification of Threshold Quantum State Tomography on a fully-reconfigurable photonic integrated circuit
• Certification of continuous-variable gates using average channel-fidelity witnesses
• Quantum circuit complexity and unsupervised machine learning of topological order
• Quantum Mpemba Effect in a Four-Site Bose-Hubbard Model
• A unifying separability criterion based on extended correlation tensor
• Quantum circuit-like learning: A fast and scalable classical machine-learning algorithm with similar performance to quantum circuit learning
• Advancing Quantum Networking: Some Tools and Protocols for Ideal and Noisy Photonic Systems
• Mitigating the measurement overhead of ADAPT-VQE with optimised informationally complete generalised measurements
• Quantum subspace verification for error correction codes
• Protecting entanglement witnesses with randomized measurements
• Learning the closest product state
• Chasing shadows with Gottesman-Kitaev-Preskill codes
• Generalized group designs: constructing novel unitary 2-, 3- and 4-designs
• Short-time simulation of quantum dynamics by Pauli measurements
• Corrupted sensing quantum state tomography
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Transport approach to quantum state tomography
• Efficient Online Quantum Circuit Learning with No Upfront Training
• Unorthodox parallelization for Bayesian quantum state estimation
• Relative-belief inference in quantum information theory
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• State-witness contraction
• Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information
• On Reducing the Execution Latency of Superconducting Quantum Processors via Quantum Job Scheduling
• On The Stabilizer Formalism And Its Generalization
• Fundamental solutions of heat equation on unitary groups establish an improved relation between $\epsilon$-nets and approximate unitary $t$-designs
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• Hardware-efficient quantum annealing with error mitigation via classical shadow
• Feasibility of performing quantum chemistry calculations on quantum computers
• Detecting genuine multipartite entanglement in multi-qubit devices with restricted measurements
• Weighted Approximate Quantum Natural Gradient for Variational Quantum Eigensolver
• Robustness of random-control quantum-state tomography
• Batched Line Search Strategy for Navigating through Barren Plateaus in Quantum Circuit Training
• The tightness of multipartite coherence from spectrum estimation
• An Error Mitigated Non-Orthogonal Quantum Eigensolver via Shadow Tomography
• Quantum Glassiness From Efficient Learning
• Variational-toolbox-based separability detection of multiqubit states
• Integrals of motion as slow modes in dissipative many-body operator dynamics
• Adaptive random compiler for Hamiltonian simulation
• Virtual Quantum Markov Chains
• Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
• Fourier-style Quantum State Tomography and Purity Measurement of a Multi-qubit System from Bloch Rotations
• Resource-efficient shadow tomography using equatorial stabilizer measurements
• Quantum-Classical Auxiliary Field Quantum Monte Carlo with Matchgate Shadows on Trapped Ion Quantum Computers
• Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme
• Circuit-Noise-Resilient Virtual Distillation
• Scalable Experimental Bounds for Entangled Quantum State Fidelities
• Artificial intelligence for representing and characterizing quantum systems
• On character table of Clifford groups
• Resource-efficient quantum algorithm for linear systems of equations
• On the Hardness of Measuring Magic
• Experimental measurement and a physical interpretation of quantum shadow enumerators
• Any DOF All at Once: Single Photon State Tomography in a Single Measurement Setup
• Learning the structure of any Hamiltonian from minimal assumptions
• Resource-efficient algorithm for estimating the trace of quantum state powers
• Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
• Shot-noise reduction for lattice Hamiltonians
• Quantum phase classification via partial tomography-based quantum hypothesis testing
• Improving shadow estimation with locally-optimal dual frames
• Analytically Continuing the Randomized Measurement Toolbox
• Moments of Quantum Channel Ensembles
• Constrained Shadow Tomography for Molecular Simulation on Quantum Devices
• Correlated Purification for Restoring $N$-Representability in Quantum Simulation
• Simple Diagonal State Designs with Reconfigurable Real-Time Circuits
• Sample Optimal and Memory Efficient Quantum State Tomography
• Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cramér-Rao bounds
• Unbiased observable estimation with approximate channels in fault-tolerant quantum computation
• Nonunitary gates using measurements only
• Optimal randomized measurements for a family of non-linear quantum properties
• Noisy Monitored Quantum Circuits
• Comprehensive Study on Heisenberg-limited Quantum Algorithms for Multiple Observables Estimation
• Optimizing State Preparation for Variational Quantum Regression on NISQ Hardware
• Neural quantum states for entanglement depth certification from randomized Pauli measurements
• Investigating the effect of noise channels on the quality of unitary t-designs
• Rigorous Maximum Likelihood Estimation for Quantum States
• Prime Number Identification Demonstrated with Quantum Processors Using a New Rescaling-Based Noise Mitigation Technique
• Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities
• Hybrid Quantum-Classical Clustering for Preparing a Prior Distribution of Eigenspectrum
• Learning Variational Quantum Circuit Parameters with Classical Artificial Intelligence for Quantum Phase Transition Detection
• Singular value transformation for unknown quantum channels
• Dynamical irreversibility and local decoherence in quantum many-body chaos
• Operator delocalization in disordered spin chains via exact MPO marginals
• Practical Quantum Reservoir Computing in Rydberg Atom Arrays
• Reducing Complexity of Shadow Process Tomography with Generalized Measurements
• Efficient Characterization of Coherent and Correlated Low-Degree Noise in Layers of Gates
• Simulating plasma wave propagation on a superconducting quantum chip
• Quantum Machine Learning for State Tomography Using Classical Data
• Circuit connectivity boosts by quantum-classical-quantum interfaces
• Diagnosing crosstalk in large-scale QPUs using zero-entropy classical shadows
• Detection of the genuine non-locality of any three-qubit state
• Optimizing Circuit Reusing and its Application in Randomized Benchmarking
• Online learning of a panoply of quantum objects
• Resource-Optimized Grouping Shadow for Efficient Energy Estimation
• Optimizing Unitary Coupled Cluster Wave Functions on Quantum Hardware: Error Bound and Resource-Efficient Optimizer
• Accelerating Fermionic System Simulation on Quantum Computers
• Shallow quantum circuit for generating extremely low-entangled approximate state designs
• Measuring entanglement without local addressing in quantum many-body simulators via spiral quantum state tomography
• Learning mixed quantum states in large-scale experiments
• Quantum Framework for Simulating Linear PDEs with Robin Boundary Conditions
• Detection of nonabsolute separability in quantum states and channels through moments
• Entanglement entropy scaling laws from fluctuations of non-conserved quantities
• Classification of quantum states of light using random measurements through a multimode fiber
• Variational Quantum Generative Modeling by Sampling Expectation Values of Tunable Observables
• Quantum Advantage via Efficient Post-processing on Qudit Classical Shadow tomography
• Entropy density benchmarking of near-term quantum circuits
• Classical Shadows with Improved Median-of-Means Estimation
• Schmidt quantum compressor
• Agnostic Tomography of Stabilizer Product States
• Learning agent-based approach to the characterization of open quantum systems
• Quantum-Enhanced Neural Exchange-Correlation Functionals
• Tensorization of neural networks for improved privacy and interpretability
• Preparation of the single-spinon wave function on a quantum computer
• Certifying entanglement dimensionality by $k$-reduction moments
• One, Two, Three: One empirical evaluation of a two-copy shadow tomography scheme with triple efficiency
• A quantum eigenvalue solver based on tensor networks
• A Unsupervised Framework for Identifying Diverse Quantum Phase Transitions Using Classical Shadow Tomography
• Quantum statistical effect induced through conditioned post-processing procedures with unitary $t$-designs
• Clustering and enhanced classification using a hybrid quantum autoencoder
• The Efficiency Frontier: Classical Shadows versus Direct Quantum Measurement
• Quantum Phase Recognition via Quantum Attention Mechanism
• Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography
• Many-Fermion Simulation from the Contracted Quantum Eigensolver without Fermionic Encoding of the Wave Function
• Work and heat exchanged during sudden quenches of strongly coupled quantum systems
• Fluctuation-guided adaptive random compiler for Hamiltonian simulation
• A Study on Stabilizer Rényi Entropy Estimation using Machine Learning
• Compression of quantum shallow-circuit states
• More global randomness from less-random local gates
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
• Scalable protocol to coherence estimation from scarce data: Theory and experiment
• Ability of entanglement and purity to help to detect systematic experimental errors
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Selective and efficient quantum state tomography for multi-qubit systems
• Measuring Incompatible Observables with Quantum Neural Networks
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing
• Realizing Unitary $k$-designs with a Single Quench
• Critical Scaling of the Quantum Wasserstein Distance