Exact and Approximate Unitary 2-Designs: Constructions and Applications

Abstract

We develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an O(n)-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on n qubits with quantum circuits of size O(n) without requiring any ancilla qubits, thereby improving upon previous approaches.

7 pages, updating to version published in 2009

References in corpus (5)

• Randomizing quantum states: Constructions and applications
• Symmetrised Characterisation of Noisy Quantum Processes
• Superdense coding of quantum states
• Remote preparation of quantum states
• Efficient Generation of Generic Entanglement

Cited by in corpus (490)

• A bound on chaos
• Barren plateaus in quantum neural network training landscapes
• Black holes as mirrors: quantum information in random subsystems
• Trapped-Ion Quantum Computing: Progress and Challenges
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Robust randomized benchmarking of quantum processes
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Entropic Uncertainty Relations and their Applications
• Noise tailoring for scalable quantum computation via randomized compiling
• Hybrid quantum-classical algorithms and quantum error mitigation
• Jerusalem Lectures on Black Holes and Quantum Information
• Characterizing Quantum Gates via Randomized Benchmarking
• Chaos and complexity by design
• Efficient measurement of quantum gate error by interleaved randomized benchmarking
• Towards the fast scrambling conjecture
• The randomized measurement toolbox
• Quantum certification and benchmarking
• Random Quantum Circuits are Approximate 2-designs
• Improved classical simulation of quantum circuits dominated by Clifford gates
• Mixed-state entanglement from local randomized measurements
• Local random quantum circuits are approximate polynomial-designs
• Self-Consistent Quantum Process Tomography
• Emergent statistical mechanics of entanglement in random unitary circuits
• Chaos, Complexity, and Random Matrices
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Characterizing large-scale quantum computers via cycle benchmarking
• Quantum Computer Systems for Scientific Discovery
• Barren Plateaus in Variational Quantum Computing
• Silicon qubit fidelities approaching incoherent noise limits via pulse engineering
• Detecting crosstalk errors in quantum information processors
• Operator growth in the SYK model
• Estimating the Coherence of Noise
• Multiqubit Clifford groups are unitary 3-designs
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks
• A decoupling approach to the quantum capacity
• Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
• Randomized Benchmarking with Confidence
• Preparing random states and benchmarking with many-body quantum chaos
• Linear growth of quantum circuit complexity
• Cross-Platform Verification of Intermediate Scale Quantum Devices
• Large gradients via correlation in random parameterized quantum circuits
• Measuring the Capabilities of Quantum Computers
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits
• Entanglement Devised Barren Plateau Mitigation
• Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
• Theory of quantum system certification: a tutorial
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Quantum Simulating Nature's Fundamental Fields
• Entanglement Hamiltonian Tomography in Quantum Simulation
• Fault-Tolerant Logical Gates in the IBM Quantum Experience
• A general framework for randomized benchmarking
• Avoiding barren plateaus using classical shadows
• Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
• Randomized Benchmarking of Multi-Qubit Gates
• Approximate unitary $t$-designs by short random quantum circuits using nearest-neighbor and long-range gates
• What randomized benchmarking actually measures
• Pseudorandom States, Non-Cloning Theorems and Quantum Money
• Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems
• Optimizing quantum process tomography with unitary 2-designs
• Efficient estimation of Pauli channels
• Models of quantum complexity growth
• Approaches for approximate additivity of the Holevo information of quantum channels
• Efficient error models for fault-tolerant architectures and the Pauli twirling approximation
• Unitary designs and codes
• Quantum Dynamics in Krylov Space: Methods and Applications
• Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
• Emergent quantum state designs from individual many-body wavefunctions
• Probing scrambling using statistical correlations between randomized measurements
• Robust Extraction of Tomographic Information via Randomized Benchmarking
• Unitarity of black hole evaporation in final-state projection models
• Characterizing Universal Gate Sets via Dihedral Benchmarking
• Disentangling Scrambling and Decoherence via Quantum Teleportation
• Symmetry-resolved dynamical purification in synthetic quantum matter
• Decoupling with random quantum circuits
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Surface code with decoherence: An analysis of three superconducting architectures
• Recent advances for quantum classifiers
• Quantum one-time programs
• Interactive Proofs For Quantum Computations
• Convergence rates for arbitrary statistical moments of random quantum circuits
• Theoretical and Experimental Perspectives of Quantum Verification
• Randomized benchmarking with gate-dependent noise
• Tensor-Network Simulations of the Surface Code under Realistic Noise
• Random quantum circuits are approximate unitary $t$-designs in depth $O\left(n{t}^{5+o(1)}\right)$
• Evaluating the noise resilience of variational quantum algorithms
• Quantum Hamiltonian Learning Using Imperfect Quantum Resources
• Quantum Fisher information from randomized measurements
• Scalable randomized benchmarking of non-Clifford gates
• Efficient unitary designs with nearly time-independent Hamiltonian dynamics
• Probing many-body quantum chaos with quantum simulators
• Coherence in quantum error-correcting codes
• Emergence of typical entanglement in two-party random processes
• How to efficiently select an arbitrary Clifford group element
• QubiC: An open source FPGA-based control and measurement system for superconducting quantum information processors
• An equality between entanglement and uncertainty
• Non-exponential Fidelity Decay in Randomized Benchmarking with Low-Frequency Noise
• Quantum Physical Unclonable Functions: Possibilities and Impossibilities
• Scrambling and Complexity in Phase Space
• Characterization of Leakage Errors via Randomized Benchmarking
• Decoupling with unitary approximate two-designs
• Chaos in Classical D0-Brane Mechanics
• Experimental Estimation of Average Fidelity of a Clifford Gate on a 7-qubit Quantum Processor
• Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering
• Nonstabilizerness determining the hardness of direct fidelity estimation
• Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
• Many-body quantum teleportation via operator spreading in the traversable wormhole protocol
• How to Verify a Quantum Computation
• Unitary designs from statistical mechanics in random quantum circuits
• Driven quantum dynamics: will it blend?
• Gate fidelity fluctuations and quantum process invariants
• Classical Simulation of Quantum Noise
• Recovering quantum gates from few average gate fidelities
• Entanglement growth in diffusive systems
• Anticoncentration theorems for schemes showing a quantum speedup
• Analytic theory for the dynamics of wide quantum neural networks
• Asymmetric Quantum LDPC Codes
• Shorter gate sequences for quantum computing by mixing unitaries
• The Clifford group fails gracefully to be a unitary 4-design
• Universal cost bound of quantum error mitigation based on quantum estimation theory
• Entanglement, quantum randomness, and complexity beyond scrambling
• Entanglement Reactivation in Separable Environments
• Re-examining the quantum volume test: Ideal distributions, compiler optimizations, confidence intervals, and scalable resource estimations
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Efficient unitary designs with a system-size independent number of non-Clifford gates
• Practical experimental certification of computational quantum gates via twirling
• Real Randomized Benchmarking
• Scrambling speed of random quantum circuits
• Quantum Commuting Circuits and Complexity of Ising Partition Functions
• Permutation Symmetry Determines the Discrete Wigner Function
• Efficient classical simulation of Clifford circuits with nonstabilizer input states
• Multi-qubit Randomized Benchmarking Using Few Samples
• Measuring Arbitrary Physical Properties in Analog Quantum Simulation
• Selective and Efficient Quantum Process Tomography
• Robust Characterization of Loss Rates
• Demonstration of Robust Quantum Gate Tomography via Randomized Benchmarking
• Estimating the coherence of noise in quantum control of a solid-state qubit
• Bounding the average gate fidelity of composite channels using the unitarity
• A taxonomy of small Markovian errors
• Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage
• Quantum advantage of unitary Clifford circuits with magic state inputs
• Universally Fisher-Symmetric Informationally Complete Measurements
• Entanglement Typicality
• The learnability of Pauli noise
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Robust and Efficient Hamiltonian Learning
• Projected Least-Squares Quantum Process Tomography
• Mitigating Barren Plateaus with Transfer-learning-inspired Parameter Initializations
• Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
• Randomized Benchmarking with Restricted Gate Sets
• Estimating the fidelity of T gates using standard interleaved randomized benchmarking
• Comment on the paper "Random Quantum Circuits are Approximate 2-designs"
• Unitary $2$-designs from random $X$- and $Z$-diagonal unitaries
• Randomized benchmarking for individual quantum gates
• Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization
• A complete Randomized Benchmarking Protocol accounting for Leakage Errors
• Generating a state $t$-design by diagonal quantum circuits
• Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
• Composite parameterization and Haar measure for all unitary and special unitary groups
• Benchmarking Quantum Simulators using Ergodic Quantum Dynamics
• Random unitary maps for quantum state reconstruction
• Quantum authentication with key recycling
• Accrediting outputs of noisy intermediate-scale quantum computing devices
• Experimental demonstration of selective quantum process tomography on an NMR quantum information processor
• On the complexity of quantum partition functions
• Readout Of Singlet-Triplet Qubits At Large Magnetic Field Gradients
• Property testing of unitary operators
• Randomized compiling for scalable quantum computing on a noisy superconducting quantum processor
• Rolling quantum dice with a superconducting qubit
• Diagonal quantum circuits: their computational power and applications
• From randomized benchmarking experiments to gateset circuit fidelity: how to interpret randomized benchmarking decay parameters
• Randomized Benchmarking using Non-Destructive Readout in a 2D Atom Array
• Verification of phased Dicke states
• Approximate Randomized Benchmarking for Finite Groups
• A semi-agnostic ansatz with variable structure for quantum machine learning
• Error statistics and scalability of quantum error mitigation formulas
• Randomized benchmarking for non-Markovian noise
• Subspace benchmarking high-fidelity entangling operations with trapped ions
• Spectral decoupling in many-body quantum chaos
• Improved spectral gaps for random quantum circuits: large local dimensions and all-to-all interactions
• Efficient verification of quantum processes
• Analysing quantum systems with randomised measurements
• Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking
• Shadow tomography from emergent state designs in analog quantum simulators
• Cryptographic approach to Quantum Metrology
• Guaranteed recovery of quantum processes from few measurements
• Optimal Universal Quantum Error Correction via Bounded Reference Frames
• Quantum Computational Phase Transition in Combinatorial Problems
• Local witness for bipartite quantum discord
• Benchmarking Information Scrambling
• Entanglement entropy production in Quantum Neural Networks
• Optimal strategies for estimating the average fidelity of quantum gates
• Entropic uncertainty relations from quantum designs
• Information-theoretic equilibration: the appearance of irreversibility under complex quantum dynamics
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength
• Efficient Simulation for Quantum Message Authentication
• Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies
• Entropic uncertainty relations from equiangular tight frames and their applications
• Quantum to Classical Randomness Extractors
• Estimating gate-set properties from random sequences
• Dynamically corrected gates suppress spatio-temporal error correlations as measured by randomized benchmarking
• Generating Haar-uniform Randomness using Stochastic Quantum Walks on a Photonic Chip
• Ensembles of physical states and random quantum circuits on graphs
• Iso-entangled mutually unbiased bases, symmetric quantum measurements and mixed-state designs
• Engineered dissipation to mitigate barren plateaus
• Efficient quantum pseudorandomness with simple graph states
• Bounding experimental quantum error rates relative to fault-tolerant thresholds
• Efficient classical simulation of noisy quantum computation
• Generalized teleportation and entanglement recycling
• Short random circuits define good quantum error correcting codes
• Optimal approximate transpose map via quantum designs and its applications to entanglement detection
• Stringy effects in scrambling
• Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits
• On the mixed-unitary rank of quantum channels
• Markovianization with approximate unitary designs
• Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice
• Single-Shot Quantum Process Tomography
• Mutually unbiased bases as minimal Clifford covariant 2-designs
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• Doubly optimal parallel wire cutting without ancilla qubits
• Provable bounds for noise-free expectation values computed from noisy samples
• Exponentially tighter bounds on limitations of quantum error mitigation
• Fast Bayesian tomography of a two-qubit gate set in silicon
• Quantum verification and estimation with few copies
• A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• 6-qubit Optimal Clifford Circuits
• Efficient Unitarity Randomized Benchmarking of Few-qubit Clifford Gates
• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems
• Robust quantum data locking from phase modulation
• Cloaking a qubit in a cavity
• Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity
• Quantum gate verification and its application in property testing
• Randomized benchmarking for qudit Clifford gates
• Firewalls and flat mirrors: An alternative to the AMPS experiment which evades the Harlow-Hayden obstacle
• Reducing resources for verification of quantum computations
• Quantum non-malleability and authentication
• Randomized Benchmarking under Different Gatesets
• Local random quantum circuits are approximate polynomial-designs - numerical results
• Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
• The Timescales of Quantum Breaking
• Multiphoton Tomography with Linear Optics and Photon Counting
• Designs via Free Probability
• The Simplest Demonstrations of Quantum Nonlocality
• An exponentially-growing family of universal quantum circuits
• Hybrid benchmarking of arbitrary quantum gates
• Randomized benchmarking in measurement-based quantum computing
• Entanglement properties of multipartite informationally complete quantum measurements
• Representations of the multi-qubit Clifford group
• ScQ cloud quantum computation for generating Greenberger-Horne-Zeilinger states of up to 10 qubits
• Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study
• Randomized gap and amplitude estimation
• Entanglement of random hypergraph states
• Derandomizing quantum circuits with measurement based unitary designs
• Scrambling with Matrix Black Holes
• Qibolab: an open-source hybrid quantum operating system
• Scalable estimation of pure multi-qubit states
• Accelerating Quantum Relaxation via Temporary Reset: A Mpemba-Inspired Approach
• Quantum Error Correction with Mixed Ancilla Qubits
• Fermionic correlation functions from randomized measurements in programmable atomic quantum devices
• Development of Zero-Noise Extrapolated Projection Based Quantum Algorithm for Accurate Evaluation of Molecular Energetics in Noisy Quantum Devices
• Diagonal-unitary 2-designs and their implementations by quantum circuits
• Randomized benchmarking of quantum gates implemented by electron spin resonance
• Improving compressed sensing with the diamond norm
• Controlled quantum operations and combs, and their applications to universal controllization of divisible unitary operations
• Observation of entanglement negativity transition of pseudo-random mixed states
• Randomized Benchmarking in the Analogue Setting
• Near-linear constructions of exact unitary 2-designs
• A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits)
• Combatting the Effects of Disorder in Quantum State Transfer
• Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors
• No-Go Theorems for Universal Entanglement Purification
• Deep thermalization under charge-conserving quantum dynamics
• Improving the speed of variational quantum algorithms for quantum error correction
• Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory
• Fluctuations of subsystem entropies at late times
• Phase Retrieval Using Unitary 2-Designs
• Holographic duality between local Hamiltonians from random tensor networks
• Unraveling the emergence of quantum state designs in systems with symmetry
• Efficient Unitary T-designs from Random Sums
• Nonadaptive fault-tolerant verification of quantum supremacy with noise
• Identification of a reversible quantum gate: assessing the resources
• Automatic quantum circuit encoding of a given arbitrary quantum state
• Efficient unitary designs and pseudorandom unitaries from permutations
• Randomized adaptive quantum state preparation
• Modeling the Performance of Early Fault-Tolerant Quantum Algorithms
• Benchmarking quantum logic operations relative to thresholds for fault tolerance
• Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
• Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-spin System
• Benchmarking quantum gates and circuits
• Improved simulation of quantum circuits dominated by free fermionic operations
• Fully scalable randomized benchmarking without motion reversal
• Continuous-variable quantum state designs: theory and applications
• Decoupling with random diagonal unitaries
• Efficient methods for one-shot quantum communication
• One-Shot Randomized and Nonrandomized Partial Decoupling
• Weak approximate unitary designs and applications to quantum encryption
• Rescuing Complementarity With Little Drama
• How to check universality of quantum gates?
• Pseudo-randomness and Learning in Quantum Computation
• On the explicit constructions of certain unitary $t$-designs
• Quantum Metrology with Delegated Tasks
• Purity of thermal mixed quantum states
• Preserving Measurements for Optimal State Discrimination over Quantum Channels
• A graphical calculus for integration over random diagonal unitary matrices
• Randomized Benchmarking of Clifford Operators
• Adaptive Compilation of Multi-Level Quantum Operations
• Emergence of noise-induced barren plateaus in arbitrary layered noise models
• Energy-filtered random-phase states as microcanonical thermal pure quantum states
• Designs from Local Random Quantum Circuits with SU(d) Symmetry
• Barren plateaus are swamped with traps
• High-fidelity gate operations for quantum computing beyond dephasing time limits
• Complexity is not Enough for Randomness
• Comparing randomized benchmarking figure with average infidelity of quantum gate-set
• Virtual distillation with noise dilution
• Realistic simulation of quantum computation using unitary and measurement channels
• Testing randomness with photons
• Rank-deficient representations in the Theta correspondence over finite fields arise from quantum codes
• Kerdock Codes Determine Unitary 2-Designs
• On the generic increase of observational entropy in isolated systems
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states
• Quantum stabilizer codes and beyond
• Efficient characterization of qudit logical gates with gate set tomography using an error-free Virtual-Z-gate model
• A Solvable Model of Quantum Darwinism-Encoding Transitions
• Linear Cross Entropy Benchmarking with Clifford Circuits
• Quantum-enhanced neural networks in the neural tangent kernel framework
• Quantum algorithms for group convolution, cross-correlation, and equivariant transformations
• A game of quantum advantage: linking verification and simulation
• Fast and robust quantum state tomography from few basis measurements
• Scalable evaluation of quantum-circuit error loss using Clifford sampling
• Benchmarking Quantum Computers: Towards a Standard Performance Evaluation Approach
• Characterization of randomness in quantum circuits of continuous gate sets
• The SWITCH test for discriminating quantum evolutions
• Fault-tolerant quantum speedup from constant depth quantum circuits
• Process fidelity estimation of linear optical quantum CZ gate: A comparative study
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• Symmetric Clifford twirling for cost-optimal quantum error mitigation in early FTQC regime
• Automatic Post-selection by Ancillae Thermalisation
• Optimal Conversion from Classical to Quantum Randomness via Quantum Chaos
• Optimal measurement strategies for fast entanglement detection
• Efficient Experimental Verification of Quantum Gates with Local Operations
• Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes
• Quantum computation by teleportation and symmetry
• Projective toric designs, quantum state designs, and mutually unbiased bases
• Efficient Construction of Quantum Physical Unclonable Functions with Unitary t-designs
• Decelerating cosmologies are de-scramblers
• A Classically Efficient Quantum Scalable Fermi-Hubbard Benchmark
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement
• Quantum complexity phase transitions in monitored random circuits
• Geometric discord: A resource for increments of quantum key distribution through twirling
• Quantum noise generated by local random Hamiltonians
• Context Aware Fidelity Estimation
• Experimental demonstration of Pauli-frame randomization on a superconducting qubit
• Efficient self-consistent learning of gate set Pauli noise
• Maximum privacy without coherence, zero-error
• A Unified Framework For Quantum Unforgeability
• Unitary $t$-designs from $relaxed$ seeds
• Efficient quantum tensor product expanders and unitary t-designs via the zigzag product
• Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
• Disti-Mator: an entanglement distillation-based state estimator
• Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks
• Coherent randomized benchmarking
• Fundamental limits on quantum cloning from the no-signalling principle
• Phase-space representations of SIC-POVM fiducial states
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Generic Entanglement Entropy for Quantum States with Symmetry
• Decoherence and Quantum Error Correction for Quantum Computing and Communications
• Lightweight Detection of a Small Number of Large Errors in a Quantum Circuit
• Thermal states of random quantum many-body systems
• Entangling power, gate typicality, and measurement-induced phase transitions
• Purification of Noisy Measurements and Faithful Distillation of Entanglement
• Restricting to the chip architecture maintains the quantum neural network accuracy
• Cross-Platform Comparison of Arbitrary Quantum Processes
• Efficient approximate unitary designs from random Pauli rotations
• Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
• Hardness of observing strong-to-weak symmetry breaking
• Non-Clifford Cost of Random Unitaries
• Quantum Polarization of Qudit Channels
• Secure Software Leasing Without Assumptions
• A framework for randomized benchmarking over compact groups
• On the Computational Hardness of Quantum One-Wayness
• Combining $T_1$ and $T_2$ estimation with randomized benchmarking and bounding the diamond distance
• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Constant Overhead Entanglement Distillation via Scrambling
• Architectures and random properties of symplectic quantum circuits
• An introduction into optimal control for quantum technologies
• Twirling channels have minimal mixed-unitary rank
• Generalized Hofmann quantum process fidelity bounds for quantum filters
• Exact spectral gaps of random one-dimensional quantum circuits
• Resource-efficient Generalized Quantum Subspace Expansion
• Measurement-Protected Quantum Key Distribution
• Measurement-based interleaved randomised benchmarking using IBM processors
• Robust Estimation of Nonlinear Properties of Quantum Processes
• Measuring NISQ Gate-Based Qubit Stability Using a 1+1 Field Theory and Cycle Benchmarking
• Resource-Efficient Cross-Platform Verification with Modular Superconducting Devices
• On construction of finite averaging sets for $SL(2,\mathbb{C})$ via its Cartan decomposition
• Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
• Matrix concentration inequalities and efficiency of random universal sets of quantum gates
• Random private quantum states
• Random Projection using Random Quantum Circuits
• Universal framework for simultaneous tomography of quantum states and SPAM noise
• Leakage Benchmarking for Universal Gate Sets
• Extending the Q-score to an Application-level Quantum Metric Framework
• A Theory of Direct Randomized Benchmarking
• Randomized measurements for multi-parameter quantum metrology
• Benchmarking the performance of a high-Q cavity qudit using random unitaries
• Complementarity relations for design-structured POVMs in terms of generalized entropies of order $\alpha \in (0,2)$
• Certification of continuous-variable gates using average channel-fidelity witnesses
• Advancing Quantum Networking: Some Tools and Protocols for Ideal and Noisy Photonic Systems
• Practical Quantum Computing: The value of local computation
• The Lie Algebra of XY-mixer Topologies and Warm Starting QAOA for Constrained Optimization
• Theory of quantum error mitigation for non-Clifford gates
• Bosonic randomized benchmarking with passive transformations
• Quantum Advantage in Distributed Sensing with Noisy Quantum Networks
• Variational quantum cloning machine on an integrated photonic interferometer
• Barren plateaus are amplified by the dimension of qudits
• Improved Strong Simulation of Universal Quantum Circuits
• Uncloneable Encryption from Decoupling
• Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
• SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning
• Implementation of single-qubit measurement-based t-designs using IBM processors
• Characterizing physical and logical errors in a transversal CNOT via cycle error reconstruction
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
• Expressibility, entangling power and quantum average causal effect for causally indefinite circuits
• Classical certification of quantum gates under the dimension assumption
• Exploiting many-body localization for scalable variational quantum simulation
• Generalized group designs: constructing novel unitary 2-, 3- and 4-designs
• Cyclic measurements and simplified quantum state tomography
• Efficient trainability of linear optical modules in quantum optical neural networks
• Geometrical Approach to Logical Qubit Fidelities of Neutral Atom CSS Codes
• Chasing shadows with Gottesman-Kitaev-Preskill codes
• Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations
• Detecting high-dimensional entanglement by randomized product projections
• Hyperfine Coupling Constants on Quantum Computers: Performance, Errors, and Future Prospects
• Symmetric channel verification for purifying noisy quantum channels
• Fundamental solutions of heat equation on unitary groups establish an improved relation between $\epsilon$-nets and approximate unitary $t$-designs
• Markov Gap and Bound Entanglement in Haar Random State
• Lie groups for quantum complexity and barren plateau theory
• QPack: Quantum Approximate Optimization Algorithms as universal benchmark for quantum computers
• Generalized Cross-Entropy Benchmarking for Random Circuits with Ergodicity
• Quantum search by continuous-time quantum walk on t-designs
• Sample-size-reduction of quantum states for the noisy linear problem
• Robustness of optimized numerical estimation schemes for noisy variational quantum algorithms
• Theory of mirror benchmarking and demonstration on a quantum computer
• Sampling and the complexity of nature
• Equilibration and Typicality in Quantum Processes
• Partial randomized benchmarking
• Fast Scramblers, Democratic Walks and Information Fields
• Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation
• Optimizing short stabilizer codes for asymmetric channels
• Moments of Quantum Channel Ensembles
• Classical-to-quantum non-signalling boxes
• Optimized fermionic SWAP networks with equivalent circuit averaging for QAOA
• Realizing Unitary $k$-designs with a Single Quench
• Exploiting biased noise in variational quantum models
• Anticoncentration is (almost) all you need
• Fundamental limits to contrast reversal of survival probability correlations
• Fault-tolerant fidelity based on few-qubit codes: Parity-check circuits for biased error channels
• Incoherent Approximation of Leakage in Quantum Error Correction
• On the query complexity of unitary channel certification
• Rigorous Maximum Likelihood Estimation for Quantum States
• Efficiently estimating average fidelity of a quantum logic gate using few classical random bits
• Bayesian ACRONYM Tuning
• Unbiased observable estimation with approximate channels in fault-tolerant quantum computation
• Distilling Entanglement with Noisy Operations
• Investigating the effect of noise channels on the quality of unitary t-designs
• Simple Diagonal State Designs with Reconfigurable Real-Time Circuits
• Basic entanglement distillation with realistic noise
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms
• Quantum statistical effect induced through conditioned post-processing procedures with unitary $t$-designs
• Optimal estimation of three parallel spins with genuine and restricted collective measurements
• Hamiltonian-reconstruction distance as a success metric for the Variational Quantum Eigensolver
• Noise-Aware Circuit Compilations for a Continuously Parameterized Two-Qubit Gateset
• Linear-optical protocols for mitigating and suppressing noise in bosonic systems
• More global randomness from less-random local gates
• Simultaneous superadditivity of the direct and complementary channel capacities
• Fast Scrambling in Classically Simulable Quantum Circuits
• A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation
• Accreditation Against Limited Adversarial Noise
• The Vector representation of the Standard Quantum Process Tomography
• Quantum Private Broadcasting
• On a Matrix Ensemble for Arbitrary Complex Quantum Systems
• Optimizing Circuit Reusing and its Application in Randomized Benchmarking
• A protocol to estimate the average fidelity of the bipartite system
• Run-length certificates in quantum learning: sample complexity and noise thresholds