Randomized Benchmarking of Quantum Gates

Abstract

A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized pi/2 pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.

13 pages

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• Efficient diagnostics for quantum error correction
• Gate-set evaluation metrics for closed-loop optimal control on nitrogen-vacancy center ensembles in diamond
• Accurate and robust unitary transformation of a high-dimensional quantum system
• Benchmarking Quantum Optimization for the Maximum-Cut Problem on a Superconducting Quantum Computer
• Fast high-fidelity geometric gates for singlet-triplet qubits
• Operational Markovianization in Randomized Benchmarking
• Randomized linear gate set tomography
• Qubit Sensing: A New Attack Model for Multi-programming Quantum Computing
• Unveiling quantum phase transitions from traps in variational quantum algorithms
• Randomized benchmarking in the presence of time-correlated dephasing noise
• Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates
• A superconducting circuit realization of combinatorial gauge symmetry
• Efficient classical simulation and benchmarking of quantum processes in the Weyl basis
• Scalable evaluation of quantum-circuit error loss using Clifford sampling
• Cross-Platform Verification in Quantum Networks
• Optimizing nonadiabatic geometric quantum gates against off-resonance error by dynamical correction in a silicon-based spin qubit
• A High-Power Clock Laser Spectrally Tailored for High-Fidelity Quantum State Engineering
• Qubit Coherent Control with Squeezed Light Fields
• Quantum computer error structure probed by quantum error correction syndrome measurements
• Probing Quantum Telecloning on Superconducting Quantum Processors
• Optimal measurement strategies for fast entanglement detection
• Variational simulation of the Lipkin-Meshkov-Glick model on a neutral atom quantum computer
• Detrimental non-Markovian errors for surface code memory
• Randomised benchmarking for characterizing and forecasting correlated processes
• Estimating the precision for quantum process tomography
• Optimal Conversion from Classical to Quantum Randomness via Quantum Chaos
• Randomised benchmarking for universal qudit gates
• A Comprehensive Cross-Model Framework for Benchmarking the Performance of Quantum Hamiltonian Simulations
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction
• Learning a quantum channel from its steady-state
• Halving the Cost of Quantum Algorithms with Randomization
• A Classically Efficient Quantum Scalable Fermi-Hubbard Benchmark
• Parametric multi-element coupling architecture for coherent and dissipative control of superconducting qubits
• Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium
• Learning to rank quantum circuits for hardware-optimized performance enhancement
• Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes
• Modelling Quantum Devices and the Reconstruction of Physics in Practical Systems
• Qubit assignment using time reversal
• Scalable fast benchmarking for individual quantum gates with local twirling
• Group twirling and noise tailoring for multi-qubit controlled phase gates
• Projective toric designs, quantum state designs, and mutually unbiased bases
• Navigating the noise-depth tradeoff in adiabatic quantum circuits
• Context Aware Fidelity Estimation
• Self-consistent tomography of temporally correlated errors
• High-fidelity quantum tomography with imperfect measurements
• Plane-selective manipulations of nuclear spin qubits in a three-dimensional optical tweezer array
• Exploring a Double Full-Stack Communications-Enabled Architecture for Multi-Core Quantum Computers
• Experimental demonstration of Pauli-frame randomization on a superconducting qubit
• Disti-Mator: an entanglement distillation-based state estimator
• Efficient self-consistent learning of gate set Pauli noise
• Counting stabiliser codes for arbitrary dimension
• Proof-of-principle experimental demonstration of quantum gate verification
• Robustness of the concatenated quantum error-correction protocol against noise for channels affected by fluctuation
• Efficient Monte Carlo characterization of quantum operations for qudits
• Coherent randomized benchmarking
• Reliable Characterization for Improving and Validating Accurate Quantum Operations
• Non-Randomness of Google's Quantum Supremacy Benchmark
• Single-Qubit Gates Beyond the Rotating-Wave Approximation for Strongly Anharmonic Low-Frequency Qubits
• Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor
• Confidence polytopes for quantum process tomography
• Estimating the bias of CX gates via character randomized benchmarking
• Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
• Testing quantum computers with the protocol of quantum state matching
• Characterization of coherent errors in gate layers with robustness to Pauli noise
• Hamiltonian Learning via Shadow Tomography of Pseudo-Choi States
• A protocol to characterize errors in quantum simulation of many-body physics
• Optimal Low-Depth Quantum Signal-Processing Phase Estimation
• Pulse family optimization for parametrized quantum gates using spectral clustering
• Methods for Classically Simulating Noisy Networked Quantum Architectures
• In situ mixer calibration for superconducting quantum circuits
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• AppQSim: Application-oriented benchmarks for Hamiltonian simulation on a quantum computer
• Operating two exchange-only qubits in parallel
• Calibrating quantum gates up to 52 qubits in a superconducting processor
• Benchmarking of universal qutrit gates
• Wildcard error: Quantifying unmodeled errors in quantum processors
• Generic Entanglement Entropy for Quantum States with Symmetry
• Supercomputer simulations of transmon quantum computers
• Experimentally efficient methods for estimating the performance of quantum measurements
• Microfabrication techniques for trapped ion quantum information processing
• Measurement-based interleaved randomised benchmarking using IBM processors
• An introduction into optimal control for quantum technologies
• Leakage Benchmarking for Universal Gate Sets
• Optimization via Quantum Preconditioning
• A Theory of Direct Randomized Benchmarking
• Randomized measurements for multi-parameter quantum metrology
• Approximate Equivalence Checking of Noisy Quantum Circuits
• Efficient Qubit Calibration by Binary-Search Hamiltonian Tracking
• Experimental Test of Contextuality based on State Discrimination with a Single Qubit
• Simultaneous model selection and parameter estimation: A superconducting qubit coupled to a bath of incoherent two-level systems
• Robust Estimation of Nonlinear Properties of Quantum Processes
• Pursuing high-fidelity control of spin qubits in natural Si/SiGe quantum dot
• Continuous monitoring for noisy intermediate-scale quantum processors
• Randomized Benchmarking Protocol for Dynamic Circuits
• Quantum noise modeling through Reinforcement Learning
• Demonstration of Maxwell Demon-assistant Einstein-Podolsky-Rosen Steering via Superconducting Quantum Processor
• Fast algorithms for classical specifications of stabiliser states and Clifford gates
• Echo-evolution data generation for quantum error mitigation via neural networks
• Qibosoq: an open-source framework for quantum circuit RFSoC programming
• Simon's algorithm in the NISQ cloud
• In-situ characterization of qubit drive-phase distortions
• Individually-addressed quantum gate interactions using dynamical decoupling
• A dressed singlet-triplet qubit in germanium
• Universal framework for simultaneous tomography of quantum states and SPAM noise
• Fidelity decay and error accumulation in random quantum circuits
• Benchmarking the performance of a high-Q cavity qudit using random unitaries
• Implementation of a quantum addressable router using superconducting qubits
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification
• Practical Quantum Computing: The value of local computation
• Q-fid: Quantum Circuit Fidelity Improvement with LSTM Networks
• Macroscopic instructions vs microscopic operations in quantum circuits
• Error Mitigation Thresholds in Noisy Random Quantum Circuits
• Gaining confidence on the correct realization of arbitrary quantum computations
• Noise resilience in adaptive and symmetric monitored quantum circuits
• Experimentally ruling out joint reality based on operational completeness
• SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning
• Bosonic randomized benchmarking with passive transformations
• Certification of continuous-variable gates using average channel-fidelity witnesses
• Singlet-only Always-on Gapless Exchange Qubits with Baseband Control
• Classical certification of quantum gates under the dimension assumption
• Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
• Crosstalk-Based Parameterized Quantum Circuit Approximation
• On Computational Complexity of Unitary and State Design Properties
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Pseudochaotic Many-Body Dynamics as a Pseudorandom State Generator
• Partial randomized benchmarking
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• QPack: Quantum Approximate Optimization Algorithms as universal benchmark for quantum computers
• Qubit Readout Error Mitigation with Bit-flip Averaging
• Equilibration and Typicality in Quantum Processes
• Zero- to ultralow-field nuclear magnetic resonance and its applications
• Generalized Cross-Entropy Benchmarking for Random Circuits with Ergodicity
• Model validation and error attribution for a drifting qubit
• Reliable confidence regions for quantum tomography using distribution moments
• Certification of a functionality in a quantum network stage
• Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations
• Accurate Qubit Control with Single Flux Quantum Pulses
• Speckle statistics of entangled photons
• Protecting entanglement witnesses with randomized measurements
• A double selection entanglement distillation-based state estimator
• Theory of mirror benchmarking and demonstration on a quantum computer
• Concatenated continuous driving of silicon qubit by amplitude and phase modulation
• Quantum correlation generation capability of experimental processes
• Approximate 3-designs and partial decomposition of the Clifford group representation using transvections
• Exploiting Different Levels of Parallelism in the Quantum Control Microarchitecture for Superconducting Qubits
• Characterization of multi-level dynamics and decoherence in a high-anharmonicity capacitively shunted flux circuit
• Fidelity Relations in an Array of Neutral Atom Qubits -- Experimental Validation of Control Noise
• Perturbative tomography of small errors in quantum gates
• A graph-state based synthesis framework for Clifford isometries
• Accreditation Against Limited Adversarial Noise
• Learning agent-based approach to the characterization of open quantum systems
• Simulating Quantum Circuits by Shuffling Paulis
• Designing a Machine Learning-Driven, Cross-Hardware Emulator for Noisy Quantum Computers with Gate-Based Protocols
• Estimating Bell Diagonal states with separable measurements
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Near-Term Fermionic Simulation with Subspace Noise Tailored Quantum Error Mitigation
• Optimizing Circuit Reusing and its Application in Randomized Benchmarking
• Optimal randomized measurements for a family of non-linear quantum properties
• Shallow quantum circuit for generating extremely low-entangled approximate state designs
• On the query complexity of unitary channel certification
• Benchmarking Single-Qubit Gates on a Neutral Atom Quantum Processor
• Fundamental limits to contrast reversal of survival probability correlations
• Enlarging the GKP stabilizer group for enhanced noise protection
• Blind-spots of Randomized Benchmarking Under Temporal Correlations
• Anticoncentration is (almost) all you need
• Benchmarking non-Clifford gates using only Pauli twirling group
• Realizing Unitary $k$-designs with a Single Quench
• Zero-Noise Extrapolation via Cyclic Permutations of Quantum Circuit Layouts
• Moments of Quantum Channel Ensembles
• Topology-Aware Block Coordinate Descent for Qubit Frequency Allocation of Superconducting Quantum Processors
• CQM: Cyclic Qubit Mappings
• Finite-Resolution Limits on Quantum Uniqueness
• O(1) benchmarking of precise rotation in a spin-squeezed Bose-Einstein condensate
• Simplifying errors by symmetry and randomisation
• Software mitigation of coherent two-qubit gate errors
• Parameterized process characterization with reduced resource requirements
• Optimized fermionic SWAP networks with equivalent circuit averaging for QAOA
• Quantum Algorithms in Cybernetics
• PyQBench: a Python library for benchmarking gate-based quantum computers
• Principles of quantum functional testing
• Universal Dephasing Noise Injection via Schrodinger Wave Autoregressive Moving Average Models
• Filter Function Formalism and Software Package to Compute Quantum Processes of Gate Sequences for Classical Non-Markovian Noise
• A context-aware gate set tomography characterization of superconducting qubits
• Simulation of Quantum Circuits via Stabilizer Frames
• More global randomness from less-random local gates
• Optimized Aaronson-Gottesman stabilizer circuit simulation through quantum circuit transformations