Optimal resource cost for error mitigation

Abstract

One of the central problems for near-term quantum devices is to understand their ultimate potential and limitations. We address this problem in terms of quantum error mitigation by introducing a framework taking into account the full expressibility of near-term devices, in which the optimal resource cost for the probabilistic error cancellation method can be formalized. We provide a general methodology for evaluating the optimal cost by connecting it to a resource-theoretic quantifier defined with respect to the noisy operations that devices can implement. We employ our methods to estimate the optimal cost in mitigating a general class of noise, where we obtain an achievable cost that has a generic advantage over previous evaluations, as well as a fundamental lower bound applicable to a broad class of noisy implementable operations. We improve our bounds for several noise models, where we give the exact optimal costs for the depolarizing and dephasing noise, precisely characterizing the overhead cost while offering an operational meaning to the resource measure in terms of error mitigation. Our result particularly implies that the heuristic approach presented by Temme et al. [K. Temme, S. Bravyi, and J. M. Gambetta, Phys. Rev. Lett. 119, 180509 (2017)] is optimal even in our extended framework, putting fundamental limitations on the advantage provided by the extra degrees of freedom inherent in near-term devices for this noise model.

arXiv comment5+6 pages, 1 figure; published version

References in corpus (39)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A computable measure of entanglement
• Surface codes: Towards practical large-scale quantum computation
• Quantum computational chemistry
• Error mitigation for short-depth quantum circuits
• Quantum Resource Theories
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Efficient variational quantum simulator incorporating active error minimisation
• Robustness of entanglement
• Practical Quantum Error Mitigation for Near-Future Applications
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Low-cost error mitigation by symmetry verification
• Error-mitigated digital quantum simulation
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Learning-based quantum error mitigation
• Estimating outcome probabilities of quantum circuits using quasiprobabilities
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Convex resource theory of non-Gaussianity
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• Quantum computation with universal error mitigation on superconducting quantum processor
• Operational Resource Theory of Quantum Channels
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Error-Mitigated Quantum Gates Exceeding Physical Fidelities in a Trapped-Ion System
• No-Go Theorems for Quantum Resource Purification
• Convex geometry of quantum resource quantification
• Mitigating realistic noise in practical noisy intermediate-scale quantum devices
• Application of the Resource Theory of Channels to Communication Scenarios
• Skew informations from an operational view via resource theory of asymmetry
• Thresholds for universal concatenated quantum codes
• Negativity of quasiprobability distributions as a measure of nonclassicality
• Universal and Operational Benchmarking of Quantum Memories
• Resource theories of quantum channels and the universal role of resource erasure
• New perspectives on covariant quantum error correction
• Fundamental limitations on photoisomerization from thermodynamic resource theories
• A deep learning model for noise prediction on near-term quantum devices
• Universal Optimal Quantum Correlator
• Error rates and resource overheads of encoded three-qubit gates

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• Universal Sampling Lower Bounds for Quantum Error Mitigation
• Universal cost bound of quantum error mitigation based on quantum estimation theory
• Quantum error mitigation via matrix product operators
• Physical Implementability of Linear Maps and Its Application in Error Mitigation
• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• Detecting and quantifying entanglement on near-term quantum devices
• Operational quantification of continuous-variable quantum resources
• Unifying and benchmarking state-of-the-art quantum error mitigation techniques
• Error mitigation and quantum-assisted simulation in the error corrected regime
• Efficient quantum readout-error mitigation for sparse measurement outcomes of near-term quantum devices
• Variational Quantum-Based Simulation of Waveguide Modes
• Testing platform-independent quantum error mitigation on noisy quantum computers
• Coherence of operations and interferometry
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Effects of quantum resources on the statistical complexity of quantum circuits
• Virtual quantum resource distillation: General framework and applications
• Noise effects on purity and quantum entanglement in terms of physical implementability
• Resource estimations for the Hamiltonian simulation in correlated electron materials
• Information recoverability of noisy quantum states
• Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
• Quantifying fermionic nonlinearity of quantum circuits
• Mitigating Quantum Errors via Truncated Neumann Series
• Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups
• Virtual quantum error detection
• Quantum algorithm for calculation of transition amplitudes in hybrid tensor networks
• Compressed quantum error mitigation
• Full Band Structure Calculation of Semiconducting Materials on a Noisy Quantum Processor
• Shadow Simulation of Quantum Processes
• Power of quantum measurement in simulating unphysical operations
• Quantum channel decomposition with pre- and post-selection
• One-Shot Static Entanglement Cost of Bipartite Quantum Channels
• Noisy Probabilistic Error Cancellation and Generalized Physical Implementability
• Detecting and Eliminating Quantum Noise of Quantum Measurements
• Enhancing quantum models of stochastic processes with error mitigation
• The Accuracy vs. Sampling Overhead Trade-off in Quantum Error Mitigation Using Monte Carlo-Based Channel Inversion
• Hardware-efficient quantum annealing with error mitigation via classical shadow
• Error Crafting in Mixed Quantum Gate Synthesis
• Ideal stochastic process modeling with post-quantum quasiprobabilistic theories
• Feed-Forward Probabilistic Error Cancellation with Noisy Recovery Gates