Universal cost bound of quantum error mitigation based on quantum estimation theory

Abstract

We present a unified approach to analyzing the cost of various quantum error mitigation methods on the basis of quantum estimation theory. By analyzing the quantum Fisher information matrix of a virtual quantum circuit that effectively represents the operations of quantum error mitigation methods, we derive for a generic layered quantum circuit under a wide class of Markovian noise that, unbiased estimation of an observable encounters an exponential growth with the circuit depth in the lower bound on the measurement cost. Under the global depolarizing noise, we in particular find that the bound can be asymptotically saturated by merely rescaling the measurement results. Moreover, we prove for random circuits with local noise that the cost grows exponentially also with the qubit count. Our numerical simulations support the observation that, even if the circuit has only linear connectivity, such as the brick-wall structure, each noise channel converges to the global depolarizing channel with its strength growing exponentially with the qubit count. This not only implies the exponential growth of cost both with the depth and qubit count, but also validates the rescaling technique for sufficiently deep quantum circuits. Our results contribute to the understanding of the physical limitations of quantum error mitigation and offer a new criterion for evaluating the performance of quantum error mitigation techniques.

7 + 14 pages, 10 figures. See also a related work by Takagi et al., which appears in the same arXiv posting as arXiv:2208.09178

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Cited by in corpus (37)

• Quantum Error Mitigation
• Machine Learning for Practical Quantum Error Mitigation
• Universal Sampling Lower Bounds for Quantum Error Mitigation
• Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry
• Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers
• Exponentially tighter bounds on limitations of quantum error mitigation
• Group-theoretic error mitigation enabled by classical shadows and symmetries
• Suppressing Correlated Noise in Quantum Computers via Context-Aware Compiling
• Dynamical simulations of many-body quantum chaos on a quantum computer
• Volumetric Benchmarking of Error Mitigation with Qermit
• Limits of noisy quantum metrology with restricted quantum controls
• Localized Virtual Purification
• Quantum error cancellation in photonic systems -- undoing photon losses
• Symmetric Clifford twirling for cost-optimal quantum error mitigation in early FTQC regime
• Quantum Dynamic Programming
• Demonstrating quantum error mitigation on logical qubits
• Multireference error mitigation for quantum computation of chemistry
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• Synergy between noisy quantum computers and scalable classical deep learning
• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion
• Readout Error Mitigation for Mid-Circuit Measurements and Feedforward
• Resource-efficient Generalized Quantum Subspace Expansion
• Echo-evolution data generation for quantum error mitigation via neural networks
• Adaptive measurement strategy for quantum subspace methods
• Error Mitigation Thresholds in Noisy Random Quantum Circuits
• Purity-Assisted Zero-Noise Extrapolation for Quantum Error Mitigation
• Density matrix representation of hybrid tensor networks for noisy quantum devices
• Resource-efficient shadow tomography using equatorial stabilizer measurements
• Error Crafting in Mixed Quantum Gate Synthesis
• Mitigating photon loss in linear optical quantum circuits
• Feasibility of performing quantum chemistry calculations on quantum computers
• Mitigating Errors in Analog Quantum Simulation by Hamiltonian Reshaping or Hamiltonian Rescaling
• Estimates of loss function concentration in noisy parametrized quantum circuits
• Symmetric channel verification for purifying noisy quantum channels
• Optimal randomized measurements for a family of non-linear quantum properties
• Resilience-Runtime Tradeoff Relations for Quantum Algorithms
• Robust Error Accumulation Suppression for Quantum Circuits