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Logical shadow tomography: Efficient estimation of error-mitigated observables
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Logical shadow tomography: Efficient estimation of error-mitigated observables
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We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting a general nonlinear function of the noisy density matrix into the codespace. The subspace expansion and virtual distillation can be viewed as special cases of the new framekwork. We show our method is favorable in the quantum and classical resources overhead. Relative to subspace expansion which requires $O\left(2^{N} \right)$ samples to estimate a logical Pauli observable with $[[N, k]]$ error correction code, our technique requires only $O\left(4^{k} \right)$ samples. Relative to virtual distillation, our technique can compute powers of the density matrix without additional copies of quantum states or quantum memory. We present numerical evidence using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only $10^5$ samples under 1% depolarizing noise.
Forward citations
Cited by 5 Pith papers
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Light-Cone Scaling of In-Circuit Noise in Randomized Measurements
Local noise in shallow randomized measurements damps Pauli observables exponentially with operator size, with slope and intercept set by the operator's light cone, enabling small-string calibration of large-string estimates.
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Classical shadows for sample-efficient measurements of gauge-invariant observables
Using the Z2 lattice-gauge-theory/Ising duality, symmetry-aware classical shadow protocols estimate gauge-invariant observables with exponentially fewer samples than symmetry-blind protocols, at the cost of deeper circuits.
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Presents unbiased uncertainty quantification for post-processing error mitigation and applies it to optimize hyperparameters in Zero Noise Extrapolation and Clifford Data Regression under finite-shot noise.
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Hardware benchmarks of repetition and triangular color codes for quantum error detection show promise for scaling despite exponential sample costs and embedding overheads.
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Steady-state entanglement with concurrence above 0.9 is generated between optical emitters by optically tuning Rabi-split dressed states to couple via a THz channel and collective dissipation.
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