Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without A Priori Knowledge

TL;DR

This paper introduces blind CQEC, a method for quantum error correction that estimates the target state from noisy outputs, enabling threshold-free recovery without prior knowledge, demonstrated on quantum algorithms and circuits.

Contribution

It removes the need for prior target knowledge in catalytic quantum error correction by developing a target estimation protocol, broadening applicability to unknown quantum outputs.

Findings

Estimation and recovery fidelities are linearly correlated ($r > 0.99$).

A crossover dimension $d^* \\approx 25$--$40$ is identified for effective correction.

Blind CQEC achieves a 3.4x energy-error reduction in a noisy-VQE demonstration.

Abstract

Near-term quantum computers must protect fragile coherence against decoherence to deliver useful results. Catalytic quantum error correction (CQEC) addresses this challenge by amplifying residual coherence with a reusable catalyst, achieving threshold-free recovery whenever the target coherent modes survive in the noisy state. However, the original protocol requires complete knowledge of the ideal target -- an assumption that fails for variational and iterative algorithms whose output is unknown to the correction module. Here we show that this requirement can be removed by estimating the target from the noisy output alone, in a two-stage protocol we call \emph{blind CQEC}. We benchmark five estimation strategies across three noise channels, four quantum algorithms ($d = 4$--$64$), Haar-random states up to $d = 256$, and mixed targets, and find that estimation and recovery fidelities are linearly correlated ($r > 0.99$); we prove an analytical Lipschitz bound $F_\mathrm{rec} \geq 1 - 2\|\hat{\rho}_\mathrm{est} - \rho_\mathrm{target}\|_1$ that explains the correlation, derive a crossover dimension $d^* \approx 25$--$40$, and show that a tunable hybrid bridges the two regimes. Unlike error-mitigation methods (zero-noise extrapolation, probabilistic error cancellation, virtual distillation), blind CQEC returns the state itself rather than corrected expectation values, with single-copy overhead. A noisy-VQE demonstration for H$_2$ yields $3.4\times$ energy-error reduction, and a \texttt{qiskit-aer} circuit-level check confirms transfer to small circuits. These results identify the bottleneck of blind error correction as a classical estimation problem, opening a route to autonomous, threshold-free recovery in algorithms where pre-encoding is unavailable.