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Error Correction of Quantum Algorithms: Arbitrarily Accurate Recovery of Noisy Quantum Signal Processing
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Friday, March 3, 2023 - 2:00pm to 3:00pm
New attendees sign up to receive weekly invite. Use event URL. The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by ε < 1 is introduced. It is shown that while Pauli Z-errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy 'recovery QSP.' Furthermore, it is found that a recovery QSP of length O(2kck2d) is sufficient to correct any length-d QSP with c unique phases to kth-order in error ε. Allowing an additional assumption, a lower bound of Ω(cd) is shown, which is tight for k = 1, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.