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A quantum-classical separation for Reed-Muller codes punctured at random points is proved, and an efficient classical algorithm under a stronger three-fold multiplication property is given, leaving intermediate regimes as candidates for quantum advantage.
Regev's reduction is a quantum algorithmic framework for finding codewords satisfying nonlinear constraints by decoding the dual code. To date, applications that have not been dequantized have relied on efficient classical decoders and coordinate-wise constraints specifying a set of allowed values for each coordinate....
A deterministic classical algorithm for the binary-error Learning-with-Errors problem, which is of independent cryptographic interest, and a full sample--time tradeoff that interpolates between exponential and polynomial runtime is established.
Quantum error correction (QEC) is the primary strategy for protecting a quantum computer from the environment1,2. The prerequisite of QEC is that errors must remain sufficiently rare, which requires perpetually adapting the control parameters of the computer to the drifting environmental conditions. The current solutio...
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