A dichotomy for path-containment problems shows some are solvable with linear queries while others are equivalent to cycle problems and admit a quantum-walk algorithm with query complexity Õ(n^{3/2 - α_k}) where α_k decays exponentially in k, plus a conditional lower bound.
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New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
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Quantum algorithms for path and cycle containment problems
A dichotomy for path-containment problems shows some are solvable with linear queries while others are equivalent to cycle problems and admit a quantum-walk algorithm with query complexity Õ(n^{3/2 - α_k}) where α_k decays exponentially in k, plus a conditional lower bound.
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Lower overhead fault-tolerant building blocks for noisy quantum computers
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.