Shorter gate sequences for quantum computing by mixing unitaries

Abstract

Fault-tolerant quantum computers compose elements of a discrete gate set in order to approximate a target unitary. The problem of minimising the number of gates is known as gate-synthesis. The approximation error is a form of coherent noise, which can be significantly more damaging than comparable incoherent noise. We show how mixing over different gate sequences can convert this coherent noise into an incoherent form. As measured by diamond distance, the post-mixing noise is quadratically smaller than before mixing, with no additional resource cost. Equivalently, we can use a shorter gate sequence to achieve the same precision as unitary gate-synthesis, with a factor 1/2 reduction for a broad class of problems.

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References in corpus (7)

• Randomized Benchmarking of Quantum Gates
• Magic state distillation with low overhead
• Symmetrised Characterisation of Noisy Quantum Processes
• Efficient synthesis of universal Repeat-Until-Success circuits
• Multilevel distillation of magic states for quantum computing
• Quantum error correction of coherent errors by randomization
• Optimal Trotterization in universal quantum simulators under faulty control

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