Wisconsin Quantum Institute

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Events on Monday, February 13th, 2023

The geometry of quantum error correction under biased noise
Time: 11:00 am - 12:00 pm
Place: 5310 Chamberlin Hall
Speaker: Arpit Dua
Abstract: Quantum error correction is necessary because physical qubits have much higher error rates per gate operation than are needed for practical tasks. The popular choice is to encode a logical qubit in a large enough planar layout of many physical qubits, called the surface code, to have sufficiently low logical error rates. The optimal logical error rates depend on the statistical mechanics of logical operators. For example, under biased Pauli noise, having more higher-weight logical operator representations with a higher ratio of low-rate Pauli operators is better. Using this idea, I will discuss how, in active error correction, measuring Clifford-rotated Pauli stabilizers of the surface code can enhance code performance: higher error thresholds and lower subthreshold logical error rates, for biased Pauli noise. Using statistical mechanics and percolation theory, I will describe a phase diagram of 50% thresholds for random Clifford-rotated surface codes under pure dephasing noise. Using tensor network numerics, I will show that certain families of these random codes outperform the best-known translation invariant Clifford-rotated surface codes for finitely biased depolarizing noise.
Host: Thad Walker
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