is the depolarizing error rate. Our formula agrees nearly perfectly with the numerical simulation results. Second, we show that CPCs are well suited for quantum processors with a limited qubit connectivity. For example, the difference between all-to-all and linear qubit connectivity is only a

3\ifmmode\times\else\texttimes\fi{}

increase in the number of cnot gates required to implement CPCs. Third, we describe simplified one-sided CPCs, which are well suited for mitigating measurement errors in the single-shot settings. Finally, we report an experimental demonstration of CPCs with up to 10 logical qubits and more than 100 logical cnot gates. Our experimental results show that CPCs provide a marked improvement in the logical error probability for the considered task of sampling the output distribution of quantum circuits.

DOI: 10.1103/physrevresearch.5.033193

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Protecting quantum memories using coherent parity check codes

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arXiv:1709.01866Quantum Science and TechnologyMay 21, 201837 citations

\ensuremath{\approx}7\ensuremath{\epsilon}n/5

, where

n

is the number of qubits and

\ensuremath{\epsilon}

3\ifmmode\times\else\texttimes\fi{}

{\approx}7εn/5

, where

n

is the number of qubits and

ε

is the depolarizing error rate. Our formula agrees nearly perfectly with the numerical simulation results. Second, we show that CPCs are well-suited for quantum processors with a limited qubit connectivity. For example, the difference between all-to-all and linear qubit connectivity is only a 3X increase in the number of CNOT gates required to implement CPCs. Third, we describe simplified one-sided CPCs which are well-suited for mitigating measurement errors in the single-shot settings. Finally, we report an experimental demonstration of CPCs with up to 10 logical qubits and more than 100 logical CNOT gates. Our experimental results show that CPCs provide a marked improvement in the logical error probability for the considered task of sampling the output distribution of quantum circuits.

[[7,1,3]]

code $|+\ensuremath{\rangle}$ state (Clifford circuits) and five- to 15-qubit

W

states (non-Clifford circuits). Our experimental circuits aggressively deploy forced commutation of cnot gates to obtain low-noise state-preparation circuits. An encoded state initialized with fewer errors marks an important step towards successful demonstration of fault-tolerant quantum computers.

|0 \rangle

readout guarantees unit fidelity in the noiseless check limit. We validate these findings numerically across dimensions

d=2

through

d=9

, achieving error-mitigated fidelities above $97.5\% $ under realistic depolarizing error rates.