Dictionary-based pitch tracking with dynamic programming
Ewout van den Berg, Bhuvana Ramabhadran
INTERSPEECH 2014
Generating samples from the output distribution of a quantum circuit is a ubiquitous task used as a building block of many quantum algorithms. Here we show how to accomplish this task on a noisy quantum processor lacking full-blown error correction for a special class of quantum circuits dominated by Clifford gates. Our approach is based on coherent Pauli checks (CPCs) that detect errors in a Clifford circuit by verifying commutation rules between random Pauli-type check operators and the considered circuit. Our main contributions are as follows. First, we derive a simple formula for the probability that a Clifford circuit protected by CPCs contains a logical error. In the limit of a large number of checks, the logical error probability is shown to approach the value ≈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 3× 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.
Ewout van den Berg, Bhuvana Ramabhadran
INTERSPEECH 2014
Andrew W. Cross, Lev S. Bishop, et al.
Physical Review A
Sergey Bravyi, David Gosset
Journal of Mathematical Physics
Sergey Bravyi, David Gosset, et al.
Journal of Mathematical Physics