Single-shot error mitigation by coherent Pauli checks
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 b...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.033193 |
| _version_ | 1797210382401536000 |
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| author | Ewout van den Berg Sergey Bravyi Jay M. Gambetta Petar Jurcevic Dmitri Maslov Kristan Temme |
| author_facet | Ewout van den Berg Sergey Bravyi Jay M. Gambetta Petar Jurcevic Dmitri Maslov Kristan Temme |
| author_sort | Ewout van den Berg |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:09:42Z |
| format | Article |
| id | doaj.art-8485be8fe5e44aac8507d96c2c968734 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:09:42Z |
| publishDate | 2023-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-8485be8fe5e44aac8507d96c2c9687342024-04-12T17:34:11ZengAmerican Physical SocietyPhysical Review Research2643-15642023-09-015303319310.1103/PhysRevResearch.5.033193Single-shot error mitigation by coherent Pauli checksEwout van den BergSergey BravyiJay M. GambettaPetar JurcevicDmitri MaslovKristan TemmeGenerating 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.http://doi.org/10.1103/PhysRevResearch.5.033193 |
| spellingShingle | Ewout van den Berg Sergey Bravyi Jay M. Gambetta Petar Jurcevic Dmitri Maslov Kristan Temme Single-shot error mitigation by coherent Pauli checks Physical Review Research |
| title | Single-shot error mitigation by coherent Pauli checks |
| title_full | Single-shot error mitigation by coherent Pauli checks |
| title_fullStr | Single-shot error mitigation by coherent Pauli checks |
| title_full_unstemmed | Single-shot error mitigation by coherent Pauli checks |
| title_short | Single-shot error mitigation by coherent Pauli checks |
| title_sort | single shot error mitigation by coherent pauli checks |
| url | http://doi.org/10.1103/PhysRevResearch.5.033193 |
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