The battle of clean and dirty qubits in the era of partial error correction
When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so the...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-07-13-1060/pdf/ |
| _version_ | 1797781001089318912 |
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| author | Daniel Bultrini Samson Wang Piotr Czarnik Max Hunter Gordon M. Cerezo Patrick J. Coles Lukasz Cincio |
| author_facet | Daniel Bultrini Samson Wang Piotr Czarnik Max Hunter Gordon M. Cerezo Patrick J. Coles Lukasz Cincio |
| author_sort | Daniel Bultrini |
| collection | DOAJ |
| description | When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the "clean and dirty" setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits. |
| first_indexed | 2024-03-12T23:51:37Z |
| format | Article |
| id | doaj.art-c9eeea4d054846828d9f2a31df321700 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-12T23:51:37Z |
| publishDate | 2023-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-c9eeea4d054846828d9f2a31df3217002023-07-13T15:28:25ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-07-017106010.22331/q-2023-07-13-106010.22331/q-2023-07-13-1060The battle of clean and dirty qubits in the era of partial error correctionDaniel BultriniSamson WangPiotr CzarnikMax Hunter GordonM. CerezoPatrick J. ColesLukasz CincioWhen error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the "clean and dirty" setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.https://quantum-journal.org/papers/q-2023-07-13-1060/pdf/ |
| spellingShingle | Daniel Bultrini Samson Wang Piotr Czarnik Max Hunter Gordon M. Cerezo Patrick J. Coles Lukasz Cincio The battle of clean and dirty qubits in the era of partial error correction Quantum |
| title | The battle of clean and dirty qubits in the era of partial error correction |
| title_full | The battle of clean and dirty qubits in the era of partial error correction |
| title_fullStr | The battle of clean and dirty qubits in the era of partial error correction |
| title_full_unstemmed | The battle of clean and dirty qubits in the era of partial error correction |
| title_short | The battle of clean and dirty qubits in the era of partial error correction |
| title_sort | battle of clean and dirty qubits in the era of partial error correction |
| url | https://quantum-journal.org/papers/q-2023-07-13-1060/pdf/ |
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