Divide-and-conquer verification method for noisy intermediate-scale quantum computation
Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2022-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2022-07-07-758/pdf/ |
| _version_ | 1818114568559263744 |
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| author | Yuki Takeuchi Yasuhiro Takahashi Tomoyuki Morimae Seiichiro Tani |
| author_facet | Yuki Takeuchi Yasuhiro Takahashi Tomoyuki Morimae Seiichiro Tani |
| author_sort | Yuki Takeuchi |
| collection | DOAJ |
| description | Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langle\psi_t|\hat{\rho}_{\rm out}|\psi_t\rangle$ between an actual $n$-qubit output state $\hat{\rho}_{\rm out}$ obtained from the noisy intermediate-scale quantum computation and the ideal output state (i.e., the target state) $|\psi_t\rangle$. Although the direct fidelity estimation method requires $O(2^n)$ copies of $\hat{\rho}_{\rm out}$ on average, our method requires only $O(D^32^{12D})$ copies even in the worst case, where $D$ is the denseness of $|\psi_t\rangle$. For logarithmic-depth quantum circuits on a sparse chip, $D$ is at most $O(\log{n})$, and thus $O(D^32^{12D})$ is a polynomial in $n$. By using the IBM Manila 5-qubit chip, we also perform a proof-of-principle experiment to observe the practical performance of our method. |
| first_indexed | 2024-12-11T03:52:48Z |
| format | Article |
| id | doaj.art-11bcb072abb94e44bef36c61a6cff625 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-11T03:52:48Z |
| publishDate | 2022-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-11bcb072abb94e44bef36c61a6cff6252022-12-22T01:21:51ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2022-07-01675810.22331/q-2022-07-07-75810.22331/q-2022-07-07-758Divide-and-conquer verification method for noisy intermediate-scale quantum computationYuki TakeuchiYasuhiro TakahashiTomoyuki MorimaeSeiichiro TaniSeveral noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langle\psi_t|\hat{\rho}_{\rm out}|\psi_t\rangle$ between an actual $n$-qubit output state $\hat{\rho}_{\rm out}$ obtained from the noisy intermediate-scale quantum computation and the ideal output state (i.e., the target state) $|\psi_t\rangle$. Although the direct fidelity estimation method requires $O(2^n)$ copies of $\hat{\rho}_{\rm out}$ on average, our method requires only $O(D^32^{12D})$ copies even in the worst case, where $D$ is the denseness of $|\psi_t\rangle$. For logarithmic-depth quantum circuits on a sparse chip, $D$ is at most $O(\log{n})$, and thus $O(D^32^{12D})$ is a polynomial in $n$. By using the IBM Manila 5-qubit chip, we also perform a proof-of-principle experiment to observe the practical performance of our method.https://quantum-journal.org/papers/q-2022-07-07-758/pdf/ |
| spellingShingle | Yuki Takeuchi Yasuhiro Takahashi Tomoyuki Morimae Seiichiro Tani Divide-and-conquer verification method for noisy intermediate-scale quantum computation Quantum |
| title | Divide-and-conquer verification method for noisy intermediate-scale quantum computation |
| title_full | Divide-and-conquer verification method for noisy intermediate-scale quantum computation |
| title_fullStr | Divide-and-conquer verification method for noisy intermediate-scale quantum computation |
| title_full_unstemmed | Divide-and-conquer verification method for noisy intermediate-scale quantum computation |
| title_short | Divide-and-conquer verification method for noisy intermediate-scale quantum computation |
| title_sort | divide and conquer verification method for noisy intermediate scale quantum computation |
| url | https://quantum-journal.org/papers/q-2022-07-07-758/pdf/ |
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