Variational Quantum Fidelity Estimation
Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity $F(\rho,\sigma)$ based on the ``truncated fidelity'' $F(\rho_m, \sigma)$, which is evaluated for a sta...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2020-03-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2020-03-26-248/pdf/ |
| _version_ | 1818953297534386176 |
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| author | Marco Cerezo Alexander Poremba Lukasz Cincio Patrick J. Coles |
| author_facet | Marco Cerezo Alexander Poremba Lukasz Cincio Patrick J. Coles |
| author_sort | Marco Cerezo |
| collection | DOAJ |
| description | Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity $F(\rho,\sigma)$ based on the ``truncated fidelity'' $F(\rho_m, \sigma)$, which is evaluated for a state $\rho_m$ obtained by projecting $\rho$ onto its $m$-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with $m$. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize $\rho$, (2) compute matrix elements of $\sigma$ in the eigenbasis of $\rho$, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where $\sigma$ is arbitrary and $\rho$ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations. |
| first_indexed | 2024-12-20T10:04:02Z |
| format | Article |
| id | doaj.art-8eed981b53f541f788318a88a7741434 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-20T10:04:02Z |
| publishDate | 2020-03-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-8eed981b53f541f788318a88a77414342022-12-21T19:44:16ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2020-03-01424810.22331/q-2020-03-26-24810.22331/q-2020-03-26-248Variational Quantum Fidelity EstimationMarco CerezoAlexander PorembaLukasz CincioPatrick J. ColesComputing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity $F(\rho,\sigma)$ based on the ``truncated fidelity'' $F(\rho_m, \sigma)$, which is evaluated for a state $\rho_m$ obtained by projecting $\rho$ onto its $m$-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with $m$. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize $\rho$, (2) compute matrix elements of $\sigma$ in the eigenbasis of $\rho$, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where $\sigma$ is arbitrary and $\rho$ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.https://quantum-journal.org/papers/q-2020-03-26-248/pdf/ |
| spellingShingle | Marco Cerezo Alexander Poremba Lukasz Cincio Patrick J. Coles Variational Quantum Fidelity Estimation Quantum |
| title | Variational Quantum Fidelity Estimation |
| title_full | Variational Quantum Fidelity Estimation |
| title_fullStr | Variational Quantum Fidelity Estimation |
| title_full_unstemmed | Variational Quantum Fidelity Estimation |
| title_short | Variational Quantum Fidelity Estimation |
| title_sort | variational quantum fidelity estimation |
| url | https://quantum-journal.org/papers/q-2020-03-26-248/pdf/ |
| work_keys_str_mv | AT marcocerezo variationalquantumfidelityestimation AT alexanderporemba variationalquantumfidelityestimation AT lukaszcincio variationalquantumfidelityestimation AT patrickjcoles variationalquantumfidelityestimation |