Scaling of variational quantum circuit depth for condensed matter systems
We benchmark the accuracy of a variational quantum eigensolver based on a finite-depth quantum circuit encoding ground state of local Hamiltonians. We show that in gapped phases, the accuracy improves exponentially with the depth of the circuit. When trying to encode the ground state of conformally...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2020-05-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2020-05-28-272/pdf/ |
| _version_ | 1819045465464766464 |
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| author | Carlos Bravo-Prieto Josep Lumbreras-Zarapico Luca Tagliacozzo José I. Latorre |
| author_facet | Carlos Bravo-Prieto Josep Lumbreras-Zarapico Luca Tagliacozzo José I. Latorre |
| author_sort | Carlos Bravo-Prieto |
| collection | DOAJ |
| description | We benchmark the accuracy of a variational quantum eigensolver based on a finite-depth quantum circuit encoding ground state of local Hamiltonians. We show that in gapped phases, the accuracy improves exponentially with the depth of the circuit. When trying to encode the ground state of conformally invariant Hamiltonians, we observe two regimes. A $\textit{finite-depth}$ regime, where the accuracy improves slowly with the number of layers, and a $\textit{finite-size}$ regime where it improves again exponentially. The cross-over between the two regimes happens at a critical number of layers whose value increases linearly with the size of the system. We discuss the implication of these observations in the context of comparing different variational ansatz and their effectiveness in describing critical ground states. |
| first_indexed | 2024-12-21T10:29:00Z |
| format | Article |
| id | doaj.art-1d70c83beb924890a56f7a816c510040 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-21T10:29:00Z |
| publishDate | 2020-05-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-1d70c83beb924890a56f7a816c5100402022-12-21T19:07:14ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2020-05-01427210.22331/q-2020-05-28-27210.22331/q-2020-05-28-272Scaling of variational quantum circuit depth for condensed matter systemsCarlos Bravo-PrietoJosep Lumbreras-ZarapicoLuca TagliacozzoJosé I. LatorreWe benchmark the accuracy of a variational quantum eigensolver based on a finite-depth quantum circuit encoding ground state of local Hamiltonians. We show that in gapped phases, the accuracy improves exponentially with the depth of the circuit. When trying to encode the ground state of conformally invariant Hamiltonians, we observe two regimes. A $\textit{finite-depth}$ regime, where the accuracy improves slowly with the number of layers, and a $\textit{finite-size}$ regime where it improves again exponentially. The cross-over between the two regimes happens at a critical number of layers whose value increases linearly with the size of the system. We discuss the implication of these observations in the context of comparing different variational ansatz and their effectiveness in describing critical ground states.https://quantum-journal.org/papers/q-2020-05-28-272/pdf/ |
| spellingShingle | Carlos Bravo-Prieto Josep Lumbreras-Zarapico Luca Tagliacozzo José I. Latorre Scaling of variational quantum circuit depth for condensed matter systems Quantum |
| title | Scaling of variational quantum circuit depth for condensed matter systems |
| title_full | Scaling of variational quantum circuit depth for condensed matter systems |
| title_fullStr | Scaling of variational quantum circuit depth for condensed matter systems |
| title_full_unstemmed | Scaling of variational quantum circuit depth for condensed matter systems |
| title_short | Scaling of variational quantum circuit depth for condensed matter systems |
| title_sort | scaling of variational quantum circuit depth for condensed matter systems |
| url | https://quantum-journal.org/papers/q-2020-05-28-272/pdf/ |
| work_keys_str_mv | AT carlosbravoprieto scalingofvariationalquantumcircuitdepthforcondensedmattersystems AT joseplumbreraszarapico scalingofvariationalquantumcircuitdepthforcondensedmattersystems AT lucatagliacozzo scalingofvariationalquantumcircuitdepthforcondensedmattersystems AT joseilatorre scalingofvariationalquantumcircuitdepthforcondensedmattersystems |