Accelerated variational algorithms for digital quantum simulation of many-body ground states
One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evol...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2020-09-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2020-09-16-324/pdf/ |
| _version_ | 1811285694683807744 |
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| author | Chufan Lyu Victor Montenegro Abolfazl Bayat |
| author_facet | Chufan Lyu Victor Montenegro Abolfazl Bayat |
| author_sort | Chufan Lyu |
| collection | DOAJ |
| description | One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we first provide a quantitative comparison between the adiabatic and variational methods with respect to required quantum resources on digital quantum simulators, namely the depth of the circuit and the number of two-qubit quantum gates. Our results show that the variational methods are less demanding with respect to these resources. However, they need to be hybridized with a classical optimization which can converge slowly. Therefore, as the second result of the paper, we provide two different approaches for speeding the convergence of the classical optimizer by taking a good initial guess for the parameters of the variational circuit. We show that these approaches are applicable to a wide range of Hamiltonian and provide significant improvement in the optimization procedure. |
| first_indexed | 2024-04-13T02:47:49Z |
| format | Article |
| id | doaj.art-94a87becf44d4ea88e46295309932ce6 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-13T02:47:49Z |
| publishDate | 2020-09-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-94a87becf44d4ea88e46295309932ce62022-12-22T03:05:57ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2020-09-01432410.22331/q-2020-09-16-32410.22331/q-2020-09-16-324Accelerated variational algorithms for digital quantum simulation of many-body ground statesChufan LyuVictor MontenegroAbolfazl BayatOne of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we first provide a quantitative comparison between the adiabatic and variational methods with respect to required quantum resources on digital quantum simulators, namely the depth of the circuit and the number of two-qubit quantum gates. Our results show that the variational methods are less demanding with respect to these resources. However, they need to be hybridized with a classical optimization which can converge slowly. Therefore, as the second result of the paper, we provide two different approaches for speeding the convergence of the classical optimizer by taking a good initial guess for the parameters of the variational circuit. We show that these approaches are applicable to a wide range of Hamiltonian and provide significant improvement in the optimization procedure.https://quantum-journal.org/papers/q-2020-09-16-324/pdf/ |
| spellingShingle | Chufan Lyu Victor Montenegro Abolfazl Bayat Accelerated variational algorithms for digital quantum simulation of many-body ground states Quantum |
| title | Accelerated variational algorithms for digital quantum simulation of many-body ground states |
| title_full | Accelerated variational algorithms for digital quantum simulation of many-body ground states |
| title_fullStr | Accelerated variational algorithms for digital quantum simulation of many-body ground states |
| title_full_unstemmed | Accelerated variational algorithms for digital quantum simulation of many-body ground states |
| title_short | Accelerated variational algorithms for digital quantum simulation of many-body ground states |
| title_sort | accelerated variational algorithms for digital quantum simulation of many body ground states |
| url | https://quantum-journal.org/papers/q-2020-09-16-324/pdf/ |
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