Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates
The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achiev...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/3/1/8 |
| _version_ | 1797417339512160256 |
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| author | Pejman Jouzdani Stefan Bringuier |
| author_facet | Pejman Jouzdani Stefan Bringuier |
| author_sort | Pejman Jouzdani |
| collection | DOAJ |
| description | The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection, an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground state and excited states of BeH<sub>2</sub> and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H<sub>2</sub> molecule. |
| first_indexed | 2024-03-09T06:18:21Z |
| format | Article |
| id | doaj.art-fcde3358fe3c4f8fae2c3d33cea8ce4c |
| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-09T06:18:21Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj.art-fcde3358fe3c4f8fae2c3d33cea8ce4c2023-12-03T11:51:37ZengMDPI AGQuantum Reports2624-960X2021-01-013113715210.3390/quantum3010008Hybrid Quantum-Classical Eigensolver without Variation or Parametric GatesPejman Jouzdani0Stefan Bringuier1General Atomics, San Diego, CA 92121, USAGeneral Atomics, San Diego, CA 92121, USAThe use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection, an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground state and excited states of BeH<sub>2</sub> and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H<sub>2</sub> molecule.https://www.mdpi.com/2624-960X/3/1/8quantum computingquantum algorithmsquantum chemistry |
| spellingShingle | Pejman Jouzdani Stefan Bringuier Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates Quantum Reports quantum computing quantum algorithms quantum chemistry |
| title | Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates |
| title_full | Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates |
| title_fullStr | Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates |
| title_full_unstemmed | Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates |
| title_short | Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates |
| title_sort | hybrid quantum classical eigensolver without variation or parametric gates |
| topic | quantum computing quantum algorithms quantum chemistry |
| url | https://www.mdpi.com/2624-960X/3/1/8 |
| work_keys_str_mv | AT pejmanjouzdani hybridquantumclassicaleigensolverwithoutvariationorparametricgates AT stefanbringuier hybridquantumclassicaleigensolverwithoutvariationorparametricgates |