Hardware-tailored diagonalization circuits
Abstract A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits can be executed reliably o...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-11-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-024-00901-1 |
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| _version_ | 1846158292381859840 |
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| author | Daniel Miller Laurin E. Fischer Kyano Levi Eric J. Kuehnke Igor O. Sokolov Panagiotis Kl. Barkoutsos Jens Eisert Ivano Tavernelli |
| author_facet | Daniel Miller Laurin E. Fischer Kyano Levi Eric J. Kuehnke Igor O. Sokolov Panagiotis Kl. Barkoutsos Jens Eisert Ivano Tavernelli |
| author_sort | Daniel Miller |
| collection | DOAJ |
| description | Abstract A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits can be executed reliably on near-term quantum computers. Generic diagonalization circuits, in contrast, often lead to an unaffordable SWAP gate overhead on quantum devices with limited hardware connectivity. A common alternative is to exclude two-qubit gates altogether. However, this comes at the severe cost of restricting the class of diagonalizable sets of Pauli operators to tensor product bases (TPBs). In this article, we introduce a theoretical framework for constructing hardware-tailored (HT) diagonalization circuits. Our framework establishes a systematic and highly flexible procedure for tailoring diagonalization circuits with ultra-low gate counts. We highlight promising use cases of our framework and – as a proof-of-principle application – we devise an efficient algorithm for grouping the Pauli operators of a given Hamiltonian into jointly-HT-diagonalizable sets. For several classes of Hamiltonians, we observe that our approach requires fewer measurements than conventional TPB approaches. Finally, we experimentally demonstrate that HT circuits can improve the efficiency of estimating expectation values with cloud-based quantum computers. |
| format | Article |
| id | doaj-art-1825a941cc414038944bf0d50fd4866c |
| institution | Kabale University |
| issn | 2056-6387 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj-art-1825a941cc414038944bf0d50fd4866c2024-11-24T12:37:33ZengNature Portfolionpj Quantum Information2056-63872024-11-0110111110.1038/s41534-024-00901-1Hardware-tailored diagonalization circuitsDaniel Miller0Laurin E. Fischer1Kyano Levi2Eric J. Kuehnke3Igor O. Sokolov4Panagiotis Kl. Barkoutsos5Jens Eisert6Ivano Tavernelli7Dahlem Center for Complex Quantum Systems, Freie Universität BerlinIBM Quantum, IBM Research Europe—ZurichDahlem Center for Complex Quantum Systems, Freie Universität BerlinDahlem Center for Complex Quantum Systems, Freie Universität BerlinIBM Quantum, IBM Research Europe—ZurichIBM Quantum, IBM Research Europe—ZurichDahlem Center for Complex Quantum Systems, Freie Universität BerlinIBM Quantum, IBM Research Europe—ZurichAbstract A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits can be executed reliably on near-term quantum computers. Generic diagonalization circuits, in contrast, often lead to an unaffordable SWAP gate overhead on quantum devices with limited hardware connectivity. A common alternative is to exclude two-qubit gates altogether. However, this comes at the severe cost of restricting the class of diagonalizable sets of Pauli operators to tensor product bases (TPBs). In this article, we introduce a theoretical framework for constructing hardware-tailored (HT) diagonalization circuits. Our framework establishes a systematic and highly flexible procedure for tailoring diagonalization circuits with ultra-low gate counts. We highlight promising use cases of our framework and – as a proof-of-principle application – we devise an efficient algorithm for grouping the Pauli operators of a given Hamiltonian into jointly-HT-diagonalizable sets. For several classes of Hamiltonians, we observe that our approach requires fewer measurements than conventional TPB approaches. Finally, we experimentally demonstrate that HT circuits can improve the efficiency of estimating expectation values with cloud-based quantum computers.https://doi.org/10.1038/s41534-024-00901-1 |
| spellingShingle | Daniel Miller Laurin E. Fischer Kyano Levi Eric J. Kuehnke Igor O. Sokolov Panagiotis Kl. Barkoutsos Jens Eisert Ivano Tavernelli Hardware-tailored diagonalization circuits npj Quantum Information |
| title | Hardware-tailored diagonalization circuits |
| title_full | Hardware-tailored diagonalization circuits |
| title_fullStr | Hardware-tailored diagonalization circuits |
| title_full_unstemmed | Hardware-tailored diagonalization circuits |
| title_short | Hardware-tailored diagonalization circuits |
| title_sort | hardware tailored diagonalization circuits |
| url | https://doi.org/10.1038/s41534-024-00901-1 |
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