Synthesizing efficient circuits for Hamiltonian simulation
Abstract We provide an approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations. The total number of gates, especially CNOT, reduce in many cases. We show...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-04-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-023-00697-6 |
| _version_ | 1797849918596972544 |
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| author | Priyanka Mukhopadhyay Nathan Wiebe Hong Tao Zhang |
| author_facet | Priyanka Mukhopadhyay Nathan Wiebe Hong Tao Zhang |
| author_sort | Priyanka Mukhopadhyay |
| collection | DOAJ |
| description | Abstract We provide an approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations. The total number of gates, especially CNOT, reduce in many cases. We show that it is possible to implement an exponentiated sum of commuting Paulis with at most m (controlled)-rotation gates, where m is the number of distinct non-zero eigenvalues (ignoring sign). Thus we can collect mutually commuting Hamiltonian terms into groups satisfying one of several symmetries identified in this work. This allows an inexpensive simulation of the entire group of terms. We further show that the cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings. |
| first_indexed | 2024-04-09T18:52:59Z |
| format | Article |
| id | doaj.art-a295874f60e44b6d8e9e1d3695309278 |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-04-09T18:52:59Z |
| publishDate | 2023-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-a295874f60e44b6d8e9e1d36953092782023-04-09T11:23:31ZengNature Portfolionpj Quantum Information2056-63872023-04-019111710.1038/s41534-023-00697-6Synthesizing efficient circuits for Hamiltonian simulationPriyanka Mukhopadhyay0Nathan Wiebe1Hong Tao Zhang2Institute for Quantum Computing, University of WaterlooDepartment of Computer Science, University of TorontoDepartment of Mathematics, University of TorontoAbstract We provide an approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations. The total number of gates, especially CNOT, reduce in many cases. We show that it is possible to implement an exponentiated sum of commuting Paulis with at most m (controlled)-rotation gates, where m is the number of distinct non-zero eigenvalues (ignoring sign). Thus we can collect mutually commuting Hamiltonian terms into groups satisfying one of several symmetries identified in this work. This allows an inexpensive simulation of the entire group of terms. We further show that the cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings.https://doi.org/10.1038/s41534-023-00697-6 |
| spellingShingle | Priyanka Mukhopadhyay Nathan Wiebe Hong Tao Zhang Synthesizing efficient circuits for Hamiltonian simulation npj Quantum Information |
| title | Synthesizing efficient circuits for Hamiltonian simulation |
| title_full | Synthesizing efficient circuits for Hamiltonian simulation |
| title_fullStr | Synthesizing efficient circuits for Hamiltonian simulation |
| title_full_unstemmed | Synthesizing efficient circuits for Hamiltonian simulation |
| title_short | Synthesizing efficient circuits for Hamiltonian simulation |
| title_sort | synthesizing efficient circuits for hamiltonian simulation |
| url | https://doi.org/10.1038/s41534-023-00697-6 |
| work_keys_str_mv | AT priyankamukhopadhyay synthesizingefficientcircuitsforhamiltoniansimulation AT nathanwiebe synthesizingefficientcircuitsforhamiltoniansimulation AT hongtaozhang synthesizingefficientcircuitsforhamiltoniansimulation |