Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
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| Format: | Preprint |
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2024
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| _version_ | 1866918151748321280 |
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| author | Li, Zhiyao Grabowska, Dorota M. Savage, Martin J. |
| author_facet | Li, Zhiyao Grabowska, Dorota M. Savage, Martin J. |
| contents | We introduce the Sequency Hierarchy Truncation (SeqHT) scheme for reducing the resources required for state preparation and time evolution in quantum simulations, based upon a truncation in sequency. For the $λϕ^4$ interaction in scalar field theory, or any interaction with a polynomial expansion, upper bounds on the contributions of operators of a given sequency are derived. For the systems we have examined, observables computed in sequency-truncated wavefunctions, including quantum correlations as measured by magic, are found to step-wise converge to their exact values with increasing cutoff sequency. The utility of SeqHT is demonstrated in the adiabatic state preparation of the $λϕ^4$ anharmonic oscillator ground state using IBM's quantum computer ${\textit ibm\_sherbrooke}$. Using SeqHT, the depth of the required quantum circuits is reduced by $\sim 30\%$, leading to significantly improved determinations of observables in the quantum simulations. More generally, SeqHT is expected to lead to a reduction in required resources for quantum simulations of systems with a hierarchy of length scales. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations Li, Zhiyao Grabowska, Dorota M. Savage, Martin J. Quantum Physics High Energy Physics - Lattice Nuclear Theory We introduce the Sequency Hierarchy Truncation (SeqHT) scheme for reducing the resources required for state preparation and time evolution in quantum simulations, based upon a truncation in sequency. For the $λϕ^4$ interaction in scalar field theory, or any interaction with a polynomial expansion, upper bounds on the contributions of operators of a given sequency are derived. For the systems we have examined, observables computed in sequency-truncated wavefunctions, including quantum correlations as measured by magic, are found to step-wise converge to their exact values with increasing cutoff sequency. The utility of SeqHT is demonstrated in the adiabatic state preparation of the $λϕ^4$ anharmonic oscillator ground state using IBM's quantum computer ${\textit ibm\_sherbrooke}$. Using SeqHT, the depth of the required quantum circuits is reduced by $\sim 30\%$, leading to significantly improved determinations of observables in the quantum simulations. More generally, SeqHT is expected to lead to a reduction in required resources for quantum simulations of systems with a hierarchy of length scales. |
| title | Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations |
| topic | Quantum Physics High Energy Physics - Lattice Nuclear Theory |
| url | https://arxiv.org/abs/2407.13835 |