Importance sampling for stochastic quantum simulations
Simulating many-body quantum systems is a promising task for quantum computers. However, the depth of most algorithms, such as product formulas, scales with the number of terms in the Hamiltonian, and can therefore be challenging to implement on near-term, as well as early fault-tolerant quantum dev...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-04-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-04-13-977/pdf/ |
| _version_ | 1797847533137952768 |
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| author | Oriel Kiss Michele Grossi Alessandro Roggero |
| author_facet | Oriel Kiss Michele Grossi Alessandro Roggero |
| author_sort | Oriel Kiss |
| collection | DOAJ |
| description | Simulating many-body quantum systems is a promising task for quantum computers. However, the depth of most algorithms, such as product formulas, scales with the number of terms in the Hamiltonian, and can therefore be challenging to implement on near-term, as well as early fault-tolerant quantum devices. An efficient solution is given by the stochastic compilation protocol known as qDrift, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. In this work, we unify the qDrift protocol with importance sampling, allowing us to sample from arbitrary probability distributions, while controlling both the bias, as well as the statistical fluctuations. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage.
Moreover, we incorporate recent work on composite channel and compute rigorous bounds on the bias and variance, showing how to choose the number of samples, experiments, and time steps for a given target accuracy. These results lead to a more efficient implementation of the qDrift protocol, both with and without the use of composite channels. Theoretical results are confirmed by numerical simulations performed on a lattice nuclear effective field theory. |
| first_indexed | 2024-04-09T18:12:59Z |
| format | Article |
| id | doaj.art-f5a8b61bdc0644deb2666d54db0c1375 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-09T18:12:59Z |
| publishDate | 2023-04-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-f5a8b61bdc0644deb2666d54db0c13752023-04-13T12:37:08ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-04-01797710.22331/q-2023-04-13-97710.22331/q-2023-04-13-977Importance sampling for stochastic quantum simulationsOriel KissMichele GrossiAlessandro RoggeroSimulating many-body quantum systems is a promising task for quantum computers. However, the depth of most algorithms, such as product formulas, scales with the number of terms in the Hamiltonian, and can therefore be challenging to implement on near-term, as well as early fault-tolerant quantum devices. An efficient solution is given by the stochastic compilation protocol known as qDrift, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. In this work, we unify the qDrift protocol with importance sampling, allowing us to sample from arbitrary probability distributions, while controlling both the bias, as well as the statistical fluctuations. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Moreover, we incorporate recent work on composite channel and compute rigorous bounds on the bias and variance, showing how to choose the number of samples, experiments, and time steps for a given target accuracy. These results lead to a more efficient implementation of the qDrift protocol, both with and without the use of composite channels. Theoretical results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.https://quantum-journal.org/papers/q-2023-04-13-977/pdf/ |
| spellingShingle | Oriel Kiss Michele Grossi Alessandro Roggero Importance sampling for stochastic quantum simulations Quantum |
| title | Importance sampling for stochastic quantum simulations |
| title_full | Importance sampling for stochastic quantum simulations |
| title_fullStr | Importance sampling for stochastic quantum simulations |
| title_full_unstemmed | Importance sampling for stochastic quantum simulations |
| title_short | Importance sampling for stochastic quantum simulations |
| title_sort | importance sampling for stochastic quantum simulations |
| url | https://quantum-journal.org/papers/q-2023-04-13-977/pdf/ |
| work_keys_str_mv | AT orielkiss importancesamplingforstochasticquantumsimulations AT michelegrossi importancesamplingforstochasticquantumsimulations AT alessandroroggero importancesamplingforstochasticquantumsimulations |