Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910309257576448 |
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| author | Begušić, Tomislav Gray, Johnnie Chan, Garnet Kin-Lic |
| author_facet | Begušić, Tomislav Gray, Johnnie Chan, Garnet Kin-Lic |
| contents | A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment, and can also be systematically converged beyond the experimental accuracy. Our most accurate technique combines a mixed Schrödinger and Heisenberg tensor network representation with the Bethe free entropy relation of belief propagation to compute expectation values with an effective wavefunction-operator sandwich bond dimension >16,000,000, achieving an absolute accuracy, without extrapolation, in the observables of <0.01, which is converged for many practical purposes. We thereby identify inaccuracies in the experimental extrapolations and suggest how future experiments can be implemented to increase the classical hardness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05077 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance Begušić, Tomislav Gray, Johnnie Chan, Garnet Kin-Lic Quantum Physics A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment, and can also be systematically converged beyond the experimental accuracy. Our most accurate technique combines a mixed Schrödinger and Heisenberg tensor network representation with the Bethe free entropy relation of belief propagation to compute expectation values with an effective wavefunction-operator sandwich bond dimension >16,000,000, achieving an absolute accuracy, without extrapolation, in the observables of <0.01, which is converged for many practical purposes. We thereby identify inaccuracies in the experimental extrapolations and suggest how future experiments can be implemented to increase the classical hardness. |
| title | Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2308.05077 |