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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.17816 |
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| _version_ | 1866910717817389056 |
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| author | Silva, Thais de Lima Borges, Lucas Aolita, Leandro |
| author_facet | Silva, Thais de Lima Borges, Lucas Aolita, Leandro |
| contents | Estimating quantum partition functions is a critical task in a variety of fields. However, the problem is classically intractable in general due to the exponential scaling of the Hamiltonian dimension $N$ in the number of particles. This paper introduces a quantum algorithm for estimating the partition function $Z_β$ of a generic Hamiltonian $H$ up to multiplicative error based on a quantum coin toss. The coin is defined by the probability of applying the quantum imaginary-time evolution propagator $f_β[H]=e^{-βH/{2}}$ at inverse temperature $β$ to the maximally mixed state, realized by a block-encoding of $f_β[H]$ into a unitary quantum circuit followed by a post-selection measurement. Our algorithm does not use costly subroutines such as quantum phase estimation or amplitude amplification; and the binary nature of the coin allows us to invoke tools from Bernoulli-process analysis to prove a runtime scaling as $\mathcal{O}(N/{Z_β})$, quadratically better than previous general-purpose algorithms using similar quantum resources. Moreover, since the coin is defined by a single observable, the method lends itself well to quantum error mitigation. We test this in practice with a proof-of-concept 9-qubit experiment, where we successfully mitigate errors through a simple noise-extrapolation procedure. Our findings offer an interesting alternative for quantum partition function estimation relevant to early-fault quantum hardware. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partition function estimation with a quantum coin toss Silva, Thais de Lima Borges, Lucas Aolita, Leandro Quantum Physics Estimating quantum partition functions is a critical task in a variety of fields. However, the problem is classically intractable in general due to the exponential scaling of the Hamiltonian dimension $N$ in the number of particles. This paper introduces a quantum algorithm for estimating the partition function $Z_β$ of a generic Hamiltonian $H$ up to multiplicative error based on a quantum coin toss. The coin is defined by the probability of applying the quantum imaginary-time evolution propagator $f_β[H]=e^{-βH/{2}}$ at inverse temperature $β$ to the maximally mixed state, realized by a block-encoding of $f_β[H]$ into a unitary quantum circuit followed by a post-selection measurement. Our algorithm does not use costly subroutines such as quantum phase estimation or amplitude amplification; and the binary nature of the coin allows us to invoke tools from Bernoulli-process analysis to prove a runtime scaling as $\mathcal{O}(N/{Z_β})$, quadratically better than previous general-purpose algorithms using similar quantum resources. Moreover, since the coin is defined by a single observable, the method lends itself well to quantum error mitigation. We test this in practice with a proof-of-concept 9-qubit experiment, where we successfully mitigate errors through a simple noise-extrapolation procedure. Our findings offer an interesting alternative for quantum partition function estimation relevant to early-fault quantum hardware. |
| title | Partition function estimation with a quantum coin toss |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.17816 |