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Abstract
We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory (QFT). Our quantum algorithm delivers a superquadratic speedup over the state-of-the-art quantum algorithm for ground-state generation, overcomes the ground-state-generation bottleneck of the prior approach and is optimal up to a polylogarithmic factor. Specifically, we establish two quantum algorithms—Fourier-based and wavelet-based—to generate the ground state of a free massive scalar bosonic QFT with gate complexity quasilinear in the number of discretized QFT modes. The Fourier-based algorithm is limited to translationally invariant QFTs. Numerical simulations show that the wavelet-based algorithm successfully yields the ground state for a QFT with broken translational invariance. Furthermore, the cost of preparing particle excitations in the wavelet approach is independent of the energy scale. Our algorithms require a routine for generating one-dimensional Gaussian (1DG) states. We replace the standard method for 1DG-state generation, which requires the quantum computer to perform lots of costly arithmetic, with a novel method based on inequality testing that significantly reduces the need for arithmetic. Our method for 1DG-state generation is generic and could be extended to preparing states whose amplitudes can be computed on the fly by a quantum computer.
Original language | English |
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Article number | 020364 |
Pages (from-to) | 020364-1-020364-66 |
Number of pages | 66 |
Journal | PRX Quantum |
Volume | 3 |
Issue number | 2 |
DOIs | |
Publication status | Published - 28 Jun 2022 |
Bibliographical note
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Dive into the research topics of 'Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory'. Together they form a unique fingerprint.Projects
- 3 Finished
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UTS led: Pushing the digital limits in quantum simulation for advanced manufacturing
Langford, N., Dehollain, J., Burgarth, D., Berry, D. & Heyl, M.
26/03/21 → 25/03/24
Project: Research
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Quantum limits on measurements in a universe with a minimum length scale
Menicucci, N. C., Brennen, G. & Kempf, A.
23/03/20 → 22/03/23
Project: Research
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