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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 stateoftheart quantum algorithm for groundstate generation, overcomes the groundstategeneration bottleneck of the prior approach and is optimal up to a polylogarithmic factor. Specifically, we establish two quantum algorithms—Fourierbased and waveletbased—to generate the ground state of a free massive scalar bosonic QFT with gate complexity quasilinear in the number of discretized QFT modes. The Fourierbased algorithm is limited to translationally invariant QFTs. Numerical simulations show that the waveletbased 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 onedimensional Gaussian (1DG) states. We replace the standard method for 1DGstate 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 1DGstate 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 

Article number  020364 
Pages (fromto)  020364102036466 
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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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

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
