On low-depth algorithms for quantum phase estimation

Hongkang, Ni,; Li, Haoya; Ying, Lexing

doi:10.48550/arxiv.2302.02454

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…But its subroutine with IQFT requires a lot of resources, in terms of gates and qubits, for even relatively small quantum systems. Although recent developments in QPE are explored to minimize depth [116] and computational resources [80], exploring the true potential of QPE is beyond the capabilities of present NISQ devices.…”

Section: Introductionmentioning

confidence: 99%

Plant biodiversity data set of eleven mountains, China

Liu¹,

Xu²,

Jin³

et al.

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Section: Introductionmentioning

confidence: 99%

Plant biodiversity data set of eleven mountains, China

Liu¹,

Xu²,

Jin³

et al.

Science Data Bank Datasets

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Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers

Ding,

Lin

2023

Quantum

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We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis demonstrates that the algorithm exhibits Heisenberg-limited scaling in terms of circuit depth and total cost. Notably, the proposed quantum circuit utilizes just one ancilla qubit, and with appropriate initial state conditions, it achieves significantly shorter circuit depths compared to circuits based on quantum phase estimation (QPE). Numerical results suggest that compared to QPE, the circuit depth can be reduced by around two orders of magnitude under several settings for estimating ground-state and excited-state energies of certain quantum systems.

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Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision

Wang,

França,

Zhang

et al. 2023

Quantum

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A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will require some degree of fault tolerance. While hardware is improving towards this milestone, optimizing quantum algorithms also brings it closer to the present. Existing methods for ground state energy estimation are costly in that they require a number of gates per circuit that grows exponentially with the desired number of bits in precision. We reduce this cost exponentially, by developing a ground state energy estimation algorithm for which this cost grows linearly in the number of bits of precision. Relative to recent resource estimates of ground state energy estimation for the industrially-relevant molecules of ethylene-carbonate and PF6−, the estimated gate count and circuit depth is reduced by a factor of 43 and 78, respectively. Furthermore, the algorithm can use additional circuit depth to reduce the total runtime. These features make our algorithm a promising candidate for realizing quantum advantage in the era of early fault-tolerant quantum computing.

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On low-depth algorithms for quantum phase estimation

Cited by 3 publications

References 16 publications

Plant biodiversity data set of eleven mountains, China

Plant biodiversity data set of eleven mountains, China

Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers

Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision

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