Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices

Dong, Yulong; Lin, Lin; Tong, Yu

doi:10.1103/prxquantum.3.040305

Cited by 65 publications

(63 citation statements)

References 53 publications

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“…• we show that this RPE algorithm satisfies the first three requirements listed above as long as the initial overlap is above 4 − 2 √ 3 ≈ 0.536. This is an improvement over the threshold 0.71 obtained in [5], and • we propose a modified algorithm with a much shorter circuit length when the overlap approaches 1. The precfactor of T max = Õ −1 can be as small as Θ(1 − p 0 ), which is better than the bound Θ( √ 1 − p 0 ) provided in [5].…”

Section: Introductionmentioning

confidence: 78%

“…Many alternatives for QPE have been proposed in the literature [3, 5, 6, 8, 13-15, 18, 19]. For a more comprehensive overview about the QPE algorithms, we refer to the detailed discussions in [5,15,17].…”

Section: Introductionmentioning

confidence: 99%

“…The third requirement is violated also by the Hadamard test. It has been pointed out in [5] that the only algorithm proven to meet all four requirements is the recent optimization-based algorithm proposed in [5].…”

Section: Introductionmentioning

confidence: 99%

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On low-depth algorithms for quantum phase estimation

Hongkang¹,

Li²,

Ying³

2023

Preprint

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Quantum phase estimation is one of the key building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant mismatch, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the overlap between the initial state and the target state approaches one. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. As a second contribution, we propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.2010 Mathematics Subject Classification. 81P60. Key words and phrases. Quantum phase estimation, early fault-tolerant quantum devices. We thank Lin Lin for communicating the recent development of quantum phase estimation.

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Section: Introductionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

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On low-depth algorithms for quantum phase estimation

Hongkang¹,

Li²,

Ying³

2023

Preprint

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“…Formally, let H = D j=1 λ j |λ j λ j | be a Hamiltonian with eigenvalues λ j 's and 1 Ref. [21] uses a technique called quantum eigenvalue transformation of unitary matrices (QET-U) which enables the implementation of certain polynomials of cos(H/2), where H is the Hamiltonian of interest. For ground state preparation, the polynomial approximates a threshold function so that the QET-U circuit approximately implements a projective measurement onto the low-energy and highenergy subspaces of H. The depths of the resulting circuits are proportional to the degree of this polynomial.…”

Section: Constructing State Preparation Boostersmentioning

confidence: 99%

“…After an earlier version of this paper was posted on arXiv, Dong et al [21] proposed two algorithms for approximately preparing the ground state of a given Hamiltonian on early fault-tolerant quantum computers. They aim to achieve a fidelity close to one in the output state, and hence the costs of their algorithms are relatively high.…”

Section: Introductionmentioning

confidence: 99%

State Preparation Boosters for Early Fault-Tolerant Quantum Computation

Wang¹,

Sim

Johnson

2022

Quantum

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Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum algorithms for quantum simulation, including VQE and many of its variants. However, for such algorithms to be useful, they need to overcome several critical barriers including the inability to prepare high-quality approximations of the ground state. Current challenges to state preparation, including barren plateaus and the high-dimensionality of the optimization landscape, make state preparation through ansatz optimization unreliable. In this work, we introduce the method of ground state boosting, which uses a limited-depth quantum circuit to reliably increase the overlap with the ground state. This circuit, which we call a booster, can be used to augment an ansatz from VQE or be used as a stand-alone state preparation method. The booster converts circuit depth into ground state overlap in a controllable manner. We numerically demonstrate the capabilities of boosters by simulating the performance of a particular type of booster, namely the Gaussian booster, for preparing the ground state of N2 molecular system. Beyond ground state preparation as a direct objective, many quantum algorithms, such as quantum phase estimation, rely on high-quality state preparation as a subroutine. Therefore, we foresee ground state boosting and similar methods as becoming essential algorithmic components as the field transitions into using early fault-tolerant quantum computers.

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