State Preparation Boosters for Early Fault-Tolerant Quantum Computation

Abstract

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.

Computing Ground State Properties with Early Fault-Tolerant Quantum Computers

“…trading time resources for space resources). All of these features make our algorithm a great candidate for realizing quantum advantage for industrially-relevant problems on early fault-tolerant quantum computers [33,25,15,14,39,47,40,48].…”

Inverse iteration quantum eigensolvers assisted with a continuous variable

“…The construction of such nonunitary operators, derived from functions of the target Hamiltonian. Examples include imaginary time evolution [15,16,17,18,19,20,21,22], QGF algorithms [23,24,25,26], cosine filter algorithms [27,28], sine filter algorithms [29], powered Hamiltonian operator algorithms [30,31], and quantum inverse iteration method [32,33]. The non-trivial implementation of these nonunitary operators on quantum computers has prompted methods like linear combination of unitaries [27], energy sequential estimation [32], and variational techniques [15].…”

Sparse Quantum State Preparation for Strongly Correlated Systems

“…The resulting quantum circuits exhibit an insignificant circuit depth in the context of early fault-tolerant era. It is worth noting that an entirely different class of procedures conducts state preparation directly within the quantum computer, either through adiabatic state preparation 5 or by leveraging ground-state boosting 44 based only on the information provided by the system's Hamiltonian. While these approaches may seem more scalable than classical state preparation algorithms, they introduce a substantial quantum resource overhead for medium-sized systems, making them inherently more appropriate for the longer term.…”