Browsing by Author "Barron, George S."

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    Adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer
    Zhu, Linghua; Tang, Ho Lun; Barron, George S.; Calderon-Vargas, F. A.; Mayhall, Nicholas J.; Barnes, Edwin Fleming; Economou, Sophia E. (American Physical Society, 2022-07-11)
    The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA Ansatz is not optimal, there is no systematic approach for finding better Ansatze. We address this problem by developing an iterative version of QAOA that is problem tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity.
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    Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm
    Gard, Bryan T.; Zhu, Linghua; Barron, George S.; Mayhall, Nicholas J.; Economou, Sophia E.; Barnes, Edwin Fleming (2020-01-28)
    The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multiqubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. We test our circuits in quantum simulations of the H2 and LiH molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth.
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    Gate-free state preparation for fast variational quantum eigensolver simulations
    Meitei, Oinam Romesh; Gard, Bryan T.; Barron, George S.; Pappas, David P.; Economou, Sophia E.; Barnes, Edwin Fleming; Mayhall, Nicholas J. (Springer Nature, 2021-10-27)
    The variational quantum eigensolver is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. The algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state, and then measuring the molecular energy. Due to finite coherence times and gate errors, the number of gates that can be implemented remains limited. In this work, we propose an alternative algorithm where device-level pulse shapes are variationally optimized for the state preparation rather than using an abstract-level quantum circuit. In doing so, the coherence time required for the state preparation is drastically reduced. We numerically demonstrate this by directly optimizing pulse shapes which accurately model the dissociation of H2 and HeH+, and we compute the ground state energy for LiH with four transmons where we see reductions in state preparation times of roughly three orders of magnitude compared to gate-based strategies.
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    Preparing Bethe Ansatz Eigenstates on a Quantum Computer
    Van Dyke, John S.; Barron, George S.; Mayhall, Nicholas J.; Barnes, Edwin Fleming; Economou, Sophia E. (2021-11-09)
    Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for which analytic results are unavailable and which are also not well described by approximate numerical methods. Preparing Bethe ansatz eigenstates directly on a quantum computer would allow straightforward extraction of these quantities via measurement. We present a quantum algorithm for preparing Bethe ansatz eigenstates of the spin-1/2 XXZ spin chain that correspond to real-valued solutions of the Bethe equations. The algorithm is polynomial in the number of T gates and the circuit depth, with modest constant prefactors. Although the algorithm is probabilistic, with a success rate that decreases with increasing eigenstate energy, we employ amplitude amplification to boost the success probability. The resource requirements for our approach are lower than for other state-of-the-art quantum simulation algorithms for small error-corrected devices and thus may offer an alternative and computationally less demanding demonstration of quantum advantage for physically relevant problems.
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    Scaling adaptive quantum simulation algorithms via operator pool tiling
    Van Dyke, John S.; Shirali, Karunya; Barron, George S.; Mayhall, Nicholas J.; Barnes, Edwin; Economou, Sophia E. (American Physical Society, 2024-02-16)
    Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wave functions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) calculation on a smaller instance of the problem using a large, but computationally inefficient, operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems.