Positional Optimization for Pulse-Based Variational Quantum Eigensolvers

We address the task of estimating the ground-state energy of Hamiltonians coming from chemistry. We study numerically the behavior of a digital-analog variational quantum eigensolver for the ${\mathrm{H}}_{2}$ , LiH, and ${\mathrm{BeH}}_{2}$ molecules, and we observe that one can estimate the energy to a few percent points of error leveraging on learning the atom register positions with respect to selected features of the molecular Hamiltonian and then an iterative pulse-shaping optimization, where each step performs a derandomization energy estimation.We address the task of estimating the ground-state energy of Hamiltonians coming from chemistry. We study numerically the behavior of a digital-analog variational quantum eigensolver for the ${\mathrm{H}}_{2}$, LiH, and ${\mathrm{BeH}}_{2}$ molecules, and we observe that one can estimate the energy to a few percent points of error leveraging on learning the atom register positions with respect to selected features of the molecular Hamiltonian and then an iterative pulse-shaping optimization, where each step performs a derandomization energy estimation.

arXiv:2301.06453Physical Review AApr 6, 202314 citations

Variational Quantum Eigensolver and Its Applications

Atsushi Matsuo

Lecture notes in computer scienceJan 1, 20211 citation

Parametrization and optimizability of pulse-level variational quantum eigensolvers

Kyle Sherbert, Hisham Amer, Sophia E. Economou +2 more

In conventional variational quantum eigensolvers (VQEs), trial states are prepared by applying series of parametrized gates to a reference state, with the gate parameters being varied to minimize the energy of the target system. Recognizing that the gates are intermediates, which are ultimately compiled into a set of control pulses to be applied to each qubit in the lab, the recently proposed ctrl-VQE algorithm takes the amplitudes, frequencies, and phases of the pulse as the variational parameters used to minimize the molecular energy. In this work, we explore how all 3 degrees of freedom interrelate with one another. To this end, we consider several distinct strategies to parametrize the control pulses, assessing each one through numerical simulations of a transmonlike device. For each parametrization, we contrast the pulse duration required to prepare a good ansatz, and the difficulty to optimize that ansatz from a well-defined initial state. We deduce several guiding heuristics to implement practical ctrl-VQE in hardware, which we anticipate will generalize for generic device architectures.In conventional variational quantum eigensolvers (VQEs), trial states are prepared by applying series of parametrized gates to a reference state, with the gate parameters being varied to minimize the energy of the target system. Recognizing that the gates are intermediates, which are ultimately compiled into a set of control pulses to be applied to each qubit in the lab, the recently proposed ctrl-VQE algorithm takes the amplitudes, frequencies, and phases of the pulse as the variational parameters used to minimize the molecular energy. In this work, we explore how all 3 degrees of freedom interrelate with one another. To this end, we consider several distinct strategies to parametrize the control pulses, assessing each one through numerical simulations of a transmonlike device. For each parametrization, we contrast the pulse duration required to prepare a good ansatz, and the difficulty to optimize that ansatz from a well-defined initial state. We deduce several guiding heuristics to implement practical ctrl-VQE in hardware, which we anticipate will generalize for generic device architectures.

arXiv:2405.15166Physical Review AppliedFeb 14, 20256 citations

A Domain-agnostic, Noise-resistant Evolutionary Variational Quantum Eigensolver for Hardware-efficient Optimization in the Hilbert Space.

Arthur G. Rattew, Shaohan Hu, Marco Pistoia +2 more

Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to $18.6\times$ shallower and use up to $12\times$ fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least $3.6\times$ less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to $18.6\times$ shallower and use up to $12\times$ fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least $3.6\times$ less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.

Oct 21, 20193 citations

Acceleration of Variational Quantum Eigen Solver

Manish Modani

Lecture notes in networks and systemsJan 1, 20240 citations

We address the task of estimating the ground-state energy of Hamiltonians coming from chemistry. We study numerically the behavior of a digital-analog variational quantum eigensolver for the

{\mathrm{H}}_{2}

, LiH, and

{\mathrm{BeH}}_{2}

molecules, and we observe that one can estimate the energy to a few percent points of error leveraging on learning the atom register positions with respect to selected features of the molecular Hamiltonian and then an iterative pulse-shaping optimization, where each step performs a derandomization energy estimation.

18.6\times

shallower and use up to

12\times

fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least

3.6\times

less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.