Minimizing state preparation times in pulse-level variational molecular simulations

Abstract

Quantum simulation on NISQ devices is severely limited by short coherence times. A variational pulse-shaping algorithm known as ctrl-VQE was recently proposed to address this issue by eliminating the need for parameterized quantum circuits, which lead to long state preparation times. Here, we find the shortest possible pulses for ctrl-VQE to prepare target molecular wavefunctions for a given device Hamiltonian describing coupled transmon qubits. We find that the time-optimal pulses that do this have a bang-bang form consistent with Pontryagin's maximum principle. We further investigate how the minimal state preparation time is impacted by truncating the transmons to two versus more levels. We find that leakage outside the computational subspace (something that is usually considered problematic) speeds up the state preparation, further reducing device coherencetime demands. This speedup is due to an enlarged solution space of target wavefunctions and to the appearance of additional channels connecting initial and target states.

Pulse based Variational Quantum Optimal Control for hybrid quantum computing

“…Quantum optimal control theory has been connected to variational state preparation in several works [1,2,33] over the last few years. Recent work has shown that pulse-based methods can indeed prepare desired states in the minimum evolution time set by the quantum speed limit [33].…”

“…Quantum optimal control theory has been connected to variational state preparation in several works [1,2,33] over the last few years. Recent work has shown that pulse-based methods can indeed prepare desired states in the minimum evolution time set by the quantum speed limit [33]. Furthermore, constructing specific control pulses for gate designs focusing on high-fidelity [34][35][36] and robust [37,38] gates have been a lively topic of research.…”

Quantum simulation of molecular response properties

“…The variational eigensolver (VQE) method [10] attempts to overcome some of these limitations by ensuring shallow quantum circuits through a variational optimization of the quantum circuit parameters. This has allowed for the development of a number of quantum algorithms for the simulation of molecular ground [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and excited states [27][28][29][30][31][32][33][34][35][36]. Aside from the VQE method, algorithms based on quantum phase estimation [37,38], adiabatic state preparation [39,40], and Krylov subspace generation [41][42][43] have also been developed for molecular simulations.…”

ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus

“…al. 4 as a hybrid quantum-classical approach to finding approximate eigenvalues of a Hamiltonian, H. In VQE, a quantum processor is used to apply a parameterized unitary transformation expressed as a quantum circuit (or even a direct pulse [5][6][7] ), U (θ), to some easily prepared reference state, |0 . 4,[8][9][10][11] The target Hamiltonian is then measured with the prepared state to obtain the energy as a function of circuit parameters:…”

“…Bittel and Kliesch have identified situations where there are so many far-from-optimal local minima that VQEs must be NP-hard in general. 13 The problem of local minima can be ameliorated through overparametrization in both quantum optimal control 5,14 and classical neural network settings. 15,16 This idea of overparametrization avoiding local minima has since been applied to VQEs: Rivera-Dean et.…”