Error Analysis of the Variational Quantum Eigensolver Algorithm

Abstract

Variational quantum algorithms have been one of the most intensively studied applications for near-term quantum computing applications. The noisy intermediate-scale quantum (NISQ) regime, where small enough algorithms can be run successfully on noisy quantum computers expected during the next 5 years, is driving both a large amount of research work and a significant amount of private sector funding. Therefore, it is important to understand whether variational algorithms are effective at successfully converging to the correct answer in presence of noise. We perform a comprehensive study of the variational quantum eigensolver (VQE) and its individual quantum subroutines. Building on asymptotic bounds, we show through explicit simulation that the VQE algorithm effectively collapses already when single errors occur during a quantum processing call. We discuss the significant implications of this result in the context of being able to run any variational type algorithm without resource expensive error correction protocols.

Noise-robust ground state energy estimates from deep quantum circuits

“…We find that, in most cases of a well chosen ansatz on current NISQ hardware and under noisy simulation, QCM finds a ground state energy estimate within this tolerance. This provides evidence in contrast to the NISQ prima facie view that useful information cannot be extracted from a noisy quantum computation over a typical circuit depth required by VQE [30].…”

“…The subfield of variational quantum computing has been burgeoning over the recent years [19] -with developments in the efficiency and scope of state preparation via adaptive algo-rithms [20,21] and symmetry preservation [22][23][24], and measurement of observables [25][26][27]. However, despite favourable NISQ-era prospects for VQE, its viability on present-day hardware is still heavily impacted by the overwhelming effect of errors and noise-induced barren plateaus [28][29][30]. VQE has been experimentally demonstrated for a variety of problem instances [16,18,25,[31][32][33], but has so far been inadequate in producing results for any problem that could be considered classically intractable [30,34].…”

“…However, despite favourable NISQ-era prospects for VQE, its viability on present-day hardware is still heavily impacted by the overwhelming effect of errors and noise-induced barren plateaus [28][29][30]. VQE has been experimentally demonstrated for a variety of problem instances [16,18,25,[31][32][33], but has so far been inadequate in producing results for any problem that could be considered classically intractable [30,34]. Solving larger problems on noisy devices using VQE is difficult because variational quantum algorithms have a tension to overcome: the necessary precision in practical application requires encoded trial states with large ground state overlap for the problem Hamiltonian, but better ansätze have high circuit depth and are thus typically incompatible with NISQ devices due to the high amount of noise introduced in the energy expectation value estimate H .…”