Reliability of Quantum Simulation on NISQ-era Devices
February 17, 2022
Title: Reliability of Quantum Simulation on NISQ-era Devices
Dissertation Committee
- Advisor: Ivan H. Deutsch
- Committee member: Pablo M. Poggi
- Committee member: Tameem Albash
- External committee member: Poul S. Jessen
Abstract: Noisy intermediate-scale quantum (NISQ)-era devices are moderately sized devices (∼100 qubits) that are well controlled but lack full fault-tolerant error correction. The main objective of these devices is to carry out tasks such as studying the dynamics of many-body quantum systems that cannot be efficiently simulated on a classical computer but that are less-demanding than universal quantum computing. We have studied the reliability of these devices in presence of errors and imperfections with a focus on exploring the relationship between the physical properties of the system being simulated and the errors in the output of the simulator. For this, we focused on the simulation of a particular class of mean-field spin systems known as 𝑝-spin models. Using these models, we have explored the reliability of quantum simulation in two different paradigms. We first considered simulation of the Lipkin-Meshkov-Glick (LMG) model (particular instance of 𝑝-spin model), which is integrable in the mean-field limit, but becomes chaotic in the presence of a background time-dependent perturbation [1]. Here, we showed that the quantities that depend on the global structure of the phase space, such as critical point estimates of the quantum phase transition, are robust to the presence of this perturbation while other aspects of the system such as the mean magnetization that depend on the local trajectories are fragile and cannot be reliably extracted from the simulator. Next, we analyzed the effects of Trotterization on the simulation of 𝑝-spin models and identified the existence of “structural instability regions” in the Trotterized unitary map that are absent in the time evolution operator of the ideal 𝑝-spin model [2]. We showed that, even in the absence of chaos, Trotter errors proliferate in these structural instability regions, as the effective Hamiltonian associated with the Trotterized unitary becomes very different from the target 𝑝-spin Hamiltonian.
