Reconstructing the ideal results of a perturbed analog quantum simulator

Abstract

Well-controlled quantum systems can potentially be used as quantum simulators. However, a quantum simulator is inevitably perturbed by coupling to additional degrees of freedom. This constitutes a major roadblock to useful quantum simulations. So far there are only limited means to understand the effect of perturbation on the results of quantum simulation. Here, we present a method which, in certain circumstances, allows for the reconstruction of the ideal result from measurements on a perturbed quantum simulator. We consider extracting the value of the correlator Ô i (t)Ô j (0) from the simulated system, whereÔ i are the operators which couple the system to its environment. The ideal correlator can be straightforwardly reconstructed by using statistical knowledge of the environment, if any n-time correlator of operatorsÔ i of the ideal system can be written as products of two-time correlators. We give an approach to verify the validity of this assumption experimentally by additional measurements on the perturbed quantum simulator. The proposed method can allow for reliable quantum simulations with systems subjected to environmental noise without adding an overhead to the quantum system.

Quantum optimization using variational algorithms on near-term quantum devices

“…Recent experiments in which the quantum simulation of small molecules was performed [72] showed that even for very short-depth circuits the effects of decoherence become apparent. For the simulation to be of value, the effect of this error needs to be mitigated, and several proposals have been made to deal with the effects of decoherence in short-depth quantum computation [106,39,55,54].…”

“…Still, novel schemes that do not require ancillas or code qubits can help mitigate induced errors, enabling longer and bigger quantum computations. Such error mitigation schemes [54,55] need to be developed further and tested to improve accuracy without the full overhead of error-correction codes for universal quantum computing.…”

Kolmogorov-Arnold-Moser Stability for Conserved Quantities in Finite-Dimensional Quantum Systems

“…The importance of robust observables is exemplified by analogue quantum simulations [5], where the aim is to run a complex Hamiltonian long enough such that observable quantities are no longer easily computable by classical computers. The problem is, however, that small perturbations in the lab are not under control and can destroy the reliability of the simulation [6,7]. On the other hand, as we show below, the expectation values of robust observables remain reliable even on the long term.…”

Mitigating Depolarizing Noise on Quantum Computers with Noise-Estimation Circuits

“…A circuit is executed multiple times with a varying degrees of noise and the measured output is extrapolated to the zero-noise limit. Other mitigation methods have been developed as well [23][24][25][26][27][28][29][30][31][32][33][34][35].…”