Quantum mechanical simulation of open electronic systems

Gajewski, Marvin, Somoza, Alejandro, Horstmann, Birger

While simple spin-boson models have been realized on quantum hardware, simulating extended electronic networks with vibrational environments remains a fundamental challenge in the presence of non-equilibrium, long-lived electronic-vibrational (vibronic) coherence. We present a toolbox for the digital simulation of large open quantum systems with structured environments. It exploits the intrinsic damping of qubits to reproduce vibrational relaxation in combination with a model-specific error mitigation scheme to filter out sources of noise that are not present in the target open system. We simulated a microscopic model of electron-transfer (ET) with a single donor and up to nine acceptor sites on a superconducting processor of IBM, using a model-specific error mitigation scheme. Our results using up to 20 qubits reveal a probability of ET that is well aligned with classical calculations where electronic and vibronic transfer resonances can be identified at the expected driving forces. We conducted 10 independent experiments per system size on different days, accounting for hourly fluctuations in error rates. We find that the most important ingredient for large-scale simulations is a large number of available qubits connected by high-fidelity gates, with coherence times above the threshold set by the target open system. Because the vibronic mechanism of electron transfer is entanglement-driven, our simulation is a natural application-based benchmark, in which the hardware capacity to produce and sustain entanglement is quantified by the maximum system size for which the hardware produces accurate results.

Damiano Marian, Enrique Colomés

When talking about noise in quantum devices two issues must be faced: how to model the evolution of an electronic system with scattering and how this noise is practically computed in a quantum device simulator. In the present paper, we address both problems from a practical and computational point of view. In particular, as the electronic quantum subsystem is an open (normally far from equilibrium) system, we use the notion of conditional wave function, the wave function of a subsystem in Bohmian mechanics, an alternative version of quantum mechanics which along with the wave function posited definite positions for the particles. This allows us to define an effective equation in several physical situations, ranging from the simple tunneling barrier to the interaction with a bath of phonons. Finally, we present how this development can be used to compute quantum noise in a quantum device simulator.

Ryan Sweke

Akakii Melikidze

Xavier Oriols

The experimental current measured in quantum‐based devices fluctuates around average values due to the quantum mechanical wave‐particle duality. An alternative quantum noise approach, based on the de Broglie‐Bohm interpretation of the quantum theory, is presented. Since this formalism directly deals with the wave and particle nature of electrons, it provides an excellent framework to study quantum noise. In fact, most of the numerical techniques used in classical Monte Carlo simulations can be directly adapted to our quantum formalism. Simulated noise results for interacting electrons tunnelling through double barriers are presented in agreement with experimental results. The present approach opens a new path for studying electron transport and quantum noise in mesoscopic systems.