IQC PhD thesis defence - Matthew Duschenes

Candidate: Matthew Duschenes
Supervisor: Roger Melko
Location: QNC 2101

Understanding interactions between a system and its environment has consistently been at the centre of scientific studies. Indeed, environmental effects are far reaching and rich in behaviour, from heat baths leading to heat engines in thermodynamics, to non-conservative forces leading to dissipation in classical mechanics, to many-body interactions leading to emergent phenomena in statistical mechanics. As we transition from technologies based on classical phenomena, to technologies based on quantum phenomena, understanding system-environment interactions is the central challenge within quantum information sciences.

These interactions arise frequently in quantum settings, due to intentional non-unitary dynamics as part of quantum algorithms, inherent random dynamics within chaotic systems, or unintentional environmental noise in the absence of error mitigation. It is thus essential to derive any underlying structure from these interactions, and to determine their implications on the viability of emerging quantum technologies.

In this thesis, we conduct systematic analytical and numerical analyses of non-unitary dynamics. First, we study the practical effects of noise and experimental constraints on variational quantum algorithms. We find that objectives are initially robust to noise, and decrease exponentially with increased evolution time, before increasing polynomially with evolution time, due to an accumulation of errors. Second, we develop analytical tools to exactly compute statistics of ensembles of random quantum channels. Such formalisms allow us to derive hierarchies between ensembles, to define channel t-designs, and to show that generalized channel-design-induced concentration phenomena can occur. Third, we study distributions of probabilities of generalized measurement outcomes, given simulated noisy random quantum circuits. We develop an accurate and interpretable effective global noise model for these locally noisy distributions. Notably, we show that non-symmetric measurement distributions are multi-modal, whereas symmetric measurement distributions are uni-modal. Fourth, we propose and benchmark a classical simulation method, where measurement probabilities of states are represented by stochastic tensor networks, and non-unitary dynamics are represented by non-negative matrix factorizations.

We conclude this thesis with a discussion of implications of the rich structures underlying non-unitary dynamics. We first interpret and provide examples and counter-examples of the utility of ensembles within channel-centric quantum algorithms. We proceed to discuss long term objectives posed by our studies, regarding constructing phase diagrams of optimization success, across ansatz expressiveness, noise scales, and system sizes. We also propose less passive applications of noise towards steering ensembles towards concentrated or non-concentrated behaviours. Finally, we raise questions of simulability of multi-modal distributions in the search for quantum versus classical advantage.