Symmetry breaking and its applications to quantum information processing

Franco Strocchi

Jincheng Zhang

This paper investigates the potential for dynamically breaking and breaking symmetry in quantum circuits, a concept with significant implications for the exploration of novel quantum phenomena and potential advancements in quantum information processing. We propose a novel method, Adaptive Symmetry Mapping, which dynamically adjusts symmetry constraints during circuit execution to facilitate the creation of unexpected quantum states. The core claim is that this approach offers a more flexible and adaptive method compared to traditional approaches, potentially unlocking new possibilities in quantum system design and control. We detail the algorithm, its implementation, and preliminary results demonstrating its ability to generate unexpected quantum behaviors.

Gilles Brassard A

Cristina Cîrstoiu, Jennings, David

What is the structure of general quantum processes on composite systems that respect a global or local symmetry principle? How does the irreversible use of quantum resources behave under such symmetry principles? Here we employ an information-theoretic framework to address these questions and show that every symmetric quantum process on a system has a highly rigid decomposition in terms of the flow of symmetry-breaking degrees of freedom between each subsystem and its environment. The decomposition has a natural causal structure that can be represented diagrammatically and makes explicit gauge degrees of freedom between subsystems. The framework also provides a novel quantum information perspective on lattice gauge theories and a method to gauge general quantum processes beyond Lagrangian formulations. This procedure admits a simple resource-theoretic interpretation, and thus offers a natural context in which features such as information flow and entanglement in gauge theories and quantum thermodynamics could be studied. The framework also provides a flexible toolkit with which to analyse the structure of general quantum processes. As an application, we make use of a `polar decomposition' for quantum processes to discuss the repeatable use of quantum resources and to provide a novel perspective in terms of the coordinates induced on the orbit of a local process under a symmetry action.

M. Asadi, M. Ali-Akbari

We study the time evolution of holographic mutual and tripartite information for a zero temperature CFT, derives to a non-relativistic thermal Lifshitz field theory by a quantum quench. We observe that the symmetry breaking does not play any role in the phase space, phase of parameters of sub-systems, and the length of disentangling transition. Nevertheless, mutual and tripartite information indeed depend on the rate of symmetry breaking. We also find that for large enough values of δt the quantity teqδt−1, where δt and teq are injection time and equilibration time respectively, behaves adiabatically, i.e. its value is independent of length of separation between sub-systems. We also show that tripartite information is always non-positive during the process indicates that mutual information is monogamous.

Davide Rossini