Disorder in Open Quantum Systems

Dramatic breakthroughs in our ability to actively manipulate the quantum mechanical properties of matter have led to landmark new technologies including trapped ion and neutral atom quantum processors. However, many of these new quantum technologies are extremely vulnerable to environmental noise and decoherence, restricting their technical capabilities and scalability. For future generations of quantum devices, we will need to develop better ways to preserve and protect the quantum mechanical phenomena that we wish to make use of. This is particularly important for quantum computers and quantum memories, where it is crucial that information is preserved over long timescales. The aim of the proposed research is to investigate to what extent impurities and disorder can be used to 'freeze' realistic quantum systems - namely open quantum systems subject to realistic sources of environmental noise - in the kind of exotic far-from-equilibrium configurations required for quantum computation. This work will enable the manipulation and preservation of robust, long-lived quantum states which can act as stable quantum memories, lessening the burden on complex error correction techniques by preventing the errors from happening in the first place. There are several high-profile examples of complex systems which are prevented from thermalising by the addition of some form of disorder. Two of the main examples are many-body localised matter, and spin glasses. Many-body localisation is a quantum mechanical phenomenon that occurs in low-dimensional quantum systems; it is a purely quantum effect, but is itself rather fragile. Spin glasses occur in highly frustrated, high-dimensional systems; they are robust, but the underlying principles are classical. The main aim of this proposal is to combine aspects of both to develop stable, long-lived non-ergodic phases of matter in two-dimensional open quantum systems, subject to realistic sources of environmental noise, comparable to the capabilities of state-of-the-art (noisy) quantum simulators. To achieve this goal, it will be necessary to develop numerical techniques capable of handling this challenging parameter regime. This key method will be the Tensor Flow Equation method which I invented and recently used to study the long-time dynamics of large two-dimensional quantum systems (arXiv:2308.13005). Using cutting-edge supercomputing resources and a radical redesign of the algorithm to make use of distributed parallelism, I will embark on an ambitious program to simulate some of the most challenging quantum phases of matter. This will be further augmented by a powerful set of AI-based tools to dramatically enhance the computational efficiency and scalability of the method.