Quantum computers and advanced materials are both governed by the behaviour of many interacting particles—electrons, spins, or qubits—and this fellowship aims to map out new, useful phases of matter that emerge when those systems are deliberately pushed out of equilibrium by driving, measurement, or energy loss. Most theoretical work on quantum phases assumes the system sits in thermal equilibrium, a calm state that real quantum devices rarely maintain. This project targets the messy, realistic conditions inside a quantum simulator, where particles are constantly driven and measured. These "open" systems can host entirely new phases that are impossible in equilibrium or in classical materials, but they remain poorly understood. The researcher has already identified mechanisms that stabilise such phases; now the goal is to find and characterise them fully. If successful, this work could identify robust quantum phenomena that protect quantum information from noise—the single biggest obstacle to useful quantum computing. Separately, the team is developing a publicly available algorithm (DAOE) that simulates quantum transport in materials far more efficiently than before, potentially allowing researchers to predict properties like electrical conductivity from first principles. This is primarily fundamental science, but past discoveries of topological phases have already become the backbone of leading quantum computers.
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The individual electrons in a metal, or the qubits in a quantum computer, are subject to peculiar but well-understood quantum mechanical laws. But metals/quantum computers have many electrons/qubits respectively and they all interact with one another, giving rise to a very complicated system. By implication, if you really want to understand a material or the operations of a quantum computer, you must grapple with the following question: What behaviours emerge when many quantum bodies (i.e., spins, electrons, qubits) interact with one another? The answer is fascinating. Surprising new behaviours can emerge due to both the complexity of many-body systems and the strangeness of the underlying quantum mechanical laws, and the continuing effort to chart this terrain accounts for two vast intersecting fields: condensed matter and quantum information theory. One insight from the study of condensed matter is that many-body systems are organised into phases. In addition to the prosaic (liquids, solids, gases) there's an ever-growing list of exotic quantum phases including superconductors and topological orders, many of which are useful. Much of condensed matter is dedicated to the search for new phases, and here it intersects with quantum information theory. For example, discovering new phases can help us to design more robust quantum computers, which may one day revolutionise computation (and will produce interesting physics in the mean-time). Indeed, the topological orders mentioned above now form the backbone of the most prominent digital quantum computers. This fellowship extension focusses on two themes within this area. 1) Find and characterise new open quantum phases The theoretical search for new phases has tended to assume that they are in thermal equilibrium. We aim to find new phases which emerge when we remove that assumption, and subject the system to driving, measurement, and dissipation. This is a timely question because the resulting so-called "non-equilibrium" or "open" systems describe well the conditions in a modern quantum simulator. Open systems are relatively understudied, but we already know that they can give rise to qualitatively new behaviours which can neither be realised in equilibrium nor in classical systems. We also now know more about the mechanisms that stabilise these phases, due to progress made in the first part of the fellowship. Going forward, our aim is to find and characterise new open quantum phases. The payoff is that if you find a new phase, then you have identified a new robust -- hence potentially useful -- quantum phenomenon. For example, new such phases may prove useful for protecting quantum information from noise, which is the main barrier to performing useful quantum computations. 2) Develop and use new classical (and quantum) algorithms for simulating many-body systems Transport properties (e.g., charge conductivity), are among the most practically important features of materials. Yet our ability to predict these properties from first principles in interacting quantum matter has until recently been limited. In the first part of the fellowship we used insights gleaned from quantum information theory to develop a new such technique (called `DAOE'), which efficiently simulates quantum transport in a range of systems, and which can probe transport in previously inaccessible regimes. This fellowship extension will further develop the algorithm, make an optimised version of it publicly available, and use it to understand new physics and experiments. DAOE is presently run on classical computers, but we will also explore the possibility of running analogous software on a quantum computer. The result may greatly enhance our ability to use quantum computers to predict experiments and, ultimately, the properties of materials.
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