Quantum Algorithms for Quantum Simulation
Simulating quantum systems is one of the obvious applications for a general-purpose programmable quantum computer. However, only recently have the available algorithms been explored with an eye towards practical applicability, and major issues in the scaling have been identified. We have been working on estimating the resource requirements for quantum simulation to go beyond what can be achieved classically, and at the same time made many improvements to the existing algorithms.
- Gate count estimates for performing quantum chemistry on small quantum computers
- Analyzing many-body localization with a quantum computer
Novel phases in non-equilibrium systems
Recent advances in our understanding of interacting quantum systems far from equilibrium have shown that these systems can host a panoply of new phases that are forbidden in equilibrium. Examples include Floquet time crystals – driven quantum systems exhibiting spontaneous breaking of time-translation symmetry – and topological phases at finite temperature, which may be used to protect quantum information from decoherence.
- Floquet Time Crystals
- Pre-thermal phases of matter protected by time-translation symmetry
- Area laws in a many-body localized state and its implications for topological order
Tensor network states and entanglement
Many recent advances in strongly correlated systems have been inspired by quantum information theory, and in particular the theory of entanglement in ground states of quantum systems. This has led to the development of powerful tensor network approaches to one- and two-dimensional quantum systems, which serve both as numerical tools as well as providing a natural language to describe many exotic phases analytically. Furthermore, tensor networks have emerged as solvable models for holographic dualities, thus establishing new connections between the theory of quantum information and high-energy theory.
- Extracting entanglement geometry from quantum states
- Matrix Product State applications for the ALPS project
Topological phases in quantum systems
Topological phases form the basic building blocks of a topological quantum computer, and as such are the focus of our attention here at Station Q. My work has been exploring topological phases both in mesoscopic superconducting systems, where the most promising experimental platforms are found, as well as in systems of strongly interacting electrons or spins. This includes topological liquid phases in frustrated spin systems, which have for decades formed a playground in the search for exotic phases.