Quantum Information and Computing

Quantum Simulation with Trapped Ions and Superconducting Qubits

Our group works closely with trapped-ion quantum computing effort at Quantinuum (merger of Honeywell | Quantum Solutions and Cambridge Quantum computing), and collaborates with experimental group of Shyam Shankar on superconducting circuit quantum electrodynamics devices and hardware. This research aims to explore both quantum algorithms for simulating materials and chemistry, as well as exploring new regimes of non-equilibrium quantum many-body dynamics.

Holographic Simulation with Quantum Tensor Networks

Simulation of materials and chemistry is a leading application area for quantum computation. However, standard methods require encoding each electron orbital into a separate qubit, limiting the model-sizes that can be simulated to the number of hardware qubits, which is likely to remain <100 for the forseeable future. By contrast, simulating 100-1000-site lattice systems on classical computers with tensor network methods is now routine, setting a significant hurdle to achieving a quantum advantage. To address this, our group has been investigating how to use the data compression afforded by tensor network representations along with mid-circuit measurements and qubit re-use, to simulate large quantum systems with a small number of qubits. Specifically, one can simulate many area-law entangled states in D-dimensions with (D-1)-dimensions' worth of qubits. We have explored variational hybrid-classical quantum algorithms using quantum circuit generated tensor networks (qTNS) of various networks.

Statistical Mechanics of Quantum Circuits

While analyzing individual quantum circuits on a large number of qubits is prohibitively difficult, it can be possible to understand statistical properties of ensembles of random quantum circuits. Our research has helped develop a theory toolset to map the calculation of entanglement features of random quantum circuits and tensor networks to partition functions and free-energy quantities in a dual lattice "spin" model. This enables us to employ powerful tools from quantum field theory to analyze the dynamics of entanglement, measurement-induced phase transitions, and computational complexity transitions in random circuit and tensor network ensembles. The statistical mechanical viewpoint is also closely related to holographic field-theory/gravity correspondences, in that it relates entanglement entropies of the "boundary" of a quantum circuit or tensor network, to geometric quantities in the "bulk" of the circuit.