Quantum Information

Classical simulation and stabilizer rank

One way to crack the code of the hardness of class BQP is to look for classes of unitary operations that we can simulate efficiently, and then understand general universal quantum computation from there. One such class contains the Clifford operations, which are known to be easy to simulate by the celebrated Gottesman-Knill theorem. The stabilizer rank approach and sum-over Clifford approach proposed by Bravyi, Gosset, and others are natural extensions of the Gottesman-Knill theorem. These two approaches are especially preferable when it comes to circuits that are dominated by Clifford operations, compared to other competing simulation methods like direct simulation, tensor network approaches, and the Feynman-Schrodinger Hybrid method.

Contextuality

The idea of contextuality originated in theory of the foundations of quantum mechanics, with the Bell-Kochen-Specker theorem. More recently, it has made its way into theory of quantum computing, with numerous results connecting contextuality to quantum resources. We contribute to this effort by studying contextuality of Hamiltonians, focusing on their application in variational quantum algorithms. In Phys. Rev. Lett. 123, 200501 (2019) and Phys. Rev. A 102, 032418, we gave necessary and sufficient conditions for contextuality of Hamiltonians, and constructed classical models for noncontextual Hamiltonians.

These studies have led to an intersection with the group's focus on quantum chemistry in the form of our new quantum-classical hybrid algorithm, contextual subspace variational quantum eigensolver, in which a Hamiltonian of interest is partitioned into a noncontextual part that is simulated classically and a contextual correction that is computed on a quantum processor. This reduces the number of qubits required. See https://arxiv.org/abs/2011.10027 for the theory, and https://github.com/wmkirby1/ContextualSubspaceVQE to download our code and simulate or use the method yourself!