695 citations · 1.6k across the 16 of their papers we have counts for
16 papers
Bounds on Effective Hamiltonians for Stabilizer Codes
Stephen S. Bullock, Dianne P. O'Leary
This manuscript introduces various notions of k-locality of stabilizer codes inherited from the associated stabilizer groups. A choice of generators for the group leads to a Hamilt…
Qudit surface codes and gauge theory with finite cyclic groups
Stephen S. Bullock, Gavin K. Brennen
Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators…
Projecting onto Qubit Irreps of Young Diagrams
Stephen S Bullock
Let K be the diagonal subgroup of U(2)^{(x)n}. We may view the one-qubit state-space H_1 as a standard representation of U(2) and the n-qubit state space H_n=(H_1)^{(x) n} as the n…
Parallelism for Quantum Computation with Qudits
Dianne P. O'Leary, Gavin K. Brennen, Stephen S. Bullock
Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to im…
Efficient Circuits for Exact-Universal Computations with Qudits
Gavin K. Brennen, Stephen S. Bullock, Dianne P. O'Leary
This paper concerns the efficient implementation of quantum circuits for qudits. We show that controlled two-qudit gates can be implemented without ancillas and prove that the gate…
Asymptotically Optimal Quantum Circuits for d-level Systems
Stephen S. Bullock, Dianne P. O'Leary, Gavin K. Brennen
As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum com…