Alex Bocharov

Resource-optimal single-qubit quantum circuits.

Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit quantum circuits, and the corresponding rules for exactly reducing an arbitrary single-qubit circuit to this canonical form. We focus on the singlequbit universal {H,T} basis due to its role in fault-tolerant quantum computing, and show how our formalism might be extended to other universal bases. We then extend our canonical representation to the family of Solovay-Kitaev decomposition algorithms, in order to find an -approximation to the single-qubit circuit in polylogarithmic time. For a given single-qubit operation, we find significantly lower-depth -approximation circuits than previous state-of-the-art implementations. In addition, the implementation of our algorithm requires significantly fewer resources, in terms of computation memory, than previous approaches.

Efficient decomposition of single-qubit gates intoVbasis circuits

We develop the first constructive algorithms for compiling single-qubit unitary gates into circuits over the universal

Efficient Synthesis of Universal Repeat-Until-Success Quantum Circuits

V

EFFICIENT SYNTHESIS OF PROBABILISTIC QUANTUM CIRCUITS WITH FALLBACK

basis. The

Asymptotically optimal topological quantum compiling.

V

Factoring with qutrits: Shor's algorithm on ternary and metaplectic quantum architectures

basis is an alternative universal basis to the more commonly studied

Optimal ancilla-free Pauli+V circuits for axial rotations

\{H,T\}

Efficient topological compilation for a weakly integral anyonic model

basis. We propose two classical algorithms for quantum circuit compilation: the first algorithm has expected polynomial time (in precision

Stability analysis of time series forecasting with ART models

\log(1/\epsilon)

Modeling and predicting behavioral dynamics on the web

) and offers a depth/precision guarantee that improves upon state-of-the-art methods for compiling into the