Designing CPHASE Gates with Arbitrary Phase by Structural Modification of the Fong-Wandzura Sequence

We design efficient arbitrary CPHASE gates for exchange-only spin-based quantum computation in which quantum gates are carried out by sequences of exchange pulses acting on qubits encoded using three or more spins. The construction we present is motivated by our analytic derivation [1] of the Fong-Wandzura sequence [2], the shortest known pulse sequence for an exact CNOT gate (for a linear array of spins). This earlier derivation is based on a type of elevation of a simple five-pulse sequence consisting only of SWAP or trivial pulses, which captures the essential structure of the Fong-Wandzura sequence. In the present construction, we introduce and evaluate a modified simple five-pulse sequence consisting of four SWAP pulses and one pulse of arbitrary duration. We then show how this sequence can be elevated in a fashion similar to that of our Fong-Wandzura derivation, to yield a leakage-free entangling two-qubit sequence that carries out a gate operation locally equivalent to arbitrary CPHASE.

[1] D. Zeuch and N. E. Bonesteel, Physical Review A 93 (2016).
[2] B. H. Fong and S. M. Wandzura, Quantum Information & Computation 11 (2011).