Approximate exchange-only entangling gates for the three-spin-1/2decoherence-free subsystem

Abstract

The three-spin-1/2 decoherence-free subsystem defines a logical qubit protected from collective noise and supports exchange-only universal gates. Such logical qubits are well-suited for implementation with electrically-defined quantum dots. Exact exchange-only entangling logical gates exist but are challenging to construct and understand. We use a decoupling strategy to obtain straightforward approximate entangling gates. A benefit of the strategy is that if the physical spins are aligned, then it can implement evolution under entangling Hamiltonians. Hamiltonians expressible as linear combinations of logical Pauli products not involving σ y can be implemented directly. Self-inverse gates that are constructible from these Hamiltonians, such as the CNOT, can be implemented without the assumption on the physical spins. We compare the control complexity of implementing CNOT to previous methods and find that the complexity for fault-tolerant fidelities is competitive.

Efficient Two-Qubit Pulse Sequences Beyond CNOT

“…Up to single-qubit rotations, the resulting sequences can be used to carry out arbitrary cphase gates of the form (19), where the phase φ can be chosen freely by adjusting the durations of a small number of exchange pulses. Other known two-qubit gate sequences either (i) result in a cnot gate [6,29,30,36], i.e., a gate locally equivalent to cphase with φ = π, or (ii) consist of significantly more exchange pulses [34].…”

“…Recently, another set of pulse sequences for cnot has been constructed using analytic tools rather than brute force search [36]. A crucial idea in this interesting development is to simplify the search for two-qubit sequences by allowing for leakage out of the encoded Hilbert space.…”

“…Under certain assumptions, some of the sequences presented in Ref. [36] have even shorter total duration (though comprising more clock cycles) than the Fong-Wandzura sequence.…”