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



Emanuel H. Knill, James R. van Meter


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 the Pauli Y matrices can be implemented directly. Gates 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.
Physical Review A


decoherence-free subsystems, quantum computing, quantum codes


Knill, E. and van, J. (2019), Approximate exchange-only entangling gates for the three-spin-1/2 decoherence-free subsystem, Physical Review A, [online], (Accessed April 17, 2024)
Created April 22, 2019, Updated September 21, 2020