Abstract
We present two strategies for performing two-qubit operations on the electron spins of an exchange-coupled pair of phosphorus donors in silicon, using the ability to set the donor nuclear spins in arbitrary states. The effective magnetic detuning of the two electron qubits is provided by the hyperfine interaction when the $^{31}$P nuclei are prepared in opposite spin states. This can be exploited to switch on and off SWAP operations with modest tuning of the electron exchange interaction. Furthermore, the hyperfine detuning enables high-fidelity conditional rotation gates based on selective resonant excitation. The latter requires no dynamic tuning of the exchange interaction at all, and offers a very attractive scheme to implement two-qubit logic gates under realistic experimental conditions.
Highlights
The electron spin of a donor atom in silicon represents a natural, highly coherent quantum bit
The effective magnetic detuning of the two electron qubits is provided by the hyperfine interaction when the two nuclei are prepared in opposite spin states
We focus on using the hyperfine interaction topswffiffiffiiffitffifficffiffihffiffiffitffihffi e amplitude of exchange oscillations to perform a SWAP gate, a rotation of angle π=2 around the J-axis of the S − T 0 Bloch sphere
Summary
The electron spin of a donor atom in silicon represents a natural, highly coherent quantum bit. While several proposals for the implementation of a two-qubit gate with donor electrons exist [13,14,15], they pose very challenging demands on the tunability of the spin exchange interaction J, which is assumed to be switchable from around 0 to > 1 GHz. It is predicted that J can vary strongly upon displacing a donor by even a single lattice site [16,17], requiring true atomic precision in the placement of the donors. We focus on using the hyperfine interaction topswffiffiffiiffitffifficffiffihffiffiffitffihffi e amplitude of exchange oscillations to perform a SWAP gate, a rotation of angle π=2 around the J-axis of the S − T 0 Bloch sphere This requires a reasonable 2-orders-of-magnitude control of J, which could be achieved with an fabricable device design. Possibly via coherent tunnelling by adiabatic passage (CTAP) rails [27] or spin buses [28], as in the framework proposed by Hollenberg et al [14], could be utilized to implement a scalable quantum computing architecture
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