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arXiv:cond-mat/0603119 · Physical Review B

Ultra-long-distance interaction between spin qubits

Guido Burkard, Ataç İmamoğlu

Published Jul 24, 2006• 151 citations
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Abstract

We describe a method for implementing deterministic quantum gates between two spin qubits separated by centimeters. Qubits defined by the singlet and triplet states of two exchange coupled quantum dots have recently been shown to possess long coherence times. When the effective nuclear fields in the two asymmetric quantum dots are different, total spin will no longer be a good quantum number and there will be a large electric dipole coupling between the two qubit states. We show that when such a double-quantum-dot qubit is embedded in a superconducting microstrip cavity, the strong coupling regime of cavity quantum electrodynamics lies within reach. Virtual photons in a common cavity mode could mediate coherent interactions between two distant qubits embedded in the same structure; the range of this two-qubit interaction is determined by the wavelength of the microwave transition.

DOI
10.1103/physrevb.74.041307

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We describe a method for implementing deterministic quantum gates between two spin qubits separated by centimeters. Qubits defined by the singlet and triplet states of two exchange coupled quantum dots have recently been shown to possess long coherence times. When the effective nuclear fields in the two asymmetric quantum dots are different, total spin will no longer be a good quantum number and there will be a large electric dipole coupling between the two qubit states. We show that when such a double-quantum-dot qubit is embedded in a superconducting microstrip cavity, the strong coupling regime of cavity quantum electrodynamics lies within reach. Virtual photons in a common cavity mode could mediate coherent interactions between two distant qubits embedded in the same structure; the range of this two-qubit interaction is determined by the wavelength of the microwave transition.
We report the coherent coupling of two electron spins at a distance via virtual microwave photons.Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spinphoton couplings up to around g s =2π ¼ 40 MHz.As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around 2J=2π ¼ 20 MHz.In addition, photon-number states are resolved from the shift 2χ s =2π ¼ -13 MHz that they induce on the spin frequency.These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins.Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.
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We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around gs/2π=40MHzg_s/2\pi = 40 \text{MHz}gs​/2π=40MHz. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around 2J/2π=20MHz2J/2\pi = 20 \text{MHz}2J/2π=20MHz. In addition, photon number states are resolved from the shift 2χs/2π=−13MHz2\chi_s/2\pi = -13 \text{MHz}2χs​/2π=−13MHz they induce on the spin frequency. These results could enable long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.
We analyze and give estimates for the long-distance coupling via floating metallic gates between different types of spin qubits in quantum dots made of different commonly used materials. In particular, we consider the hybrid, the singlet-triplet, and the spin-12\frac{1}{2}21​ qubits, and the pairwise coupling between each type of these qubits with another hybrid qubit in GaAs, InAs, Si, and Si0.9Ge0.1{\mathrm{Si}}_{0.9}{\mathrm{Ge}}_{0.1}Si0.9​Ge0.1​. We show that hybrid qubits can be capacitively coupled strongly enough to implement two-qubit gates, as long as the distance of the dots from the metallic gates is small enough. Thus, hybrid qubits are good candidates for scalable implementations of quantum computing in semiconducting nanostructures.
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