Entangling distant solid-state spins via thermal phonons

Abstract

The implementation of quantum entangling gates between qubits is essential to achieve scalable quantum computation. Here, we propose a robust scheme to realize an entangling gate for distant solid-state spins via a mechanical oscillator in its thermal equilibrium state. By appropriate Hamiltonian engineering and usage of a protected subspace, we show that the proposed scheme is able to significantly reduce the thermal effect of the mechanical oscillator on the spins. In particular, we demonstrate that a high entangling gate fidelity can be achieved even for a relatively high thermal occupation. Our scheme can thus relax the requirement for ground-state cooling of the mechanical oscillator, and may find applications in scalable quantum information processing in hybrid solid-state architectures.

Pulsed characteristic-function measurement of a thermalizing harmonic oscillator

“…i.e., a probe-state dependent constant force acting on the harmonic oscillator [14,33], with the same strength but opposite signs depending on the probe state. Such a coupling can be realized in a variety of electromechanical systems, for example, when an electronic spin is coupled to the motional degree of freedom of a mechanical element emanating a magnetic field or is embedded in a mechanical oscillator subject to a spatially inhomogeneous magnetic field [34][35][36]. Also, such an interaction can be realized in harmonically trapped particles with an internal electronic degree of freedom, such as ions in a linear Paul trap.…”

Proposal to test quantum wave-particle superposition on massive mechanical resonators

“…When vibrating along theŷ-direction, the CNTs can parametrically modulate the Zeeman splitting of the intermediate spin through the magnetic field, yielding a magnetic coupling to the spin. [33][34][35][36][37] For simplicity, below we assume that the CNTs are identical such that they have the same vibrational frequency ω m and the same vibrational mass m. The mechanical vibrations are modelled by quantized harmonic oscillators with a Hamiltonian…”

Scalable nuclear-spin entanglement mediated by a mechanical oscillator

“…In Fig. 2 we show a comparison of the dynamics under the exact Hamiltonian (7) (numerical propagation) and the effective nuclear spinspin Hamiltonian (18). The fast oscillation of the individual nuclear spins with frequency ω due to the local terms in the Hamiltonian (5), which are absent in the rotating frame, can be eliminated by applying a spinecho pulse [47] after half the evolution time t, in order to clearly see the nuclear-interaction dynamics in the original frame [19].…”

“…Here, we propose a hybrid system, consisting of an array of NV centers magnetically coupled to a mechanical oscillator, in which such an effective long-range nuclear spin-spin interaction is established by two mediators. The mechanical oscillator couples the electronic spins [18], which in turn act as a second mediator and induce an Ising interaction between the nuclear spins [19]. We show that the effective interaction strength can be high enough to maintain a coherent nuclear-nuclear coupling in the presence of environmental noise for realistic parameters by merely applying a small number of spinecho pulses on the nuclear spins in addition to the continuous microwave driving field of the electronic spins.…”

“…x /2 in the effective nuclear Hamiltonian (18), which clearly does not commute with the effective Ising interaction and thereby leads to a nonequivalence to the graph-state Hamiltonian (27). Therefore, in order to still make the creation possible, we employ a pulsed decoupling, which we showed in Sec.…”