Optimal dispersive readout of a spin qubit with a microwave resonator

Abstract

Strong coupling of semiconductor spin qubits to superconducting microwave resonators was recently demonstrated [X. Mi et al., Nature 555, 599 (2018); A. J. Landig et al., Nature 560, 179 (2018); N. Samkharadze et al., Science 359, 1123 T. Cubaynes et al., npj Quantum Inf. 5, 47 (2019)]. These breakthroughs pave the way for quantum information processing that combines the long coherence times of solid-state spin qubits with the long-distance connectivity, fast control, and fast high-fidelity quantum-non-demolition readout of existing superconducting qubit implementations. Here, we theoretically analyze and optimize the dispersive readout of a single spin in a semiconductor double quantum dot (DQD) coupled to a microwave resonator via its electric dipole moment. The strong spin-photon coupling arises from the motion of the electron spin in a local magnetic field gradient. We calculate the signal-to-noise ratio (SNR) of the readout accounting for both Purcell spin relaxation and spin relaxation arising from intrinsic electric noise within the semiconductor. We express the maximum achievable SNR in terms of the cooperativity associated with these two dissipation processes. We find that while the cooperativity increases with the strength of the dipole coupling between the DQD and the resonator, it does not depend on the strength of the magnetic field gradient. We then optimize the SNR as a function of experimentally tunable DQD parameters. We identify wide regions of parameter space where the unwanted backaction of the resonator photons on the qubit is small. Moreover, we find that the coupling of the resonator to other DQD transitions can enhance the SNR by at least a factor of two, a "straddling" effect [J. Koch et al., Phys. Rev. A 76, 042319 (2007)] that occurs only at nonzero energy detuning of the DQD double-well potential. We estimate that with current technology, single-shot readout fidelities in the range 82 − 95% can be achieved within a few µs of readout time without requiring the use of Purcell filters. arXiv:1905.09702v2 [cond-mat.mes-hall]

Proposal for a cavity-induced measurement of the exchange coupling in quantum dots

“…This allows coupling between distant qubits [35][36][37][38][39]. Furthermore, by injecting a probe field into the resonator and monitoring the output field it is possible to read out the qubit state [40][41][42][43][44][45][46] and to investigate the electronic energy spectrum [47,48]. In particular, resonators coupled to silicon QDs can successfully aid the characterization the valley Hamiltonian [49][50][51][52][53][54][55] which is hard to access otherwise.…”

Thermal Entanglement and Correlated Coherence in Two Coupled Double Quantum Dots Systems

“…In the last decades, solid-state realizations of it have received considerable attention due to the fact that semiconductor nanostructures such as quantum dots [4,5] and double quantum dots (also known as quantum dot molecules) [6,7] are promising candidates for the physical implementation of quantum information processing [8]. There are proposals for quantum dots using either charge [9] or spin [10][11][12] as qubits, or even both at the same time [13,14]. These quantum systems are of great interest due to their easy integration with the existing electronics and the advantage of scalability [15,16].…”

Coherent spin-spin coupling mediated by virtual microwave photons

“…Other contributing factors include a large spin-orbit interaction through the micromagnet's ∆B ⊥ , and stateof-the-art resonator losses despite the large resonator coupling to its environment [34]. Interestingly, the charge qubit linewidth Γ c /2π 60 MHz at 2t c /h = 12 GHz is not particularly small, suggesting that the good overall performance of the device comes from other factors, like the low g s /g c ratio [38], and could be improved further [39].…”

“…We expect the progress to happen in parallel and the improvements to be transversal. The regime of circuit QED achieved here is quite promising for the platform; it could enable two-qubit gates between spin qubits mediated by resonators [22], single-shot dispersive spin-qubit readout (without spin-to-charge conversion) [38], preparation of quantum photon states with spins, coherent links between dense spin qubit networks [6], or quantum simulation with spin QED networks [40].…”