Simulation of Measurement-Based Entanglement in Silicon Spin Qubits

Abstract

Electron spin qubits in silicon show promise for quantum computing applications due to their long spin-coherence times, small qubit sizes, and the applicability of existing nanofabrication infrastructure and techniques to their construction.One drawback is the relative difficulty of manipulating the electron’s spin state. Measurement-based entanglement (MBE) is a method of generating entangled qubit pairs through the state projection that accompanies a parity or similar measurement.Instead of generating entangled states via direct qubit-qubit interactions, one can use a suitable measurement to project an initial unentangled two-qubit system into an entangled subspace. This entanglement mechanism does not require the creation of any direct qubit-qubit interactions that would need to be turned off before using entangled pairs in a quantum algorithm; only the cessation of measurement is required. Adaptations of these techniques may be an effective addition to the current set of entanglement-generation techniques for silicon spin qubits. This thesis is intended to assess the feasibility of implementing measurement-based entanglement with silicon spin qubits. We will first review the design and operation of electron-spin double-quantum-dot (DQD) qubits in Si/SiGe, outline theoretical models for continuous quantum measurements and open quantum systems, and discuss how parity measurements can be used to establish entanglement between initially unentangled qubits. We will then discuss how such a parity measurement protocol could be implemented in a two-qubit circuit-quantum-electrodynamics experiment.After deriving a stochastic master equation describing the evolution of two flopping-mode DQDs coupled to a resonant cavity, we present and interpret numerical simulation results demonstrating the influence of qubit and cavity parameters on the corresponding final state fidelity. Using simulation results corresponding to current silicon spin-qubit devices, we determine which device parameters must be altered or improved in order to make measurement-based entanglement of silicon spin qubits experimentally viable.Specifically, with cavity loss and qubit decoherence rates κ and γ and charge-photon coupling strength gc corresponding to proposed devices designed to perform coherent cavity-mediated spin-spin coupling, we predict a maximum entangling gate fidelity of ~60%, indicating poor MBE performance. After increasing the cavity output coupling κout by a factor of ten, we predict an overlap between the final state of the MBE protocol and the target Bell state ∣Ψ+⟩ of ~81% for a postselection success probability of 33%, as well as a significant enhancement in the entanglement-of-formation of postselected states. Therefore, we predict that an experimental realization of MBE with silicon quantum dots will be feasible with such a device. Finally, we will discuss the design changes to existing coplanar-waveguide cavity geometries needed to achieve this increase in output coupling, as well as results from the fabrication of prototypes of these designs.