Study On Physical Realization Of Remote Toffoli Gate And Non-Adiabatic Holonomic Quantum Gates

Quantum gate is the basic unit for quantum computation. To realize specif-ic quantum information processing tasks, one needs to perform a series of unitary operations on quantum bits with the help of quantum gates. Distributed quan-tum computer can be viewed as quantum communication network in which each node can realize quantum information processing and can process very large num-bers of qubits. The realization of remote quantum gates, i.e., nonlocal quantum gates only using local operations, classical communication, and previously shared entanglement, among qubits in different nodes is the essential requirement for dis-tributed quantum computation. By combining the coherence stabilization virtues of decoherence-free subspaces and the built-in fault tolerance of holonomic control, holonomic quantum computation in decoherence-free subspaces is an effective way to realize robust quantum gates. Due to multi-qubit quantum gate can manipulate more qubits than one-and two-qubit quantum gate, the directly realization of it is an attractive problem. In this dissertation, we investigate the physical imple-mentation of multi-qubit quantum logic gates, and the main research contents are following:1. A remote Toffoli gate is realized based on semiconductor-quantum-dot-optical-microcavity system. We consider the optical selection rules for the optical transition of negatively charged exciton X-, the Heisenberg equations of motion for the cavity field operator and X- dipole operator, and the input-output for-mulation of optical microcavity, then get the interaction relationship between the incident photon and the electron of semiconductor quantum dot. We realize a re-mote Toffoli gate among electron spin qubits by using local linear optical operations, an auxiliary electron spin, two circularly-polarized entangled photon pairs, photon measurements, and classical communication based on the relationship. We assess the performance and the feasibility of the scheme, which show that the scheme can be achieved with high average fidelity under the current technology and can work in both the weak coupling and the strong coupling regimes. What’s more, the scheme is achieved with success probability of 100% by the sequential detection of photons and auxiliary electron spin and the single-qubit rotations of photon and electron spin in principle.2. Realzation of non-adiabatic holonomic quantum gates in decoherence-free subspaces. By using non-adiabatic holonomy, we realize two- and three-qubit con-trolled unitary quantum gates and Fredkin gate in decoherence-free subspaces di-rectly, which avoids the extra errors from universal gates combination and long evolution time in adiabatic case. It is of great advantage due to built-in fault toler-ance, coherence stabilization virtues, and short run-time in this way. The controlled unitary quantum gates means the unitary operation acting on the target qubit is an arbitrary single-qubit gate. The required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing col-lective dephasing to encode a logical qubit.