Nonadiabatic holonomic quantum computation with all-resonant control

Abstract

The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a scalable circuit QED lattice with simple realization of a universal set of nonadiabatic holonomic quantum gates. Compared with the existing proposals, we can achieve both the single and two logical qubit gates in an tunable and all-resonant way through a hybrid transmon-transmission-line encoding of the logical qubits in the decoherence-free subspaces. This distinct advantage thus leads to quantum gates with very fast speeds and consequently very high fidelities. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.Comment: v2: thoroughly rewritten version with major revission; v3: Accepted by PRA; V4: Published versio

Nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases

“…Specifically, we use three physical qubits undergoing collective dephasing to encode one logical qubit, and further realize a universal set of geometric gates in DFSs nonadiabatically and unconventionally. Similarly to the schemes of nonadiabatic holonomic quantum computation in DFSs or noiseless subsystems [13,[21][22][23][24]29], our scheme uses Hamiltonians with three-level structures. However, the dynamical phases of our scheme are proportional to the total phases, while the dynamical phases of the schemes of nonadiabatic holonomic quantum computation in DFSs or noiseless subsystems are equal to 0.…”

“…Despite this, impressive progress has been made in this direction [13,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] and many works have been done to realize GQC in decoherence-free subspaces (DFSs) [13,[15][16][17][18][19][20][21][22][23][24]. Among these works, most of them realized conventional GQC in DFSs [13,15,16,[20][21][22][23][24]. Since unconventional GQC in DFSs shares all the robustness of conventional GQC in DFSs while avoiding the additional operations required to cancel the dynamical phases, realizing unconventional GQC in DFSs is of more practical importance.…”

Composite nonadiabatic holonomic quantum computation

“…As long as the Hamiltonians have three-level structures, our composite scheme can be realized. It has been shown that realizing Hamiltonians with three-level structures in decoherence-free subspaces is feasible [9,25]. Thus, our scheme can be protected by decoherence-free subspaces.…”

Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces

“…After a great effort, the first protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces has been developed in Ref. [14], and a number of implementation schemes in various physical systems, such as trapped ions [22], nitrogen-vacancy centers [23] and superconducting circuits [24,25], have been proposed recently. Nonadiabatic holonomic quantum computation in decoherence-free subspaces has the merits of short runtime and resilience to both control errors and decoherence.…”