Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

Abstract

Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation (GQC) on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric phase, π/8 and Hadamard gates can be obtained as 99.93%, 99.95% and 99.95%, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as 99.87%. Therefore, our scheme provides a new perspective for GQC, making it more promising in the application of large-scale fault-tolerant quantum computation.

State‐Independent Geometric Quantum Gates via Nonadiabatic and Noncyclic Evolution

“…Subsequently, Aharonov and Anandan [9] found that the adiabatic condition is not necessary, as long as certain requirements are met. This paved the way for geometric quantum computation based on the nonadiabatic evolution, i.e., nonadiabatic geometric quantum computation (NGQC), [10][11][12][13][14][15] with experimental demonstrations in many quantum systems, such as trapped ions, [16][17][18] NV center in diamond, [19,20] nuclear magnetic resonance, [21][22][23] and superconducting quantum circuits [24,25] , etc.…”

Nonadiabatic Holonomic Quantum Computation via Path Optimization

“…The shortestpath NHQC scheme [31] based on a round evolution path also can accomplish the same gates with the single-loop NHQC scheme. Yet, the noise resistance varies greatly with different evolution paths [45][46][47], and thus, for a same gate, different evolution paths have different advantages in terms of gate fidelity and robustness. However, the previous schemes can not relax the freedom of path to complete a same gate, and thus fail to balance simultaneously the gate fidelity and robustness by choosing a suitable path.…”

Robust nonadiabatic geometric quantum computation by dynamical correction

“…Recently, many different NGQC protocols have been developed [13][14][15][16][17][18][19]; however, after experimental verification in var-ious quantum systems [20][21][22][23][24][25], it turns out that the advantages of geometric phase are compromised by local noises and the limitations of the protocol. To find better implementations, the orange-slice-shaped scheme [16][17][18][19] is proposed with simplified pulses, and the time and path optimal control techniques [26][27][28][29][30][31] are proposed to shorten the gate time and thus reducing the decoherence induced error. Meanwhile, when the Z error is the main error source, the dynamical decoupling method can be introduced [32][33][34].…”