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.
Recently, nonadiabatic geometric quantum computation has received much attention due to its fast manipulation and intrinsic error-resilience characteristics. However, to obtain universal geometric quantum control, only limited and special evolution paths have been proposed, which usually require longer gate-time and more operational steps, and thus lead to lower quality of the implemented quantum gates. Here, we present an effective scheme to find the shortest geometric path under conventional conditions of geometric quantum computation, where high-fidelity and robust geometric gates can be realized by only single-loop evolution, and the gate performances are better than the corresponding dynamical ones. Furthermore, we can optimize the pulse shapes in our scheme to further shorten the gate-time, which is determined by how fast the path is traveled. In addition, we also present its physical implementation on superconducting circuits, consisting of capacitively coupled transmon qubits, where fidelities of geometric single- and two-qubit gates can be higher than 99.95% and 99.80% within the current state-of-the-art experimental technologies, respectively. These results indicate that our scheme is promising for large-scale fault-tolerant quantum computation.
Nonadiabatic geometric quantum computation is dedicated to the realization of high‐fidelity and robust quantum gates, which are necessary for fault‐tolerant quantum computation. However, it is limited by cyclic and mutative evolution path, which usually requires longer gate‐time and abrupt pulse control, weakening the gate performance. Here, a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolution via invariant‐based shortcuts is proposed, where universal quantum gates can be induced in one step without path mutation and the gate time is also effectively shortened. Our numerical simulations show that, comparing with the conventional dynamical gates, the constructed geometric gates have stronger resistance not only to systematic errors, induced by both qubit‐frequency drift and the deviation of the amplitude of the driving fields, but also to environment‐induced decoherence effect. In addition, this scheme can also be implemented on a superconducting circuit platform, with the fidelities of single‐qubit and two‐qubit gates higher than 99.97% and 99.84%, respectively. Therefore, this scheme provides a promising way to realize high‐fidelity fault‐tolerant quantum gates for scalable quantum computation.
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