Scalable nonadiabatic holonomic quantum computation on a superconducting qubit lattice

Abstract

Geometric phase is an indispensable element for achieving robust and high-fidelity quantum gates due to its built-in noise-resilience feature. However, due to the complexity of manipulation and the intrinsic leakage of the encoded quantum information to non-logical-qubit basis, the experimental realization of universal nonadiabatic holonomic quantum computation is very difficult. Here, we propose to implement scalable nonadiabatic holonomic quantum computation with decoherence-free subspace encoding on a two-dimensional square superconducting transmon-qubit lattice, where only the two-body interaction of neighbouring qubits, from the simplest capacitive coupling, is needed. Meanwhile, we introduce qubit-frequency driving to achieve tunable resonant coupling for the neighbouring transmon qubits, and thus avoiding the leakage problem. In addition, our presented numerical simulation shows that high-fidelity quantum gates can be obtained, verifying the advantages of the robustness and scalability of our scheme. Therefore, our scheme provides a promising way towards the physical implementation of robust and scalable quantum computation.

Realization of Deutsch–Jozsa Algorithm in Rydberg Atoms by Composite Nonadiabatic Holonomic Quantum Computation with Strong Robustness Against Systematic Errors

“…The early proposals of GQC, based on adiabatic Abelian [33] or adiabatic non-Abelian geometric phases, [34][35][36][37] always suffer from the detrimental influence of decoherence due to slow operations. [38,39] To deal with this problem, nonadiabatic geometric quantum computation (NGQC) [40][41][42] and nonadiabatic holonomic quantum computation (NHQC), [43][44][45][46][47] based on nonadiabatic Abelian geometric phases [48][49][50] and nonadiabatic non-Abelian geometric phases, [21,35,44,51] respectively, have been proposed. However, in most cases, fast operations generalized by the general NGQC and NHQC cannot work better than the usual dynamic gates in resisting systematic errors.…”

Ultrafast Holonomic Quantum Gates

“…Moreover, we present a physical realization of our protocol, with decoherence-free subspace (DFS) encoding [44][45][46], on a two-dimensional (2D) superconducting quantum circuit. In our implementation, for the two-logical qubit gates, we only needs coupling two physical qubits, each from a logical qubit, and thus greatly simplified previous investigations [22,29,[47][48][49]. Therefore, our scheme provides a ultrafast and implementable alternation for NHQC, and thus is promising for future fault-tolerant quantum computation.…”

Noncyclic nonadiabatic holonomic quantum gates via shortcuts to adiabaticity

“…In implementing of NHQC, to improve the gate robustness against systematic control errors, various protocols have been proposed with preliminary experimental demonstrations. As the first stage, the conventional encoding methods have been proposed [12,[34][35][36][37][38][39][40][41][42][43][44], which require more resources of physical qubits. Then, other quantum control techniques are introduced in cooperating with NHQC, such as the composite scheme or dynamical decoupling strategy [45][46][47], the delib- * zyxue83@163.com erately optimal pulse control technique [48][49][50][51][52][53][54][55], and complex pulses target to shorten the gate-time [56][57][58][59][60], etc.…”