Implementing universal nonadiabatic holonomic quantum gates with transmons

Abstract

Geometric phases are well known to be noise resilient in quantum evolutions and operations. Holonomic quantum gates provide us with a robust way towards universal quantum computation, as these quantum gates are actually induced by non-Abelian geometric phases. Here we propose and elaborate how to efficiently implement universal nonadiabatic holonomic quantum gates on simpler superconducting circuits, with a single transmon serving as a qubit. In our proposal, an arbitrary single-qubit holonomic gate can be realized in a single-loop scenario by varying the amplitudes and phase difference of two microwave fields resonantly coupled to a transmon, while nontrivial two-qubit holonomic gates may be generated with a transmission-line resonator being simultaneously coupled to the two target transmons in an effective resonant way. Moreover, our scenario may readily be scaled up to a two-dimensional lattice configuration, which is able to support large scalable quantum computation, paving the way for practically implementing universal nonadiabatic holonomic quantum computation with superconducting circuits.

Ultrafast Holonomic Quantum Gates

“…In the Bloch sphere, as shown in Fig. 1(b), the evolution path of our scheme is shorter than that of single-loop schemes [40][41][42], and the evolution path can be further shortened by increasing the detuning |∆ 2 |, which can also be shorter that previous TOC schemes [37][38][39].…”

“…In the following, we will show that this additional parameter enable us to accelerate the induced holonomic quantum gates, and the gate-time can be greatly shortened within the hardware limitation. This novel effect is the main difference between this work and previous ones [37][38][39][40][41][42], and can be explained intuitively as following. Any target gate is act on the qubit states of {|0 |1 }, and thus the main contribution of the gates will be attributed to the |0 ↔ |1 transition, while the other transitions are introduced to make the gate to be holonomic.…”

“…In these two proposals, they can achieve shorter gatetime and stronger robustness, as experimentally demonstrated in Ref. [39], compared to conventional NHQC in single-loop way [40][41][42]. Then, it is naturally to ask: "how fast can holonomic quantum gates eventually be?…”

Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace

“…Here, we propose and experimentally realize an NHQC scheme in a three-qubit DFS [39,40], based on the resonant single-loop scenario [42]. Therefore, comparing with previous schemes [39,40], our implementation simplifies the needed gate sequences for large-scale algorithm, as it can achieve an arbitrary gate in a single step.…”

Nonadiabatic Geometric Quantum Computation with Parametrically Tunable Coupling

“…However, the GQC is originally proposed by using the adiabatic cycle evolution, where quantum systems will be exposed to the external environment for a long time. To remove this adiabatic limitation, nonadiabatic GQC schemes have been proposed to achieve fast and high-fidelity quantum gates based on Abelian [27][28][29][30] and non-Abelian geometric phases [31][32][33][34][35][36][37], which can still have the merit of robustness against certain local noises [38][39][40][41][42]. Recently, geometric phases or elementary geometric quantum gates have been experimentally demonstrated on various systems [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59].…”