Fast and robust quantum gates are the cornerstones of fault-tolerance quantum computation. In this paper, as opposed to the previous proposals which use cyclic geometric phases, we propose to realize quantum computation based on noncyclic geometric evolution. The superiority of the noncyclic scheme is that the operation time is proportional to the rotation angle of the quantum state. Therefore, the noncyclic scheme becomes fairly fast in the case of quantum gates with small rotation angle, which will be more insensitive to the decoherence and the leakage to the states outside the computational basis. Similar to the cyclic version of geometric quantum computation, dynamical phases here during the evolution are canceled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabaticity. The proposed scheme is robust against random noise due to the geometric characteristic of projective Hilbert space. Since the proposed scheme is fast and robust, it is a particularly suitable way to manipulate the physical systems with weak nonlinearity, such as superconducting systems.
Fast and robust quantum gates are the cornerstones of fault-tolerance quantum computation. In this paper, as opposed to the previous proposals which use cyclic geometric phases, we propose to realize quantum computation based on noncyclic geometric evolution. The superiority of the noncyclic scheme is that the operation time is proportional to the rotation angle of the quantum state. Therefore, the noncyclic scheme becomes fairly fast in the case of quantum gates with small rotation angle, which will be more insensitive to the decoherence and the leakage to the states outside the computational basis. Similar to the cyclic version of geometric quantum computation, dynamical phases here during the evolution are canceled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabaticity. The proposed scheme is robust against random noise due to the geometric characteristic of projective Hilbert space. Since the proposed scheme is fast and robust, it is a particularly suitable way to manipulate the physical systems with weak nonlinearity, such as superconducting systems.
Possessing the noise-resilience feature, geometric phases have become important in robust quantum computation. Gates based on the Abelian and non-Abelian geometric phases have been experimentally demonstrated in different physical systems. However, previous proposals require cyclic evolution with a constant operation time even for small rotation angles, which set a limit to the gate operation time. Here, we experimentally realize noncyclic geometric gates, where the cyclic condition is removed and the operation time is proportional to the rotation angle. With the adiabatic process sped up by shortcut to adiabaticity, the fidelities of a noncyclic geometric gate characterized by randomized benchmarking are above 99.5%. Comparing with the dynamic scheme, we demonstrate the robustness of our gate against control instability in the experiment. Moreover, our results indicate that the noncyclic geometric gate with a smaller rotation angle corresponds to a shorter evolution time and higher fidelity. As small rotation angles are essential in the quantum algorithm, the superiority of noncyclic geometric gates makes them promising candidates in fast and robust quantum computation.
Nonadiabatic geometric quantum computation is dedicated to the realization of high-fidelity and robust quantum gates, which is the necessity of fault-tolerant quantum computation. However, it is limited by cyclic and mutative evolution path, which usually requires longer gate-time and abrupt pulse control, and thus weaken the gate performance. Here, we propose a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolutions, which effectively shorten the gate duration, and universal quantum gates can be realized in one step without path mutation. Our numerical simulation shows that, comparing with the conventional dynamical gates, the constructed geometric gates have stronger resistant not only to noise but also to decoherence effect. In addition, our 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, our scheme provides a promising way to realize high-fidelity fault-tolerant quantum gates for scalable quantum computation.
High-fidelity quantum gates are essential for large-scale quantum computation. However, any quantum manipulation will inevitably affected by noises, systematic errors and decoherence effects, which lead to infidelity of a target quantum task. Therefore, implementing high-fidelity, robust and fast quantum gates is highly desired. Here, we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity. In our proposal, the target Hamiltonian to induce noncyclic non-Abelian geometric phases can be inversely engineered with less evolution time and demanding experimentally, leading to high-fidelity quantum gates in a simple setup. Besides, our scheme is readily realizable in physical system currently pursued for implementation of quantum computation. Therefore, our proposal represents a promising way towards fault-tolerant geometric quantum computation.
Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geomet-ric gate. However, the conventiona NGQC is that all of the gates are performed with exactly the same amount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation (NNGQC), that arbitrary single- and two-qubit geometric gate can be constructed via noncyclic non-Abelian geometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gates against the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied in various quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate, wemake simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can berealized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, our scheme provides a promising way for fast and robust neutral-atom-based quantum computation.
Quantum control that is robust against control errors and dephasing process is a key ingredient of quantum computation. In article no. 1900013, Yanxiong Du and co-workers review the recent progresses on the geometric quantum computation with shortcut to adiabaticity. Geometric phase, as acquired in the evolution of Hilbert space, can be used to realize geometric quantum computation that is robust against random noise and systematic errors. Through optimizing the control waveform with shortcut to adiabatic manner, the operation will consolidate the virtues of being fast and robust. Theoretical and experimental results have proven the effectiveness of combining the geometric phase and shortcut to adiabaticity.
Abstract 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.