We analyze the performance of holonomic quantum gates in semi-conductor quantum dots, driven by ultrafast lasers, under the effect of a dissipative environment. In agreement with the standard practice, the environment is modeled as a thermal bath of oscillators linearly coupled with the excitonic states of the quantum dot. Standard techniques of quantum dissipation make the problem amenable to a numerical treatment and allow to determine the fidelity (the common gate-performance estimator), as a function of all the relevant physical parameters. As a consequence of our analysis, we show that, by varying in a suitable way the controllable parameters, the disturbance of the environment can be (approximately) suppressed, and the performance of the gate optimized--provided that the thermal bath is purely superhomic. We conclude by showing that such an optimization it is impossible for ohmic environments.
The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an alternative scheme which operates a protected CNOT gate via the holonomic control of a handful of system parameters, without requiring any measurement. We show how the adiabatic tuning of pair-wise couplings between Majoranas can robustly lead to the full entanglement of two qubits, insensitive with respect to small variations in the control of the parameters.
Robustness of non-abelian holonomic quantum gates against parametric noise
本文对一类非阿贝尔完整量子门的鲁棒性进行了数值研究。我们考虑到由于控制场的随机波动的参数噪声驱动的时间相关的哈密顿沿绝热环。所用的性能估计器是无噪声和有噪声完整门之间的状态保真度。我们进行了我们的分析与不同的相关时间，我们发现，有噪声的完整门似乎是接近无噪声的“短”和“长”噪声相关时间。这个结果可以解释为完整算子的几何性质的结果。我们的模拟是通过使用与激子方案有关的参数来实现完整量子计算的[P.Solinas et al.Phys.Rev.B67，121307（2003）]
Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault tolerant quantum computation, due to its robustness against operational noises. However, because of the parametric restriction of previous schemes, the main robust advantage of holonomic quantum gates is smeared. Here, we experimentally demonstrate a solution scheme, demonstrating nonadiabatic holonomic single qubit quantum gates with optimal control in a trapped Yb ion based on three level systems with resonant drives, which also hold the advantages of fast evolution and convenient …
It has been shown that a Weyl point in a superconducting nanostructure may give rise to a Weyl disk where two quantum states are almost degenerate in a 2D manifold in the parametric space. This opens up the possibility of a holonomic quantum manipulation: a transformation of the wave function upon adiabatic change of the parameters within the degenerate manifold. In this paper, we investigate in detail the opportunities for holonomic manipulation in Weyl disks. We compute the connection at the manifold in quasiclassical approximation to show it is Abelian and can be used for a phase gate. To p…
Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits
为了实现一组基于非阿贝尔几何相位的通用量子逻辑门，传统的观点是需要超过两个能级的量子系统，这对于超导量子比特来说是非常困难的，这似乎是为什么在最近的实验中只实现单量子比特门的主要原因[A. A. Abdumalikov Jr \emph{et al} .，Nature 496，482（2013）]。本文提出在无消相干子空间中利用电路QED实现非绝热完整量子计算，其中只需要传输子比特中的两个能级，一个通常的相互作用，以及一个最小的无消相干子空间编码资源.特别是，我们的方案不仅克服了以往研究中遇到的困难，而且仍然可以获得相当大的有效耦合强度，从而可以实现高保真度的量子门。因此，本方案为利用超导电路实现鲁棒完整量子计算提供了一条很有前途的途径。
Non-Abelian geometric phases acquired in cyclic quantum evolution can be utilized as natural resources for constructing robust holonomic gates for quantum information processing. Recently, an extensible holonomic quantum computation (HQC) was proposed and demonstrated in a recent superconducting experiment [T. Yan et al., Phys. Rev. Lett. 122, 080501 (2019)]. However, for the weakly anharmonic system, this HQC was given of low gate fidelity due to leakage to states outside of the computational subspace. Here, we propose a scheme that to construct nonadiabatic holonomic gates via dynamical inva…
Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation
给出了齐次丛中的等完整力学问题的精确表达式和求解方法。该问题的形式是变分方程的边值问题。将该解应用于完整量子计算机中的最优控制问题。我们提供了一个处方，以构建一个最优控制器的任意酉门，并将其应用到$ k $维酉门，其操作上的$ N $维希尔伯特空间与$ N \geq 2k $。我们的建设被应用到几个重要的酉门，如阿达玛门，CNOT门，和两个量子位离散傅立叶变换门。这些门的控制器是显式构造的。
The main obstacles to the realization of high-fidelity quantum gates are the control errors arising from inaccurate manipulation of a quantum system and the decoherence caused by the interaction between the quantum system and its environment. Nonadiabatic holonomic quantum computation allows for high-speed implementation of whole-geometric quantum gates, making quantum computation robust against control errors. Dynamical decoupling provides an effective method to protect quantum gates against environment-induced decoherence, regardless of collective decoherence or independent decoherence. In t…
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus faster gate operations are highly desired. Here, we propose a nonadiabatic holonomic quantum computation (NHQC) scheme with detuned interactions on $Δ$-type three-level system, which combines the time-optimal control technique with the time-independent detuning adjustment to further accelerate universal gate operations, {so that the gate-time can be greatly…
