Entangling Qubits with High Fidelity via Nonlocal Echo Sequences

量子计算机有潜力为现代信息经济提供许多好处，例如更快的搜索算法、增强的安全性和更有效的数学计算方法。然而，为量子计算机制造可靠的组件（如量子门）是一项挑战。量子计算机的运行方式与目前的计算机大不相同，因为它利用了一套不寻常的规则——量子力学——来控制构成计算机逻辑比特或“量子位”的非常小的物体的行为。问题是量子比特非常微妙，控制中的任何缺陷或不希望的扰动（噪声）都可能破坏计算。该项目的目标是发现操作量子计算机的方法，使其能够自我纠正计算过程中可能出现的某些类型的错误。这将通过使用受控的光脉冲序列来“纠缠”成对的量子比特来实现，量子力学的一个独特特征是，它们可以以一种无法通过单独测量量子比特来访问的方式共享信息。通过设计一系列能够可靠地纠缠量子比特对的控制信号，应该有可能使量子比特经历一个自我纠正的轨迹，即使在存在噪声的情况下也能达到特定的、期望的量子态，从而使量子计算领域更接近实现。该项目将产生一种新的双量子位动态保护纠缠协议，该协议假设只能访问高保真的单量子位门（可以用现有方法产生）和一个有噪声但特征良好的双量子位门。这个项目的主要应用将是量子点自旋量子比特的纠缠，因为这些非常有前途的系统中的噪声目前特别有限。噪声（包括电噪声和超细噪声）主要是低频的，通常具有1/f的功率谱密度，因此这种复合脉冲序列方法是合理的。分析和计算方法的结合将用于搜索最优鲁棒序列，使用模拟随机基准来表征其性能。这些解决方案将被设计成模块化的，这样它们就可以与脉冲整形和其他保真度增强技术同时使用，从而大大减少任何量子位平台逻辑空间内的误差。这是迈向可扩展、容错量子计算应用的重要一步。

Quantum computers have the potential to provide numerous benefits for the modern information-based economy, for example faster search algorithms, enhanced security, and more efficient ways to do mathematical calculations. However, it is challenging to make reliable components, such as quantum gates, for quantum computers. A quantum computer operates quite differently from current computers, since it takes advantage of the fact that an unusual set of rules, quantum mechanics, governs the behavior of the very small objects that make up the logical bits, or "qubits" of the computer. The problem is that qubits are very delicate, and any imperfections in the control or undesired perturbations (noise) can ruin the computation. The goal of this project is to discover ways to operate a quantum computer so that it self corrects certain types of errors that may occur during the computation. This will be done through the use of a controlled sequence of light pulses to "entangle" pairs of qubits, a unique feature of quantum mechanics that allows them to share information in such a way that it cannot be accessed by measuring the qubits individually. By designing a sequence of control signals that can reliably entangle pairs of qubits, it should be possible to enable qubits to undergo a self-correcting trajectory and end up in a particular, desired quantum state even in the presence of noise, bringing the field of quantum computation a step closer to realization. This project will produce a novel two-qubit dynamically protected entangling protocol that assumes only access to high-fidelity single-qubit gates (which can be produced with existing methods) and a noisy, but well-characterized, two-qubit gate. The primary application of this project will be to the entangling of quantum dot spin qubits, since noise in these otherwise very promising systems is particularly limiting at the moment. The noise (both electrical and hyperfine) is predominantly low-frequency, typically with a 1/f power spectral density, so that such a composite pulse sequence approach is reasonable. A combination of analytical and computational methods will be used to search for optimally robust sequences, using simulated randomized benchmarking to characterize their performance. The solutions will be designed to be modular such that they can be used simultaneously with pulse shaping and other fidelity-enhancing techniques to substantially reduce errors within the logical space of any qubit platform. This is a vital step towards the application of scalable, fault-tolerant quantum computing.