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Register a new userImproving quantum gate performance through neighboring optimal control
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Successful implementation of a fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold $P_{a}$ exists for any quantum gate that is to be used in such a computation. Specifically, the error probability $P_{e}$ for such a gate must fall below the accuracy threshold: $P_{e} < P_{a}$. Estimates of $P_{a}$ vary widely, though $P_{a}sim 10^{-4}$ has emerged as a challenging target for hardware designers. In this paper we present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. We illustrate this approach by applying it to all gates in a universal set of quantum gates produced using non-adiabatic rapid passage that has appeared in the literature. Performance improvements are substantial, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall well below the target threshold of $10^{-4}$.
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We present an approach to single-shot high-fidelity preparation of an $n$-qubit state based on neighboring optimal control theory. This represents a new application of the neighboring optimal control formalism which was originally developed to produce single-shot high-fidelity quantum gates. To illustrate the approach, and to provide a proof-of-principle, we use it to prepare the two qubit Bell state $|beta_{01}rangle = (1/sqrt{2})left[, |01rangle + |10rangle,right]$ with an error probability $epsilonsim 10^{-6}$ ($10^{-5}$) for ideal (non-ideal) control. Using standard methods in the literature, these high-fidelity Bell states can be leveraged to fault-tolerantly prepare the logical state $|overline{beta}_{01}rangle$.
Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.
Manipulating quantum computing hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise limits the performance and capabilities of noisy intermediate-scale quantum (NISQ) devices, as well as any future quantum computing technologies. Fortunately quantum control enables efficient execution of quantum logic operations and algorithms with built-in robustness to errors, without the need for complex logical encoding. In this manuscript we introduce software tools for the application and integration of quantum control in quantum computing research, serving the needs of hardware R&D teams, algorithm developers, and end users. We provide an overview of a set of python-based classical software tools for creating and deploying optimized quantum control solutions at various layers of the quantum computing software stack. We describe a software architecture leveraging both high-performance distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other software packages and quantum programming languages. Our presentation includes a detailed mathematical overview of central product features including a flexible optimization toolkit, filter functions for analyzing noise susceptibility in high-dimensional Hilbert spaces, and new approaches to noise and hardware characterization. Pseudocode is presented in order to elucidate common programming workflows for these tasks, and performance benchmarking is reported for numerically intensive tasks, highlighting the benefits of the selected cloud-compute architecture. Finally, we present a series of case studies demonstrating the application of quantum control solutions using these tools in real experimental settings for both trapped-ion and superconducting quantum computer hardware.
We theoretically investigate electron spin operations driven by applied electric fields in a semiconductor double quantum dot (DQD). Our model describes a DQD formed in semiconductor nanowire with longitudinal potential modulated by local gating. The eigenstates for two electron occupation, including spin-orbit interaction, are calculated and then used to construct a model for the charge transport cycle in the DQD taking into account the spatial dependence and spin mixing of states. The dynamics of the system is simulated aiming at implementing protocols for qubit operations, that is, controlled transitions between the singlet and triplet states. In order to obtain fast spin manipulation, the dynamics is carried out taking advantage of the anticrossings of energy levels introduced by the spin-orbit and interdot couplings. The theory of optimal quantum control is invoked to find the specific electric-field driving that performs qubit logical operations. We demonstrate that it is possible to perform within high efficiency a universal set of quantum gates ${$CNOT, H$otimes$I, I$otimes$H, T$otimes$I, and T$otimes$I$}$, where H is the Hadamard gate, T is the $pi/8$ gate, and I is the identity, even in the presence of a fast charge transport cycle and charge noise effects.
Quantum memories with high efficiency and fidelity are essential for long-distance quantum communication and information processing. Techniques have been developed for quantum memories based on atomic ensembles. The atomic memories relying on the atom-light resonant interaction usually suffer from the limitations of narrow bandwidth. The far-off-resonant Raman process has been considered a potential candidate for use in atomic memories with large bandwidths and high speeds. However, to date, the low memory efficiency remains an unsolved bottleneck. Here, we demonstrate a high-performance atomic Raman memory in Rb87 vapour with the development of an optimal control technique. A memory efficiency of 82.6% for 10-ns optical pulses is achieved and is the highest realized to date in atomic Raman memories. In particular, an unconditional fidelity of up to 98.0%, significantly exceeding the no-cloning limit, is obtained with the tomography reconstruction for a single-photon level coherent input. Our work marks an important advance of atomic Raman memory towards practical applications in quantum information processing.
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