No Arabic abstract
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.
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 $10^{-4}$.
Frequently, subroutines in quantum computers have the structure $mathcal{F}mathcal{U}mathcal{F}^{-1}$, where $mathcal{F}$ is some unitary transform and $mathcal{U}$ is performing a quantum computation. In this paper we suggest that if, in analogy to spin echoes, $mathcal{F}$ and $mathcal{F}^{-1}$ can be implemented symmetrically such that $mathcal{F}$ and $mathcal{F}^{-1}$ have the same hardware errors, a symmetry boost in the fidelity of the combined $mathcal{F}mathcal{U}mathcal{F}^{-1}$ quantum operation results. Running the complete gate--by--gate implemented Shor algorithm, we show that the fidelity boost can be as large as a factor 10. Corroborating and extending our numerical results, we present analytical scaling calculations that show that a symmetry boost persists in the practically interesting case of a large number of qubits. Our analytical calculations predict a minimum boost factor of about 3, valid for all qubit numbers, which includes the boost factor 10 observed in our low-qubit-number simulations. While we find and document this symmetry boost here in the case of Shors algorithm, we suggest that other quantum algorithms might profit from similar symmetry-based performance boosts whenever $mathcal{F}mathcal{U}mathcal{F}^{-1}$ sub-units of the corresponding quantum algorithm can be identified.
Quantum metrology offers an enhanced performance in experiments such as gravitational wave-detection, magnetometry or atomic clocks frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features such as entanglement or squeezing. For any practical application the inevitable impact of decoherence needs to be taken into account in order to correctly quantify the ultimate attainable gain in precision. We compare the applicability and the effectiveness of various methods of calculating the ultimate precision bounds resulting from the presence of decoherence. This allows us to put a number of seemingly unrelated concepts into a common framework and arrive at an explicit hierarchy of quantum metrological methods in terms of the tightness of the bounds they provide. In particular, we show a way to extend the techniques originally proposed in Demkowicz-Dobrzanski et al 2012 Nat. Commun. 3 1063, so that they can be efficiently applied not only in the asymptotic but also in the finite-number of particles regime. As a result, we obtain a simple and direct method, yielding bounds that interpolate between the quantum enhanced scaling characteristic for small number of particles and the asymptotic regime, where quantum enhancement amounts to a constant factor improvement. Methods are applied to numerous models including noisy phase and frequency estimation, as well as the estimation of the decoherence strength itself.
We demonstrate unconditional quantum-noise suppression in a collective spin system via feedback control based on quantum non-demolition measurement (QNDM). We perform shot-noise limited collective spin measurements on an ensemble of $3.7times 10^5$ laser-cooled 171Yb atoms in their spin-1/2 ground states. Correlation between two sequential QNDMs indicates $-0.80^{+0.11}_{-0.12},mathrm{dB}$ quantum noise suppression in a conditional manner. Our feedback control successfully converts the conditional quantum-noise suppression into the unconditional one without significant loss of the noise
The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the interaction with an another optimally initialized auxiliary quantum system, we show that the quantum channel capacity sets the scaling behaviour of the optimal control error. Specifically, we prove that the minimum control error is ensured by maximizing the quantum capacity of the channel mapping the initial control state into the target state of the controlled system, i.e., optimizing the quantum information flow from the controller to the system to be controlled. Analytical results, supported by numerical evidences, are provided when the systems and the controller are either qubits or single Bosonic modes and can be applied to a very large class of platforms for controllable quantum devices.