Adaptive hybrid optimal quantum control for imprecisely characterized systems

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.

Bayesian-Based Hybrid Method for Rapid Optimization of NV Center Sensors

NV centers are among the most promising platforms in the field of quantum sensing. Magnetometry based on NV centers, especially, has achieved concrete development in areas of biomedicine and medical diagnostics. Improving the sensitivity of NV center sensors under wide inhomogeneous broadening and fieldamplitude drift is a crucial issue of continuous concern that relies on the coherent control of NV centers with high average fidelity. Quantum optimal control (QOC) methods provide access to this target; nevertheless, the high time consumption of current methods due to the large number of needful sample points as well as the complexity of the parameter space has hindered their usability. In this paper, we propose the Bayesian estimation phase-modulated (B-PM) method to tackle this problem. In the case of the state transforming of an NV center ensemble, the B-PM method reduced the time consumption by more than 90% compared with the conventional standard Fourier basis (SFB) method while increasing the average fidelity from 0.894 to 0.905. In the AC magnetometry scenario, the optimized control pulse obtained with the B-PM method achieved an eight-fold extension of coherence time T2 compared with the rectangular π pulse. Similar application can be made in other sensing situations. As a general algorithm, the B-PM method can be further extended to the open- and closed-loop optimization of complex systems based on a variety of quantum platforms.

Towards fully optimised and automated ESR spectroscopy

To address the problems of instrumental imperfection and time-consuming experimental setup in electron spin resonance (ESR), we present ESR-POISE, a user-friendly software package for fully automated and fast on-the-fly optimisation...

Algorithmic Primitives for Quantum-Assisted Quantum Control

We present two primitive algorithms to evaluate overlaps and transition matrix time series, which are then used to construct several quantum-assisted quantum control algorithms. Unlike previous approaches, our method bypasses tomographically complete measurements and instead relies solely on single qubit measurements. We analyze circuit complexity of composed algorithms and sources of noise arising from Trotterization and measurement errors.

Filter Functions for Quantum Processes under Correlated Noise

Many qubit implementations are afflicted by correlated noise not captured by standard theoretical tools that are based on Markov approximations. While independent gate operations are a key concept for quantum computing, it is actually not possible to fully describe noisy gates locally in time if noise is correlated on times longer than their duration. To address this issue, we develop a method based on the filter function formalism to perturbatively compute quantum processes in the presence of correlated classical noise. We derive a composition rule for the filter function of a sequence of gates in terms of those of the individual gates. The joint filter function allows us to efficiently compute the quantum process of the whole sequence. Moreover, we show that correlation terms arise which capture the effects of the concatenation and, thus, yield insight into the effect of noise correlations on gate sequences. Our generalization of the filter function formalism enables both qualitative and quantitative studies of algorithms and state-of-the-art tools widely used for the experimental verification of gate fidelities like randomized benchmarking, even in the presence of noise correlations.

Closed-loop control of a GaAs-based singlet-triplet spin qubit with 99.5% gate fidelity and low leakage

Semiconductor spin qubits have recently seen major advances in coherence time and control fidelities, leading to a single-qubit performance that is on par with other leading qubit platforms. Most of this progress is based on microwave control of single spins in devices made of isotopically purified silicon. For controlling spins, the exchange interaction is an additional key ingredient which poses new challenges for high-fidelity control. Here, we demonstrate exchange-based single-qubit gates of two-electron spin qubits in GaAs double quantum dots. Using careful pulse optimization and closed-loop tuning, we achieve a randomized benchmarking fidelity of (99.50±0.04)% and a leakage rate of 0.13% out of the computational subspace. These results open new perspectives for microwave-free control of singlet-triplet qubits in GaAs and other materials.

The exchange interaction between spins poses considerable challenges for high-fidelity control of semiconductor spin qubits. Here, the authors use pulse optimization and closed-loop control to achieve a gate fidelity of 99.5% for exchange-based single-qubit gates of two-electron spin qubits in GaAs.

An improved differential evolution algorithm for learning high-fidelity quantum controls

Precisely and efficiently designing control pulses for the preparation of quantum states and quantum gates are the fundamental tasks for quantum computation. Gradient-based optimal control methods are the routine to design such pulses. However, the gradient information is often difficult to calculate or measure, especially when the system is not well calibrated or in the presence of various uncertainties. Gradient-free evolutionary algorithm is an alternative choice to accomplish this task but usually with low-efficiency. Here, we design an efficient mutation rule by using the information of the current and the former individuals together. This leads to our improved differential evolution algorithm, called daDE. To demonstrate its performance, we numerically benchmark the pulse optimization for quantum states and quantum gates preparations on small-scale NMR system. Further numerical comparisons with conventional differential evolution algorithms show that daDE has great advantages on the convergence speed and robustness to several uncertainties including pulse imperfections and measurement errors.

Approaching the adiabatic timescale with machine learning

The control and manipulation of quantum systems without excitation are challenging, due to the complexities in fully modeling such systems accurately and the difficulties in controlling these inherently fragile systems experimentally. For example, while protocols to decompress Bose-Einstein condensates (BECs) faster than the adiabatic timescale (without excitation or loss) have been well developed theoretically, experimental implementations of these protocols have yet to reach speeds faster than the adiabatic timescale. In this work, we experimentally demonstrate an alternative approach based on a machine-learning algorithm which makes progress toward this goal. The algorithm is given control of the coupled decompression and transport of a metastable helium condensate, with its performance determined after each experimental iteration by measuring the excitations of the resultant BEC. After each iteration the algorithm adjusts its internal model of the system to create an improved control output for the next iteration. Given sufficient control over the decompression, the algorithm converges to a solution that sets the current speed record in relation to the adiabatic timescale, beating out other experimental realizations based on theoretical approaches. This method presents a feasible approach for implementing fast-state preparations or transformations in other quantum systems, without requiring a solution to a theoretical model of the system. Implications for fundamental physics and cooling are discussed.

Feedback control optimisation of ESR experiments

Numerically optimised microwave pulses are used to increase excitation efficiency and modulation depth in electron spin resonance experiments performed on a spectrometer equipped with an arbitrary waveform generator. The optimisation procedure is sample-specific and reminiscent of the magnet shimming process used in the early days of nuclear magnetic resonance - an objective function (for example, echo integral in a spin echo experiment) is defined and optimised numerically as a function of the pulse waveform vector using noise-resilient gradient-free methods. We found that the resulting shaped microwave pulses achieve higher excitation bandwidth and better echo modulation depth than the pulse shapes used as the initial guess. Although the method is theoretically less sophisticated than simulation based quantum optimal control techniques, it has the advantage of being free of the linear response approximation; rapid electron spin relaxation also means that the optimisation takes only a few seconds. This makes the procedure fast, convenient, and easy to use. An important application of this method is at the final stage of the implementation of theoretically designed pulse shapes: compensation of pulse distortions introduced by the instrument. The performance is illustrated using spin echo and out-of-phase electron spin echo envelope modulation experiments. Interface code between Bruker SpinJet arbitrary waveform generator and Matlab is included in versions 2.2 and later of the Spinach library.

Tunable, Flexible, and Efficient Optimization of Control Pulses for Practical Qubits

Quantum computation places very stringent demands on gate fidelities, and experimental implementations require both the controls and the resultant dynamics to conform to hardware-specific constraints. Superconducting qubits present the additional requirement that pulses must have simple parameterizations, so they can be further calibrated in the experiment, to compensate for uncertainties in system parameters. Other quantum technologies, such as sensing, require extremely high fidelities. We present a novel, conceptually simple and easy-to-implement gradient-based optimal control technique named gradient optimization of analytic controls (GOAT), which satisfies all the above requirements, unlike previous approaches. To demonstrate GOAT's capabilities, with emphasis on flexibility and ease of subsequent calibration, we optimize fast coherence-limited pulses for two leading superconducting qubits architectures-flux-tunable transmons and fixed-frequency transmons with tunable couplers.

Quantum information processing with superconducting circuits: a review

During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

Experimental Demonstration of a Cheap and Accurate Phase Estimation

We demonstrate an experimental implementation of robust phase estimation (RPE) to learn the phase of a single-qubit rotation on a trapped Yb^{+} ion qubit. We show this phase can be estimated with an uncertainty below 4×10^{-4}  rad using as few as 176 total experimental samples, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We crossvalidate the results of RPE with the more resource-intensive protocol of gate set tomography.

Fast machine-learning online optimization of ultra-cold-atom experiments

We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our ‘learner’ discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system.

Robust manipulation of superconducting qubits in the presence of fluctuations

Superconducting quantum systems are promising candidates for quantum information processing due to their scalability and design flexibility. However, the existence of defects, fluctuations, and inaccuracies is unavoidable for practical superconducting quantum circuits. In this paper, a sampling-based learning control (SLC) method is used to guide the design of control fields for manipulating superconducting quantum systems. Numerical results for one-qubit systems and coupled two-qubit systems show that the "smart" fields learned using the SLC method can achieve robust manipulation of superconducting qubits, even in the presence of large fluctuations and inaccuracies.

High-fidelity single-qubit gates for two-electron spin qubits in GaAs

Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency 1/f-like noise) and show, theoretically, that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.

Optimal quantum control using randomized benchmarking

We present a method for optimizing quantum control in experimental systems, using a subset of randomized benchmarking measurements to rapidly infer error. This is demonstrated to improve single- and two-qubit gates, minimize gate bleedthrough, where a gate mechanism can cause errors on subsequent gates, and identify control crosstalk in superconducting qubits. This method is able to correct parameters so that control errors no longer dominate and is suitable for automated and closed-loop optimization of experimental systems.