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arXiv:2110.02849 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Efficient Quantum Gate Discovery with Optimal Control

Paul Kairys, Travis S. Humble

Published Oct 1, 2021• 2 citations
arXivHTMLPDF

Abstract

Optimal control theory provides a framework for numerical discovery of device controls that implement quantum logic gates, but common objective functions used for optimization often assign arbitrarily high costs to otherwise useful controls. We propose a framework for designing objective functions that permit novel gate designs such as echo pulses or locally-equivalent gates. We use numerical simulations to demonstrate the efficacy of the new objective functions by designing microwave-only pulses that act as entangling gates for superconducting transmon architectures. We observe that the proposed objective functions lead to higher fidelity controls in fewer optimization iterations than obtainable by traditional objective functions.

DOI
10.1109/qce52317.2021.00062

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Optimal control theory provides a framework for numerical discovery of device controls that implement quantum logic gates, but common objective functions used for optimization often assign arbitrarily high costs to otherwise useful controls. We propose a framework for designing objective functions that permit novel gate designs such as echo pulses or locally-equivalent gates. We use numerical simulations to demonstrate the efficacy of the new objective functions by designing microwave-only pulses that act as entangling gates for superconducting transmon architectures. We observe that the proposed objective functions lead to higher fidelity controls in fewer optimization iterations than obtainable by traditional objective functions.
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations on a superconducting transmon qubit, using detailed numerical simulations. We demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of about 99.99%.
In the current NISQ era, there is demand for functional quantum devices to solve relevant computational problems, which motivates a utilitarian perspective on device design: The goal is to create a device that is able to run a given algorithm with state-of-the-art performance. In this work, we use optimal control tools to derive the gate set required by a toy algorithm and, in tandem, explore the model space of superconducting quantum computer design, from dispersively coupled to stronger interacting qubits, to maximize gate fidelity. We employ perfect entangler theory to provide flexibility in the search for a two-qubit gate on a given platform and to compare designs with different entangling mechanisms, e.g., CPHASE\texttt{CPHASE}CPHASE and iSWAP\sqrt{\texttt{iSWAP}}iSWAP​. To ensure the applicability of our investigation, we limit ourselves to "simple" (i.e., sparse parametrization) pulses and quantify, where results differ from using the full complexity of piecewise constant controls.
We present an efficient approach to achieving arbitrary, high-fidelity control of a multilevel quantum system using optimal control techniques. As an demonstration, we implement a continuous, software-defined microwave pulse to realize a 0↔2 SWAP gate that achieves an average gate fidelity of 99.4%. We describe our procedure for extracting the system Hamiltonian, calibrating the quantum and classical hardware chain, and evaluating the gate fidelity. Our work represents an alternative, fully generalizable route towards achieving universal quantum control by leveraging optimal control techniques.
Abstract The utility of a quantum computer is highly dependent on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for the quantum processor—in contrast to many established gate implementation strategies. In this work, we utilize a continuous control reinforcement learning algorithm to design entangling two-qubit gates for superconducting qubits; specifically, our agent constructs cross-resonance and CNOT gates without any prior information about the physical system. Using a simulated environment of fixed-frequency fixed-coupling transmon qubits, we demonstrate the capability to generate novel pulse sequences that outperform the standard cross-resonance gates in both fidelity and gate duration, while maintaining a comparable susceptibility to stochastic unitary noise. We further showcase an augmentation in training and input information that allows our agent to adapt its pulse design abilities to drifting hardware characteristics, importantly, with little to no additional optimization. Our results exhibit clearly the advantages of unbiased adaptive-feedback learning-based optimization methods for transmon gate design.
Superconducting circuits are one of the leading architectures in quantum computing. To undertake quantum computing one must be able to perform quantum gates; however, two-qubit gates are still limited in fidelity and gate time. The cross-resonance gate is a two-qubit gate that uses direct microwave drives and has seen much success in its implementation; but, there are theoretical indications that it has not yet reached the coherence limited fidelity value and its gate time is still relatively long compared with other quantum gate methods. Quantum optimal control theory is a powerful tool in the design of controls for quantum operations and has shown the capability to improve gate fidelities and reduce gate times. Robust quantum optimal control methodologies have further built on this to develop high fidelity quantum gates that are robust to uncertainties and noise in the system. In this thesis we use robust quantum optimal control theory to achieve these goals for the cross-resonance gate in a variety of superconducting qubit architectures. First, we investigate two superconducting qubits embedded in a common 3D microwave cavity in which the control drive is implemented via the common cavity mode of the cavity. We determine pulse shapes that implement the cross-resonance gate that are robust to uncertainty in the qubit transition frequencies for both a strictly two-level superconducting qubit and a three-level qubit. Second, we look at the cross-resonance gate with direct drives on each qubit, finding the minimal time to perform the cross-resonance gate with pulses that are robust to uncertainty in a measured system parameter for three cases: two three-level qubits with no drive crosstalk, two three-level qubits with some drive crosstalk, and two two-level qubits. Lastly, we report on simulations undertaken towards implementing a robust, high fidelity cross-resonance gate in a novel superconducting quantum device known as the coaxmon.
Abstract Reaching high-speed, high-fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. We directly optimize the amplitude and phase of each sample point of the digitized control pulse. We thereby fully exploit the capabilities of the pulse generation electronics and create a 4.16 ns single-qubit pulse with 99.76 % fidelity and 0.044 % leakage. This is a sevenfold reduction of the leakage rate and a threefold reduction in standard errors of the best DRAG pulse we have calibrated at such short durations on the same system.