Controlling Quantum Devices with Nonlinear Hardware

Abstract

High fidelity coherent control of quantum systems is critical to building quantum devices and quantum computers. We provide a general optimal control framework for designing control sequences that account for hardware control distortions while maintaining robustness to environmental noise. We demonstrate the utility of our algorithm by presenting examples of robust quantum gates optimized in the presence of nonlinear distortions. We show that nonlinear classical controllers do not necessarily incur additional computational cost to pulse optimization, enabling more powerful quantum devices. PACS numbers:The ability to coherently control the dynamics of quantum systems with high fidelity is a critical component of the development of modern quantum devices, including quantum computers [1], actuators [2,3], and sensors [4][5][6] that push beyond the capabilities of classical computation and metrology. In recent years, quantum computation has presented a compelling application for quantum control, as high-fidelity control is essential to implement quantum information processors that achieve fault-tolerance [7][8][9].The performance of numerically optimized quantum gates in laboratory applications strongly depends on the accuracy of the system model used to approximate the response of the experimental system to the applied control sequence. Here we develop a general framework whereby classical control hardware components are modelled explicitly, such that their effect on a quantum system can be computed and compensated for using numerical optimal control theory (OCT) [10] algorithms to optimize control sequences. Control sequences designed using OCT algorithms, such as the GRadient Ascent Pulse Engineering (GRAPE) [11] algorithm, can be made robust to a wide variety of inhomogenities, pulse errors and noise processes [12][13][14]. These methods are also easily extended [15][16][17][18] to other applications and may be integrated into other protocols [19]. Recently, it was demonstrated how a model of linear distortions of the control sequence, such as those arising from finite bandwidth of the classical control hardware, may also be integrated into OCT algorithms [20][21][22].Here, we improve and generalize those results beyond linear kernels to any operation that smoothly maps a list of control steps to a classical field seen by the quantum system. Importantly, our framework naturally allows for robustness against uncertainties and errors due to classical control hardware. We begin developing our method generally, without making assumptions about the device of interest, so that our results may be broadly applicable to a wide range of quantum devices. We briefly discuss how our theory is easily applied to any linear distortion, and then in more detail, demonstrate with numerics how nonlinearities in control hardware, such as those found in strongly-driven superconducting resonators used for pulsed electron spin resonance (PESR) [23][24][25], may be included in OCT algorithms.With this goal in mind, we briefly review th...

Training Schrödinger’s cat: quantum optimal control

“…Also, readout has been addressed [462,463]. In order to adapt to the strong filtering of control lines in superconducting qubits, transfer functions had to be taken into account [107,108,110,464] and experimental fluctuations and noise were accomodated [117,364,465]. Fidelity limits on two-qubit gates due to decoherence were studied for Markovian [56,114,117] as well as non-Markovian [116] time evolutions.…”

“…the simplex algorithm. Other techniques specifically cover robustness against experimental fluctuations or noise [56,117,364,444] or filters in experimental implementation of controls [107,108,110,464].…”

“…SIMPSON [100], SPINACH [101], DYNAMO [94], and QuTiP [102]. Modifications to account for experimental imperfections and limitations and to ensure robustness of the solution have been introduced [53,[103][104][105][106][107][108][109][110][111], and numerical optimal control theory has been extended to open quantum systems [112][113][114][115][116][117].…”

Tunable photonic cavity coupled to a voltage-biased double quantum dot system: Diagrammatic nonequilibrium Green's function approach

“…Recent years have seen a significant progress in probing and controlling hybrid lightmatter systems at the interface of quantum optics and condensed matter physics [1][2][3][4]. Few examples of hybrid quantum systems include cavity-Quantum Electrodynamics (c-QED) arrays [2,[5][6][7], cold atoms coupled to light [8][9][10], optomechanical devices [11,12] and cavity-coupled quantum dots [2,[13][14][15][16][17][18][19][20][21].…”

Giant photon gain in large-scale quantum dot-circuit QED systems

“…Optical amplification is explained based on a sum rule for the transmission function, and it is determined by an intricate competition between two different processes: charge density response in the gain medium, and cavity losses to input and output ports. The same design principle is also responsible for the corresponding giant amplification in other photonic observables, mean photon number and emission spectrum, thereby realizing a quantum device that behaves as a giant microwave amplifier.Introduction.-Remarkable progress has been made in engineering, probing, and controlling hybrid light-matter systems which sit at the confluence of quantum optics and condensed matter physics [1][2][3][4][5][6]. Important examples include cavity-quantum electrodynamics arrays [7][8][9], trapped cold atoms coupled to photon degrees of freedom [10-13], interconnected copper waveguide cavities, each housing a qubit [14][15][16].…”