Bandwidth-limited control and ringdown suppression in high-Q resonators

Borneman, Troy W.; Cory, David G.

doi:10.1016/j.jmr.2012.10.011

Cited by 44 publications

(36 citation statements)

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“…The convolution kernel φ models any distortion that can be described by a linear differential equation, such as a simple exponential rise time, control line crosstalk, or the transfer function of the control hardware [20,21,32,33]. We compute the discretized distortion operator to be…”

Section: Pacs Numbersmentioning

confidence: 99%

Section: Since Our Hamiltonian In Equation 11mentioning

confidence: 99%

“…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.…”

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confidence: 99%

“…Therefore if we can compute the Jacobian J p (g), we can then compute the total gradient of Φ. The rest of the algorithm follows as described in the original GRAPE [11].Since the cost of evaluating g will typically not grow more than polynomially with the number of qubits, the computational cost of the optimization effectively remains unchanged from standard GRAPE, as it is still dominated by the cost of computing the M matrix exponentials.Our first example is the continuous distortion operator given by the convolution with an L × K kernel φ(t),The convolution kernel φ models any distortion that can be described by a linear differential equation, such as a simple exponential rise time, control line crosstalk, or the transfer function of the control hardware [20,21,32,33]. We compute the discretized distortion operator to be…”

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confidence: 99%

“…We therefore utilize an active ringdown suppression scheme with three compensation steps of lengths 4ns, 2ns, and 1ns. This is a generalization of ringdown suppression in linear circuits [21,44,45] and is discussed in detail in the Appendix.The inclusion of a distortion operator causes an alteration to the control landscape which might be expected to make finding optimal solutions more expensive. Therefore, a tradeoff between computational cost and gate time length might be anticipated.…”

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Controlling Quantum Devices with Nonlinear Hardware

et al. 2015

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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...

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Section: Pacs Numbersmentioning

confidence: 99%

Section: Since Our Hamiltonian In Equation 11mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Controlling Quantum Devices with Nonlinear Hardware

et al. 2015

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Kompensation von Pulsimperfektionen in der Festkörper‐NMR‐ Spektroskopie: ein Schlüssel zu verbesserter Reproduzierbarkeit und Effizienz

et al. 2015

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Das Potential und die Vielseitigkeit der NMR‐Spektroskopie beruhen auf der Möglichkeit, NMR‐Wechselwirkungen gezielt mittels Radiofrequenzpulssequenzen zu beeinflussen. Allerdings unterscheiden sich die Radiofrequenzfelder (RF), die auf die Spins wirken, von denen, die der Experimentator am Spektrometer programmiert. So genannte Pulstransienten, d. h. Abweichungen des RF‐Feldes in Amplitude und Phase von den erwarteten Werten, können einen erheblichen Einfluss auf die Effizienz von Pulssequenzen haben und daher zu unterschiedlichen Ergebnissen führen. Wir zeigen, dass transientenkompensierte Pulse sowohl die Effizienz als auch die Reproduzierbarkeit von NMR‐Experimenten deutlich erhöhen können. Die Implementierung basiert auf den Charakteristiken des Schwingkreises und nicht auf einer experimentellen Optimierung des NMR‐Signals. Wir zeigen, wie die Pulssequenz für die Verwendung transientenkompensierter Pulse verändert werden muss. Die Effizienz und die Reproduzierbarkeit der transientenkompensierten Sequenz sind gegenüber der ursprünglichen POST‐C7‐Sequenz deutlich verbessert.

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Compensating Pulse Imperfections in Solid‐State NMR Spectroscopy: A Key to Better Reproducibility and Performance

et al. 2015

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The power and versatility of NMR spectroscopy is strongly related to the ability to manipulate NMR interactions by the application of radio-frequency (rf) pulse sequences. Unfortunately, the rf fields seen by the spins differ from the ones programmed by the experimentalist. Pulse transients, i.e., deviations of the amplitude and phase of the rf fields from the desired values, can have a severe impact on the performance of pulse sequences and can lead to inconsistent results. Here, we demonstrate how transient-compensated pulses can greatly improve the efficiency and reproducibility of NMR experiments. The implementation is based on a measurement of the characteristics of the resonance circuit and does not rely on an experimental optimization of the NMR signal. We show how the pulse sequence has to be modified to use it with transient-compensated pulses. The efficiency and reproducibility of the transient-compensated sequence is greatly superior to the original POST-C7 sequence.

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Bandwidth-limited control and ringdown suppression in high-Q resonators

Cited by 44 publications

References 58 publications

Controlling Quantum Devices with Nonlinear Hardware

Controlling Quantum Devices with Nonlinear Hardware

Kompensation von Pulsimperfektionen in der Festkörper‐NMR‐ Spektroskopie: ein Schlüssel zu verbesserter Reproduzierbarkeit und Effizienz

Compensating Pulse Imperfections in Solid‐State NMR Spectroscopy: A Key to Better Reproducibility and Performance

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