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Shortcuts to adiabaticity in spin echo

Anton Gregefalk, Erik Sjöqvist

Published Jul 14, 2021• 0 citations
OpenAlex

Abstract

Spin echo can be used to refocus random dynamical phases caused by inhomogeneities in control fields and thereby retain the purity of a spatial distribution of quantum spins. This technique for accurate spin control is an essential ingredient in many applications, such as nuclear magnetic resonance, magnetic resonance imaging, and quantum information processing. Here, we show how all the elements of a spin echo sequence can be performed at high speed by means of shortcuts to adiabaticity. Our proposal promises accurate control of rapid quantum spin evolution. We illustrate our scheme for a universal nonadiabatic geometric single-qubit gate.

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Spin echo can be used to refocus random dynamical phases caused by inhomogeneities in control fields and thereby retain the purity of a spatial distribution of quantum spins. This technique for accurate spin control is an essential ingredient in many applications, such as nuclear magnetic resonance, magnetic resonance imaging, and quantum information processing. Here, we show how all the elements of a spin echo sequence can be performed at high speed by means of shortcuts to adiabaticity. Our proposal promises accurate control of rapid quantum spin evolution. We illustrate our scheme for a universal nonadiabatic geometric single-qubit gate.
Spin echo can be used to refocus random dynamical phases caused by inhomogeneities in control fields and thereby retain the purity of a spatial distribution of quantum spins. This technique for accurate spin control is an essential ingredient in many applications, such as nuclear magnetic resonance, magnetic resonance imaging, and quantum information processing. Here, we show how all the elements of a spin echo sequence can be performed at high speed by means of transitionless quantum driving. This technique promises accurate control of rapid quantum spin evolution. We apply the scheme to universal nonadiabatic geometric single- and two-qubit gates in a nuclear magnetic resonance setting.
Abstract Within the framework of quantum information and quantum processing, spin quantum systems are one of the most promising technologies, so they are extensively studied nowadays. It has provided several notable applications centred around the manipulation and control of spin ensembles through magnetic fields, particularly in Nuclear Magnetic Resonance. Also, such control is crucial for the settlement of qubit states and the construction of quantum gates. In this work, a review of methods to get the single spin dynamics is presented, thus regarding the simplest analytical solutions, the rotating frame approach, and general numerical procedures. Besides, some applications such as Evolution-loops, Spin-echo, and local Quantum gates are discussed. Finally, we deal with adiabatic pulses to explore a recent research implementation of quantum memories using single-spin systems.
The phase coherence of a physical qubit is essential for quantum information processing, motivating fast control methods to preserve that phase. Ultrafast optical techniques allow complete spin control to be performed on a much faster timescale than microwave or electrical control (ps vs. ns at best). Using our ultrafast control techniques, we demonstrate our experimental approach towards a spin echo sequence on the spin of a single electron confined in a semiconductor quantum dot (QD), increasing the observed decoherence time of a single QD electron spin from nanoseconds to several microseconds. The ratio of the observed decoherence time to the demonstrated single-qubit gate time exceeds 105, suggesting strong promise for future quantum information processors.
High-fidelity quantum operations are a key requirement for fault-tolerant quantum information processing. Manipulation of electron spins is usually achieved with time-dependent microwave fields. In contrast to the conventional dynamic approach, adiabatic geometric phase operations are expected to be less sensitive to certain kinds of noise and field inhomogeneities. Here, we introduce an adiabatic geometric phase gate for the electron spin. Benchmarking it against existing dynamic and nonadiabatic geometric gates through simulations and experiments, we show that it is indeed inherently robust against inhomogeneity in the applied microwave field strength. While only little advantage is offered over error-correcting composite pulses for modest inhomogeneities $\ensuremath{\lesssim}10%$, the adiabatic approach reveals its potential for situations where field inhomogeneities are unavoidably large.
Fast and robust quantum gates are the cornerstones of fault-tolerance quantum computation. In this paper, as opposed to the previous proposals which use cyclic geometric phases, we propose to realize quantum computation based on noncyclic geometric evolution. The superiority of the noncyclic scheme is that the operation time is proportional to the rotation angle of the quantum state. Therefore, the noncyclic scheme becomes fairly fast in the case of quantum gates with small rotation angle, which will be more insensitive to the decoherence and the leakage to the states outside the computational basis. Similar to the cyclic version of geometric quantum computation, dynamical phases here during the evolution are canceled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabaticity. The proposed scheme is robust against random noise due to the geometric characteristic of projective Hilbert space. Since the proposed scheme is fast and robust, it is a particularly suitable way to manipulate the physical systems with weak nonlinearity, such as superconducting systems.
Abstract Quantum control allows a wide range of quantum operations employed in molecular physics, nuclear magnetic resonance and quantum information processing. Thanks to the existing microelectronics industry, semiconducting qubits, where quantum information is encoded in spin or charge degree freedom of electrons or nuclei in semiconductor quantum dots, constitute a highly competitive candidate for scalable solid-state quantum technologies. In quantum information processing, advanced control techniques are needed to realize quantum manipulations with both high precision and noise resilience. In this review, we first introduce the basics of various widely-used control methods, including resonant excitation, adabatic passage, shortcuts to adiabaticity, composite pulses, and quantum optimal control. Then we review the practical aspects in applying these methods to realize accurate and robust quantum gates for single semiconductor qubits, such as Loss–DiVincenzo spin qubit, spinglet-triplet qubit, exchange-only qubit and charge qubit.