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arXiv:quant-ph/0502119 · Physical Review Letters

High Fidelity Single Qubit Operations Using Pulsed Electron Paramagnetic Resonance

John J. L. Morton, Alexei M. Tyryshkin, Arzhang Ardavan, Kyriakos Porfyrakis, S. A. Lyon, G. A. D. Briggs

Published Nov 8, 2005• 87 citations
arXivHTMLPDF

Abstract

Systematic errors in spin rotation operations using simple rf pulses place severe limitations on the usefulness of the pulsed magnetic resonance methods in quantum computing applications. In particular, the fidelity of quantum logic operations performed on electron spin qubits falls well below the threshold for the application of quantum algorithms. Using three independent techniques, we demonstrate the use of composite pulses to improve this fidelity by several orders of magnitude. The observed high-fidelity operations are limited by pulse phase errors, but nevertheless fall within the limits required for the application of quantum error correction.

DOI
10.1103/physrevlett.95.200501

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Systematic errors in spin rotation operations using simple rf pulses place severe limitations on the usefulness of the pulsed magnetic resonance methods in quantum computing applications. In particular, the fidelity of quantum logic operations performed on electron spin qubits falls well below the threshold for the application of quantum algorithms. Using three independent techniques, we demonstrate the use of composite pulses to improve this fidelity by several orders of magnitude. The observed high-fidelity operations are limited by pulse phase errors, but nevertheless fall within the limits required for the application of quantum error correction.
The ability to measure and reduce systematic errors in single-qubit logic gates is crucial when evaluating quantum computing implementations. We describe pulsed electron paramagnetic resonance (EPR) sequences that can be used to measure precisely even small systematic errors in rotations of electron-spin-based qubits. Using these sequences we obtain values for errors in the rotation angle and axis for single-qubit rotations using a commercial EPR spectrometer. We conclude that errors in qubit operations by pulsed EPR are not limiting factors in the implementation of electron-spin-based quantum computers.
Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.
Abstract Semiconductor spin qubits demonstrated single-qubit gates with fidelities up to 99.9 % benchmarked in the single-qubit subspace. However, tomographic characterizations reveal non-negligible crosstalk errors in a larger space. Additionally, it was long thought that the two-qubit gate performance is limited by charge noise, which couples to the qubits via the exchange interaction. Here, we show that coherent error sources such as a limited bandwidth of the control signals, diabaticity errors, microwave crosstalk, and non-linear transfer functions can equally limit the fidelity. We report a simple theoretical framework for pulse optimization that relates erroneous dynamics to spectral concentration problems and allows for the reuse of existing signal shaping methods on a larger set of gate operations. We apply this framework to common gate operations for spin qubits and show that simple pulse shaping techniques can significantly improve the performance of these gate operations in the presence of such coherent error sources. The methods presented in the paper were used to demonstrate two-qubit gate fidelities with F > 99.5 % in Xue et al (2022 Nature 601 343). We also find that single and two-qubit gates can be optimized using the same pulse shape. We use analytic derivations and numerical simulations to arrive at predicted gate fidelities greater than 99.9% with duration less than, 4 / ( Δ E z ) where Δ E z is the difference in qubit frequencies.
Quantum computing set a goal to harness the quantum laws of physics and create \ncomputers more powerful than ever imagined. Different technologies can be chosen to implement quantum bits (qubits), each with their advantages and drawbacks. The idea of combining different technologies then seems natural in order to come up with an optimal quantum computer. \n \nIn this sense, Nuclear Magnetic Resonance (NMR) and Electron Spin Resonance (ESR) seem to be the perfect marriage. Indeed, while electron spins can perform quantum gates within nanoseconds, they have to fight very fast decoherence phenomena, the nuclear spins, on the other hand, require longer electromagnetic pulses to be rotated but can be controlled longer without loss of quantum information. Using electron spins as actuators and nuclear spins as memory then appears as the optimal use of this hybrid system. Another fact accounting for this association is that the control of the system through the electron spin requires techniques very similar to the well-known NMR ones. \n \nThis work focuses on characterizing as precisely as possible the Hamiltonian of a hybrid spin system in a solid-state single crystal, especially the electron-nuclear interactions, to perform high-fidelity control in a home-built pulsed ESR spectrometer. Using this knowledge, we show that we can choose the orientation of the magnetic field with respect to our crystal to obtain optimal experimental conditions. Indeed, with a good knowledge of the Hamiltonian of the system, we want demonstrate high-fidelity quantum control. \n \nThe final aim of this work is to dynamically supply highly polarized ancilla qubits that can be used in a Quantum Error Correction (QEC) experiment by implementing heat bath algorithmic cooling using a cold electron spin bath. This is an important step towards demonstrating the viability of spin systems for building quantum computers.