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arXiv:0805.4726 · Journal of Physics A Mathematical and Theoretical

Generalization of short coherent control pulses: extension to arbitrary rotations

Stefano Pasini, Götz Silvester Uhrig

Published Jul 9, 2008• 20 citations
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Abstract

We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.

DOI
10.1088/1751-8113/41/31/312005

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•Nov 16, 2025•0 citations
We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.
The coherent control of a small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the noncommutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for $\ensuremath{\pi}$ and $\frac{\ensuremath{\pi}}{2}$ pulses.
Abstract The problem of speeding up quantum computations through controlling the states of qubits by short large-amplitude unipolar pulses is discussed. A new method is proposed to describe the dynamics of qubits that is based on the Magnus representation for the evolution operator (propagator) of qubits, which allows one to find a solution to the quantum control problem outside the framework of perturbation theory. The evolution of the states of a multiqubit system is represented as a motion on a special unitary group SU(N), similar to the rotation of the Bloch vector on the group SU(2) in the case of a single qubit. As an example, unitary transformations of single-qubit states under different excitation modes are considered. A general formula is found that establishes a relation between the shape of a pulse and the result of its action, similar to the well-known “area theorem” for Rabi pulses. The effect of unipolar pulses on a two-qubit system is analyzed in detail. Two situations are considered: first, a symmetric configuration, when the parameters of qubits do not differ and are acted upon by the same magnetic field from a fluxon, and second, when the configuration of levels arises in which, for one of the qubits, a transition to the nearest level becomes possible under perturbation. The general case of two interacting qubits—a four-level system—is considered analytically. A direct numerical simulation of the dynamics of a multiqubit system is performed to estimate the accuracy of approximation, and fidelity is used as a criterion of accuracy of operations. It is shown that the expressions obtained for the propagator allow one to formulate conditions for the pulse parameters that are necessary to perform logical operations.
Abstract A frequently encountered source of systematic error in quantum computations is imperfections in the control pulses which are the classical fields that control qubit gate operations. From an analysis of the quantum-mechanical time-evolution operator of the spin wavefunction, it has been demonstrated that composite pulses can mitigate certain systematic errors and an appealing geometric interpretation was developed for the design of error-suppressing composite pulses. Here we show that these same pulse sequences can be obtained within a quasi-classical framework. This raises the question of whether error-correction procedures exist that exploit entanglement in a manner that can not be reproduced in the quasi-classical formulation.
Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities F_{ρ}>0.98 for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.
We present an experimental technique to better control the phase of an electron charge qubit, formed by a GaAs double quantum dot. A standard non-adiabatic gate pulse is used to generate the qubit rotation around the x -axis of the Bloch sphere. To gain good control of the z -rotation (the phase) on a short time scale, a fast 130 ps tipping pulse is superimposed on the non-adiabatic pulse. The two-axis gate operation is exhibited in the composite pulse excited qubit evolution spectrum. We demonstrate that the dynamic phase can be varied continuously from 0 to by varying the amplitude of the tipping pulse. The understanding of the spectrum is validated through simulation of the von Neumann equation.
We introduce UDC-3, a compact three-pulse composite control sequence designed to suppress mixed-axis coherent drift in single-qubit rotations. Standard composite pulses such as SK1 and BB1 primarily target symmetric amplitude errors, assuming that the control Hamiltonian remains aligned with the intended rotation axis. However, real quantum hardware often exhibits distorted effective rotation axes due to asymmetric calibration drift in multiple control channels. UDC-3 uses a short XYX prefix whose rotation angles are numerically optimized to maximize worst-case fidelity over two-axis drift (εx, εy ∈ [−0.12, 0.12]). Our optimized sequence improves worst-case fidelity from 66% (unoptimized UDC-3) to 98.79%, while preserving near-perfect performance at zero drift (99.91%). The optimized pulse also displays complete immunity to pure Y-axis drift, achieving 0% fidelity drop, outperforming SK1 and matching BB1 in symmetric regions while using fewer pulses. These results suggest that UDC-3 is an adaptable, hardware-aware correction primitive for coherent error suppression in near-term quantum devices. The sequence is compact, tunable, and suitable for calibration-limited platforms such as superconducting qubits, trapped ions, and spin qubits.