In this work, we address the problem of designing single-qubit quantum gates by means of a linearly-polarized field. We show that any desired one-qubit gate corresponding to a special unitary matrix can be generated by a modulated sinusoidal field. The only approximation involved is the rotating-wave-approximation. The formula for the control field is obtained by inverting the equation of motion for the evolution operator and imposing the conditions for the desired gate. We give a simple procedure to obtain closed analytical formulas for the fields in terms of a priori chosen dynamical functions. Additionally, these dynamical functions can depend on tunable free parameters intentionally introduced to meet a desired performance criteria.
A scheme for controlling a charge qubit on a semiconductor asymmetric double quantum dot with suppressed tunnel coupling between individual quantum dots is proposed. Laser pulses convert the logical single-electron states of the qubit into auxiliary trion states, for which the resonant tunneling condition is restored due to the compensation of structural asymmetry by the Coulomb interaction of the particles. The conditions for performing orthogonal single-qubit rotations are formulated. For a two-dimensional structure, the parameters of the qubit are calculated, and the dependence of the fidelity of the inversion operation on the parameters of the laser field and the rates of dissipative processes is obtained. It is shown that the considered algorithm is characterized by high speed and reliability.
Spin qubits in gate-defined quantum dots provide a highly programmable platform for simulating condensed-matter phenomena. In this work, we introduce a digital-analog quantum simulation protocol for extracting the single-particle spectrum of a Kitaev chain. The Kitaev chain is mapped onto qubits via the standard Jordan-Wigner transformation and implemented as a drive-engineered, $N$-site transverse-field Ising model (TFIM) in a linear array of quantum dots. We show that periodically toggling the analog-simulation parameters conditioned on the state of a control qubit causes the dynamics of this control qubit to stroboscopically match the output of the one-clean-qubit (DQC1) model of computation, thereby yielding the full spectrum of the TFIM from measurements of a single spin. Classical postprocessing can then be used to isolate the $N$ single-particle energies of the Kitaev chain from the $2^N$ eigenenergies of the TFIM. By varying the strength of the Rabi drive used to engineer the synthetic transverse field, the spectral signature of the crossover from the trivial to the topological regime of the Kitaev chain could then be mapped out with measurements of just one spin.
Z. McIntyre, Daniel Loss· 0 citations
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