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arXiv:1210.7302

Information transfer and orthogonality speed via pulsed-driven qubit

NASSER METWALLY, Saad S. M. Hassan

Published Oct 27, 2012• 4 citations
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Abstract

We investigate the transfer and exchange information between a single qubit system excited by a rectangular pulse. The dynamics of the system is treated within and outside rotating wave approximation (RWA). The initial state of the qubit plays an important role for sending information with high fidelity. Within RWA, and as the fidelity of the transformed information increases the exchange information with the environment increases. For increasing values of atomic detuning, the fidelity decreases faster and the exchange information has an upper limit. Outside RWA,the fidelity of the transformed information increases as one increases the perturbation parameter. However the exchange information is very high compared with that within RWA. The orthogonality speed of the travelling qubit is investigated for different classes of initial atomic state settings and field parameters.

DOI
10.48550/arxiv.1210.7302

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We investigate the transfer and exchange information between a single qubit system excited by a rectangular pulse. The dynamics of the system is treated within and outside rotating wave approximation (RWA). The initial state of the qubit plays an important role for sending information with high fidelity. Within RWA, and as the fidelity of the transformed information increases the exchange information with the environment increases. For increasing values of atomic detuning, the fidelity decreases faster and the exchange information has an upper limit. Outside RWA,the fidelity of the transformed information increases as one increases the perturbation parameter. However the exchange information is very high compared with that within RWA. The orthogonality speed of the travelling qubit is investigated for different classes of initial atomic state settings and field parameters.
We use a rectangular pulse to freeze the possibility of estimating the coherent parameters (θ, [Formula: see text]) of a single qubit, the local information, and the fidelity of the driven qubit. The possibility of freezing these three quantities depends on the initial state settings and the strength of the pulse. It is shown that the freezing areas increase as the detuning increases, while they decrease at smaller values of the pulse strength. Moreover, as the Fisher information reaches its minimum bounds, the local information and the fidelity are maximized. We show that, when the Fisher information is completely frozen, the pulsed local information and the fidelity are frozen. The freezing degree depends on the initial detuning and the pulse strength. Our results show that, despite the initial and final states of the system being different, the amount of local information is independent of the initial state of the system. These results may be useful in the context of quantum cryptography, teleportation, and secure communication.
The transient spectrum of scattered radiation from a qubit (represented by a spin-1/2 system or a two-level atom) driven by a resonant rectangular pulse is calculated analytically without adopting the rotating wave approximation (RWA). Operator solutions for the non-autonomous model of Heisenberg equations of motion are obtained within an iterative approach to O (λ) where λ is the system parameter representing the ratio of the Rabi frequency of the driving pulse to its circular frequency. The spectrum in the case of an initial ground-state atom and for increasing pulse area shows asymmetric profiles outside the RWA compared with a symmetric profile within the RWA. For the qubit this asymmetry is much pronounced with splitting of side peaks, which develops to ‘ringing’ for larger pulse area (within and outside the RWA). As shown analytically, this is attributed to the strong Rabi oscillations and interference between various amplitude spectral components initiated by the finite atomic coherent dispersion.
Abstract We estimate the initial weight and phase parameters ( θ , ϕ ) of a single qubit system initially prepared in the coherent state | θ , ϕ 〉 and in interaction with three different shapes of pulses; rectangular, exponential, and sin 2 -pulses. In general, we show that the estimation degree of the weight parameter depends on the pulse shape and the initial phase angle, ( ϕ ) . For the rectangular pulse case, increasing the estimating rate of the weight parameter via the Fisher information function ( F θ ) is possible with small values of the atomic detuning parameter and larger values of pulse strength. Fisher information ( F ϕ ) increases suddenly at the resonant case to reach its maximum value if the initial phase ϕ = π / 2 and consequently one may estimate the phase parameter with a high degree of precision. If the initial system is coded with classical information, the upper bounds of Fisher information for resonant and non-resonant cases are much larger and consequently, one may estimate the phase parameter with a high degree of accuracy. Similarly, as the detuning increases the Fisher information decreases and therefore the possibility of estimating the phase parameter decreases. For exponential and sin 2 -pulses the Fisher information is maximum ( F θ , ϕ = 1 ) and consequently, one can always estimate the weight and the phase parameters ( θ , ϕ ) with a high degree of precision.
We present a theoretical study of single-qubit operations by oscillatory fields on various semiconductor platforms. We explicitly show how to perform faster gate operations by going beyond the universally used rotating-wave approximation (RWA) regime, while using only two sinusoidal pulses. We first show for specific published experiments how much error is currently incurred by implementing pulses designed using standard RWA. We then show that an even modest increase in gate speed would cause problems in using RWA for gate design in the singlet-triplet (ST) and resonant-exchange (RX) qubits. We discuss the extent to which analytically keeping higher orders in the perturbation theory would address the problem. More strikingly, we give a new prescription for gating with strong coupling far beyond the RWA regime. We perform numerical calculations for the phases and the durations of two consecutive pulses to realize the key Hadamard and $\frac{\ensuremath{\pi}}{8}$ gates with coupling strengths up to several times the qubit splitting. Working in this manifestly non-RWA regime, the gate operation speeds up by two to three orders of magnitude and nears the quantum speed limit without requiring complicated pulse shaping or optimal control sequences.
Single-qubit quantum gates are implemented as the time-controlled unitary evolution of a two-level system under harmonic driving. The rotating-wave approximation (RWA) provides closed-form gate parameters for weak coupling. Larger amplitudes, desirable to speed up the dynamics, make the RWA-designed gates inaccurate because of the neglected counter-rotating term, which also shifts the resonance (Bloch-Siegert shift). Here we study theoretically the infidelity of gates beyond the RWA, using the effective Magnus-Taylor Hamiltonian through second order in the inverse of the driving frequency. By detuning the driving frequency by an amplitude-dependent shift of Bloch-Siegert type and rescaling the operation time, the RWA gate conditions are recovered with corrected parameters. Numerical solutions of the Schrodinger equation show that these corrections lower the gate infidelity by several orders of magnitude, extending the range of usable amplitudes
We use a rectangular pulse to freeze the possibility of estimating the coherent parameters (θ,ϕθ,ϕθ,ϕ) of a single qubit and the encoded information. It is shown that, as the possibility of estimating the parameters increases, the amount of encoded information decreases. The pulse strength and the detuning between the qubit and the pulse have a different effect on the estimation degree and the encoded information. We show that if the weight parameter, θθθ is estimated, the encoded information depends on the initial state settings. Meanwhile, the encoded information doesn't depend on the estimated phase parameter,ϕϕϕ. These results may be useful in the context of quantum cryptography, teleportation and secure communication.