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Quantum Information and Computation

Phase control for entanglement preparation in two-qubit systems

Vladimir S. Malinovsky, Ignacio R. Solá

Published Jul 1, 2005• 2 citations
Publisher

Abstract

The theory of Quantum Control is starting to lay bridges with the field of Quantum Information and Quantum Computation. Using key ideas of laser control of the dynamics by means of phase manipulation and adiabatic passage, we review laser schemes that allow entanglement preparation in a two-qubit system. The schemes are based on sequences that use four time-delayed pulses, with or without concerted decay, in or off resonance with the intermediate levels of the qubit space. We show how to control the fidelity and phase of the entanglement, as well as the sensitivity of the preparation to the different pulse parameters. In general the schemes provide an improvement in robustness and in the finesse of the control to phase, with respect to previously proposed schemes based on sequences of $\pi$ pulses.

DOI
10.26421/qic5.45-7

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The theory of Quantum Control is starting to lay bridges with the field of Quantum Information and Quantum Computation. Using key ideas of laser control of the dynamics by means of phase manipulation and adiabatic passage, we review laser schemes that allow entanglement preparation in a two-qubit system. The schemes are based on sequences that use four time-delayed pulses, with or without concerted decay, in or off resonance with the intermediate levels of the qubit space. We show how to control the fidelity and phase of the entanglement, as well as the sensitivity of the preparation to the different pulse parameters. In general the schemes provide an improvement in robustness and in the finesse of the control to phase, with respect to previously proposed schemes based on sequences of π\piπ pulses.
A method of entangled states preparation of two-qubit systems is proposed. The method combines the techniques of coherent control by manipulation of the relative phase between the pulses and adiabatic control by using time-delayed pulse sequences. Simple analytic expressions are given for the wave function of the system as a function of phase and pulse area which show that complete control of entanglement is possible with resonant pulses. The connection between the phase of the entanglement and the control parameters is clarified and the effects of different pulse sequences are analyzed to design the optimal schemes. An off-resonant scheme is proposed that simplifies the preparation of certain entangled states.
We investigate coherent population transfer in double-$\ensuremath{\Lambda}$ and diamond-type four-level systems driven by two pairs of time-delayed laser pulses. We show that the relative phase between the pulses induces interference so that the adiabatic passage dynamics is only possible for a particular phase. Both pulse area and phase are control knobs that can be used to prepare specific coherent superpositions using counterintuitive and intuitive pulse sequences. Since the diamond-type four-level system maps the Hamiltonian of two interacting two-level systems, the schemes can be used to manipulate entanglement. In particular we propose robust schemes to prepare specific entangled states by phase control with time-delayed pulse sequences.
Stark shifts introduce additional phases that constrain the set of entangling gates that can be prepared via two-photon transitions in the strong Rydberg blockade limit. For non-independently addressed qubits, by controlling the absolute phases and the local amplitudes of the pulses at each qubit, we show that any two-qubit phase gate can be prepared with high fidelity using a three-pulse sequence. Based on these insights, we introduce two robust control schemes tailored to different phase gates that yield better results with pulse sequences of either even or odd length.
Coherent control and the creation of entangled states are discussed in a system of two superconducting flux qubits interacting with each other through their mutual inductance and identically coupling to a reservoir of harmonic oscillators. We present different schemes using continuous-wave control fields or Stark-chirped rapid adiabatic passages, both of which rely on a dynamic control of the qubit transition frequencies via the external bias flux in order to maximize the fidelity of the target states. For comparison, also special area pulse schemes are discussed. The qubits are operated around the optimum point, and decoherence is modeled via a bath of harmonic oscillators. As our main result, a coherent control scheme is presented which is robust against imperfections in the driving fields, and that enables one to prepare different Bell states consisting of the collective ground and excited states of the two-qubit system.
A scalable multatom entangled system, capable of high-performance quantum computations, can be realized by resonant dipole-dipole interacting dopants in a solid state host. In one realization, the qubits are represented by ground and subradiant states of effective dimers formed by pairs of closely spaced two-level systems (TLS). Such qubits are highly robust against radiative decay. The two-qubit entanglement in this scheme relies on coherent excitation exchange between the dimers by external laser fields. This scheme is challenging because of the nanosize control and addressability it requires. Another realization involves dipole-dipole interacting TLS whose resonance frequency lies in a photonic band gap of a dielectric photonic crystal. A sequence of abrupt changes of the resonance frequency can produce controlled entanglement (logic gates) with improved protection from radiation decay and decoherence.