Decoherence of quantum registers

Abstract

The dynamical evolution of a quantum register of arbitrary length coupled to an environment of arbitrary coherence length is predicted within a relevant model of decoherence. The results are reported for quantum bits (qubits) coupling individually to different environments (`independent decoherence') and qubits interacting collectively with the same reservoir (`collective decoherence'). In both cases, explicit decoherence functions are derived for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: we show that this sensitivity is a characteristic of $both$ types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A non-trivial behaviour ("recoherence") is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. Our results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system's Hilbert space that do not get entangled with the environment, making them ideal elements for the engineering of ``noiseless'' quantum codes. We also discuss the relations between decoherence of the quantum register and computational complexity based on the new dynamical results obtained for the register density matrix.Comment: Typos corrected. Discussion and references added. 1 figure + 3 tables added. This updated version contains 13 (double column) pages + 8 figures. PRA in pres

Temperature-independent teleportation of qubits in Davies environments

“…Let us notice that the pure dephasing serves as a good approximation of various models studied in wide range of contexts [19,21,22]. Relationship between temperature dependence of the fidelity and the particular choice of initial preparation is well visible in, otherwise not very interesting for teleportation, long time limit lim t→∞ F. In Fig.…”

Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

“…(3) into Eq. (4), we obtain, after some algebra, the following expression for the time evolution operator [10]:…”

“…In Sec. II, we describe the exact dissipative dynamics of the N -qubit system interacting with a common dephasing environment [10]. In Sec.…”

“…The interaction of the qubits with the environment, which depends on the quantum computer architecture, is a crucial problem that is far from being well understood. However, it is known that this interaction can result in nonmonotonical dynamics of the density-matrix coherences [10][11][12] and so a complete understanding of this behavior is a matter of great importance. Moreover, this nonmonotonical behavior is a subject of broad interest [13][14][15][16] since this peculiar property brings up unexpected dynamics for quantum fidelity [17], as well as for quantum entanglement [12,[18][19][20] and quantum discord [21].…”

“…Based on the foregoing reasoning, we use an exact solvable model [10] to calculate the dissipative fidelity dynamics in a linear measurement-based quantum computer (MBQC) [1] composed of a few qubits, which interact collectively with a dephasing environment. Although this kind of model does not describe relaxation processes, it does indeed adequately describe decoherence effects.…”