Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment

Abstract

Decoherence in quantum computer memory due to the inevitable coupling to the external environment is examined. We take the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits are decohered collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of this decoherence model for quantum measurements.

Resonance theory of decoherence and thermalization

“…The former are induced by interactions having nonvanishing probabilities for processes of absorption and emission of field quanta with energies corresponding to the Bohr frequencies of S (this is the "Fermi Golden Rule Condition", [9,18,29,31,32]). Energy preserving interactions suppress such processes, allowing only for a phase change of the system during the evolution ("phase damping", [35,12,15,17,24,33,37]). …”

“…for quantum-optical systems, p = 1/2, and for the quantized electromagnetic field, p = −1/2. Decoherence of models with interaction (1.6) with c = 0 is considered in [12,15,17,24,33,35,37,39] (see also Section 7.2). This is the situation of a non-demolition (energy conserving) interaction, where v commutes with the Hamiltonian H S and consequently energy-exchange processes are suppressed.…”

“…The resulting decoherence is called phasedecoherence. A particular model of phase-decoherence is obtained by the so-called position-position coupling, where the matrix in the interaction (1.6) is the Pauli matrix σ z [12,17,35,39]. On the other hand, energy-exchange processes, responsible for driving the system to equilibrium, have a probability proportional to |c| 2n , for some n ≥ 1 (and a, b do not enter) [1,9,18,22,29,31,32].…”

“…Decoherence is reflected in the temporal decay of off-diagonal elements of the reduced density matrix of the system in a given basis. So far, this phenomenon has been analyzed rigorously only for explicitly solvable models, [15,17,24,33,36,37,35,40,41]. In this paper we consider the decoherence phenomenon for quite general nonsolvable models.…”

Self-protected quantum algorithms based on quantum state tomography

“…While the active strategies to prevent errors, such as quantum error correcting codes [17,18,19,20] may, in principle, be universal as claimed, passive prevention methods have hardware resource advantages. For example, decoherence-free subspaces (DFS) and noiseless subsystems (NS) [21,22,23,24] are based on the symmetry of the system-bath interaction, so do not require active detection and correction of errors. Another passive technique, holonomic quantum computation, is robust against stochastic errors in the control process [25,26].…”