Decoherence and relevant universality in quantum algorithms via a dynamic theory for quantum measurement

Abstract

The possible effect of environment on the efficiency of a quantum algorithm is considered explicitely. It is illustrated through the example of Shor's prime factorization algorithm that this effect may be disastrous. The influence of environment on quantum computation is probed on the basis of its analogy to the problem of wave function collapse in quantum measurement.Techniques from the Hepp-Colemen approach and its generalization are used to deal with decoherence problems in quantum computation including dynamic mechanism of decoherence , quantum error avoiding tricks and calculation of decoherence time.

Loschmidt echo and Berry phase of a quantum system coupled to anXYspin chain: Proximity to a quantum phase transition

“…(10) has a norm less than unity, we may expect L(t) to decrease to zero in the large N limit under some reasonable conditions. This kind of factorized structure was first discovered and systematically studied [21] in developing the quantum measurement theory in classical or macroscopic limit and has been applied to analyze the universality of decoherence influence from environment on quantum computing [23]. Now we study in detail the critical behavior of of LE near the critical point λ c = 1 for finite lattice size N of spin chain.…”

Electromagnetic manipulation for the anti-Zeno effect in an engineered quantum tunneling process

“…When the dynamics of the system we are interested is only the quantum dot A, the quantum dot array can be regarded as an engineered environment. In terminology of quantum open system approach, the Hamiltonian (3) describes a single level system interacting with an environment [27]. Such an engineered environment is composed of an ensemble of 2N qubits.…”

“…By the Fourier transformation for the boson operatorŝ b † j andb j , the boson model (27) can be transformed into a dual model similar to that of fermions (see the Eq.3)…”

Effects of Imperfect Gate Operations in Shor's Prime Factorization Algorithm

“…Sun et al discussed the effect of decoherence on the algorithm by modeling the environment [5]. Palma studied the effects of both decoherence and gate imperfection in ion trap quantum computers [6].…”