Collective decoherence of the superpositional entangled states in the quantum Shor algorithm

Berman, G. P.; Kamenev, D. I.; Tsifrinovich, V. I.

doi:10.1103/physreva.71.032346

Cited by 11 publications

(16 citation statements)

References 18 publications

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“…Collective decoherence has been studied extensively in the literature. Among the many theoretical, numerical and experimental works we mention here only [1,2,4,7,8,17,20], which are closest to the present work. We are not aware of any prior work giving explicit decoherence rates of a register for not explicitly solvable models, and without making master equation technique approximations.…”

Section: Introductionmentioning

confidence: 78%

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Dynamics of collective decoherence and thermalization

2008

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We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N 2 , while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N . For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born-or weak coupling (van Hove) approximations.

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Section: Introductionmentioning

confidence: 78%

“…acting on the eigenspace of L S associated to e. 4 Theorem 2.1 (Dynamics of matrix elements) Denote by β the inverse temperature of R. There is a λ 0 > 0 such that if max{|λ 1 |, |λ 2 |} < λ 0 /β then the limit (1.16) exists for all σ, τ , and we have for t ≥ 0…”

Section: Effective Dynamics Of Smentioning

confidence: 99%

Dynamics of collective decoherence and thermalization

2008

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“…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.…”

Section: 2)mentioning

confidence: 99%

“…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]). …”

Section: 2)mentioning

confidence: 99%

“…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].…”

Section: 2)mentioning

confidence: 99%

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Resonance theory of decoherence and thermalization

2008

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We present a rigorous analysis of the phenomenon of decoherence for general N −level systems coupled to reservoirs. The latter are described by free massless bosonic fields. We apply our general results to the specific cases of the qubit and the quantum register. We compare our results with the explicitly solvable case of systems whose interaction with the environment does not allow for energy exchange (non-demolition, or energy conserving interactions). We suggest a new approach which applies to a wide variety of systems which are not explicitly solvable.

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Universal quantum logic gates in a scalable Ising spin quantum computer

Mkrtchian

2008

Physics Letters A

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We consider the model of quantum computer, which is represented as a Ising spin lattice, where qubits (spin-half systems) are separated by the isolators (two spinhalf systems). In the idle mode or at the single bit operations the total spin of isolators is 0. There are no need of complicated protocols for correcting the phase and probability errors due to permanent interaction between the qubits. We present protocols for implementation of universal quantum gates with the rectangular radiofrequency pulses.

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Collective decoherence of the superpositional entangled states in the quantum Shor algorithm

Cited by 11 publications

References 18 publications

Dynamics of collective decoherence and thermalization

Dynamics of collective decoherence and thermalization

Resonance theory of decoherence and thermalization

Universal quantum logic gates in a scalable Ising spin quantum computer

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