Alexander I. Nesterov, Gennady P. Berman, Juan C. Beas Zepeda, Alan R. Bishop
A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to N=1024 spins) that our approach leads to a significant reduction of the annealing time that is proportional to \(\ln N\), which is much less than the time (proportional to \(N^2\)) required for the quantum annealing based on the corresponding Hermitian algorithm. We propose to use this approach to achieve similar speed-up for NP-complete problems by using classical computers in combination with quantum algorithms.
http://arxiv.org/abs/1302.6555
Quantum Physics (quant-ph); Mathematical Physics (math-ph)
Alexander I. Nesterov, Gennady P. Berman, Alan R. Bishop
We model the quantum electron transfer (ET) in the photosynthetic reaction center (RC), using a non-Hermitian Hamiltonian approach. Our model includes (i) two protein cofactors, donor and acceptor, with discrete energy levels and (ii) a third protein pigment (sink) which has a continuous energy spectrum. Interactions are introduced between the donor and acceptor, and between the acceptor and the sink, with noise acting between the donor and acceptor. The noise is considered classically (as an external random force), and it is described by an ensemble of two-level systems (random fluctuators). Each fluctuator has two independent parameters, an amplitude and a switching rate. We represent the noise by a set of fluctuators with fitting parameters (boundaries of switching rates), which allows us to build a desired spectral density of noise in a wide range of frequencies. We analyze the quantum dynamics and the efficiency of the ET as a function of (i) the energy gap between the donor and acceptor, (ii) the strength of the interaction with the continuum, and (iii) noise parameters. As an example, numerical results are presented for the ET through the active pathway in a quinone-type photosystem II RC.
http://arxiv.org/abs/1204.0805
Quantum Physics (quant-ph); Biological Physics (physics.bio-ph)