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, Juan Carlos Beas Zepeda, Gennady P. Berman
We create a non-Hermitian quantum optimization algorithm to find the ground state of an Ising model with up to 1024 spins (qubits). Our approach leads to significant reduction of the annealing time. Analytic and numerical results demonstrate that the total annealing time is proportional to ln N, where N is the number of spins. This encouraging result is important for the rapid solution of NP-complete problems. Additional research is proposed for extending our dissipative algorithm to more complicated problems.
http://arxiv.org/abs/1211.3178
Quantum Physics (quant-ph); Mathematical Physics (math-ph); Computational Physics (physics.comp-ph)
Alexander I. Nesterov, Gennady P. Berman
We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover’s problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment.
http://arxiv.org/abs/1208.4642
Quantum Physics (quant-ph); Mathematical Physics (math-ph); Computational Physics (physics.comp-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)