We investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The excitation energy transfer due to the coupling of the light harvesting complex to the reaction center ("sink") is analyzed using an effective non-Hermitian Hamiltonian. We show that, as the coupling to the reaction center is varied, maximal efficiency in energy transport is achieved in the vicinity of the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. Our results demonstrate that the presence of the sink (which provides a quasi-continuum in the energy spectrum) is the dominant effect in the energy transfer which takes place even in absence of a thermal bath. This approach allows one to study the effects of finite temperature and the effects of any coupling scheme to the reaction center. Moreover, taking into account a realistic electric dipole interaction, we show that the optimal distance from the reaction center to the Fenna-Matthews-Olson system occurs at the superradiance transition, and we show that this is consistent with available experimental data.

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We simulate Shor's algorithm on an Ising spin quantum computer. The influence of non-resonant effects is analyzed in detail. It is shown that our "2πk"-method successfully suppresses non-resonant effects even for relatively large values of the Rabi frequency. 1 I. The Quantum Shor AlgorithmThe quantum Shor algorithm [1] provides an exciting opportunity for prime-factorization of large integers -a problem beyond the capabilities of today's powerful digital computers. Shor's algorithm utilizes two quantum registers (the x-and y-registers), which contain quantum bits two-level quantum systems called qubits [1]-[3]. First, the quantum computer produces the uniform superposition of all states in the x-register -all possible values of x. Second, the quantum computer computes the periodic function: y(x) = q x (mod N), where N is the number to factorize, and q is any number which is coprime to N. Third, the quantum computer creates a discrete Fourier transform of the x-register. The measurement of the state of the x-register yields the period, T , of the function y(x), which is used to produce a factor of the number N.In Dirac notation, the wave function of the quantum computer can be represented as a superposition of digital states,where a k (0 ≤ k ≤ L − 1) denotes the state of the k-th qubit in the x-register, and b n (0 ≤ n ≤ M − 1) denotes the state of the n-th qubit in the y-register. For example, if the k-th qubit of the x-register is in the ground state, then: a k = 0, and if it is in the excited state, a k = 1. In decimal notation, the digital state can be represented as |x, y , whereIn this notation, the initial wave function of a quantum system is: |0, 0 . The uniform superposition of the states created in the x-register can be written as,where D = 2 L is the number of states in the x-register. After computation of the function y(x), we have,After the discrete Fourier transform, one measures the state of the x-register. The probability of the measurement, P (x), must be a peaked distribution with peak separation, ∆x, equal to a multiple of 1/T . In particular, if the number of states, D, in the x-register is divisible by the period, T , then: ∆x = D/T . From the value ∆x one can find the period, T . A factor of the number N can be found by computing the greatest common divisor of (q T /2 + 1) and N, or (q T /2 − 1) and N (for even T ). 2It was shown in [4], that the simplest demonstration of the quantum Shor's algorithm can be done with only four qubits. (Two qubits represent the x-register and two qubits represent the y-register.) This primitive quantum computer is able to find a factor of the number 4. For N = 4, the only coprime number is q = 3. The function, y(x) = 3x (mod 4), has only two values: y = 1 and y = 3, and a period is, T = 2. In Dirac notation, the wave function (4) has the form, Ψ = 1 2 (|00, 01 + |01, 11 + |10, 01 + |11, 11 ).After the Discrete Fourier transform, the wave function of the quantum computer is, Ψ = 1 2 (|00, 01 + |00, 11 + |10, 01 + |10, 11 ).Measuring x can produce two ...

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We study a one-dimensional chain of nuclear 1/2−spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. The standard viewpoint is that the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a non-homogeneous magnetic field can strongly reduce quantum chaos effects. We give analytical estimates which explain this effect, together with numerical data supporting our analysis.PACS numbers: 05.45Pq, 05.45Mt, 03.67,Lx Much attention is paid in recent years to the idea of quantum computation (see, for example, [1][2][3] and references therein). The burst of interest to this subject is caused by the discovery of fast quantum algorithm for the factorization of integers [4] demonstrating the effectiveness of quantum computers in comparison to the classical ones. Nowadays, there are different projects for the experimental realization of quantum computers, based on interacting two-level systems (qubits). One of the most important problems widely discussed in the literature, is the problem of decoherence which arises in many-qubit systems due to the influence of an environment [5]. However, even in the absence of the environment, the interaction between qubits may lead to the "internal decoherence" related to the onset of quantum chaos [6].The latter subject of quantum chaos in closed systems of interacting particles has been developed recently in application to nuclear, atomic and solid state physics (see, e.g., [7] and references therein). When the (two-body) interaction between particles exceeds the critical value, fast transition to chaos occurs in the Hilbert space of manyparticle states [8]. Different aspects of this transition are now well understood, such as statistical description of eigenstates and the onset of thermalization in finite systems (see, e.g., [9] and references therein).Direct application of the quantum chaos theory to a simple model of quantum computer [6] has shown that for a strong enough interaction between qubits the onset of quantum chaos is unavoidable. Although for L = 14 − 16 qubits the critical value J cr for quantum chaos threshold is quite large, with an increase of L it decreases as J cr ∼ 1/L. From the viewpoint of the standard approach for closed systems of interacting particles, the decrease of the chaos threshold with an increase of qubits looks generic. However, in this Letter we demonstrate that this conclusion is not universal and the quantum chaos can be avoided, for example, with a proper choice of the external magnetic field.Our consideration is based on the one-dimensional model of L nuclear 1/2−spins subjected to the timedependent magnetic field of the following form [10],w...

We propose a nuclear spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that an MRFM single-electron spin measurement provides three essetial requirements for quantum computation in solids: (a) preparation of the ground state, (b) one-and two-qubit quantum logic gates, and (c) a measurement of the final state. The proposed quantum computer can operate at temperatures up to 1K.

We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. The phase and probability errors caused by unwanted transitions are minimized and computed numerically.