Open quantum system approaches are widely used in the description of physical, chemical and biological systems. A famous example is electronic excitation transfer in the initial stage of photosynthesis, where harvested energy is transferred with remarkably high efficiency to a reaction center. This transport is affected by the motion of a structured vibrational environment, which makes simulations on a classical computer very demanding. Here we propose an analog quantum simulator of complex open system dynamics with a precisely engineered quantum environment. Our setup is based on superconducting circuits, a well established technology. As an example, we demonstrate that it is feasible to simulate exciton transport in the Fenna-Matthews-Olson photosynthetic complex. Our approach allows for a controllable single-molecule simulation and the investigation of energy transfer pathways as well as non-Markovian noise-correlation effects.
The accurate evaluation of diagonal unitary operators is often the most resourceintensive element of quantum algorithms such as real-space quantum simulation and Grover search. Efficient circuits have been demonstrated in some cases but generally require ancilla registers, which can dominate the qubit resources. In this paper, we give a simple way to construct efficient circuits for diagonal unitaries without ancillas, using a correspondence between Walsh functions and a basis for diagonal operators. This correspondence reduces the problem of constructing the minimal-depth circuit within a given error tolerance, for an arbitrary diagonal unitaryê ( ) if x in the x basis, to that of finding the minimallength Walsh-series approximation to the function f(x). We apply this approach to the quantum simulation of the classical Eckart barrier problem of quantum chemistry, demonstrating that high-fidelity quantum simulations can be achieved with few qubits and low depth. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New J. Phys. 16 (2014) 033040 J Welch et al. The second equality shows that the functional form is the same whether x is continuous or discrete, the only difference being the number of bits in the expansion of x. This makes Walsh series useful for representing discretely sampled continuous functions. New J. Phys. 16 (2014) 033040 J Welch et al =Û e if that is diagonal in this basis is given in terms of its eigenvalues asˆ= f k f k k . New J. Phys. 16 (2014) 033040 J Welch et al 0 1 j j New J. Phys. 16 (2014) 033040 J Welch et al 5 New J. Phys. 16 (2014) 033040 J Welch et al 7 7, which means that 7 qubits are necessary to represent the series. New J. Phys. 16 (2014) 033040 J Welch et al
Most investigations devoted to the conditions for adiabatic quantum computing are based on the first-order correction Ψ ground (t)|Ḣ(t)|Ψ excited (t) /∆E 2 (t) ≪ 1. However, it is demonstrated that this first-order correction does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections as well and shows that the computational error can be made exponentially small -which facilitates significantly shorter evolution times than the above first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time T of order of the inverse minimum energy gap ∆Emin is sufficient and necessary, i.e., T = O(∆E −1 min ). For some examples, these analytical investigations are confirmed by numerical simulations.
Compressed sensing is a processing method that significantly reduces the number of measurements needed to accurately resolve signals in many fields of science and engineering. We develop a two-dimensional variant of compressed sensing for multidimensional spectroscopy and apply it to experimental data. For the model system of atomic rubidium vapor, we find that compressed sensing provides an order-ofmagnitude (about 10-fold) improvement in spectral resolution along each dimension, as compared to a conventional discrete Fourier transform, using the same data set. More attractive is that compressed sensing allows for random undersampling of the experimental data, down to less than 5% of the experimental data set, with essentially no loss in spectral resolution. We believe that by combining powerful resolution with ease of use, compressed sensing can be a powerful tool for the analysis and interpretation of ultrafast spectroscopy data.
For the prototypical example of the Ising chain in a transverse field, we study the impact of decoherence on the sweep through a second-order quantum phase transition. Apart from the advance in the general understanding of the dynamics of quantum phase transitions, these findings are relevant for adiabatic quantum algorithms due to the similarities between them. It turns out that ͑in contrast to first-order transitions studied previously͒ the impact of decoherence caused by a weak coupling to a rather general environment increases with system size ͑i.e., number of spins or qubits͒, which might limit the scalability of the system.Recently, the dynamics of quantum phase transitions ͓1͔ has attracted increasing interest, see, e.g., ͓2-4͔. In contrast to thermal transitions ͑usually driven by the competition between energy and entropy͒, they are characterized by a fundamental change of the ground state structure ͑e.g., from para-to ferromagnetic͒ at the critical value of a variable external parameter ͑e.g., magnetic field͒. Quantum phase transitions are induced by quantum rather than thermal fluctuations and thus may occur at zero temperature. At the critical point, the energy levels become arbitrarily close and thus the response times diverge ͑in the continuum limit͒. Consequently, during the sweep trough such a phase transition by means of a time-dependent external parameter, small external perturbations or internal fluctuations become strongly amplified-leading to many interesting effects, see, e.g., ͓5-9͔. One of them is the anomalously high susceptibility to decoherence ͑see also ͓4͔͒: Due to the convergence of the energy levels at the critical point, even low-energy modes of the environment may cause excitations and thus perturb the system. Here, we study the decoherence caused by a small coupling to a rather general reservoir for the quantum Ising chain in a transverse field, which is considered a prototypical example ͓1͔ for a second-order quantum phase transition ͑and further possesses the advantage of being analytically solvable͒.Apart from the general understanding of quantum phase transitions, these investigations are also relevant for quantum computing: By constructing the Hamiltonian appropriately, it is possible to encode the solution to hard computational problems ͑such as factoring large numbers͒ in its ground state. In order to reach this solution state, we may start off with a simpler Hamiltonian whose ground state is easy to prepare as the initial configuration. If we now steadily transform it to the problem Hamiltonian, the adiabatic theorem tells us that we stay near the ground state if the evolution is slow enough-and thus finally end up in ͑or close to͒ the desired solution state ͑adiabatic quantum computing ͓10,11͔͒. However, somewhere on the way from the simple initial configuration to the final state, there is typically a critical point that bears strong similarities to a quantum phase transition ͑e.g., vanishing gap and diverging entanglement in the continuum limit ͓12,13͔͒. Based on this ...
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