Optimal control of a qubit coupled to a non-Markovian environment

A central challenge for implementing quantum computing in the solid state is decoupling the qubits from the intrinsic noise of the material. We investigate the implementation of quantum gates for a paradigmatic, non-Markovian model: A single qubit coupled to a two-level system that is exposed to a heat bath. We systematically search for optimal pulses using a generalization of the novel open systems Gradient Ascent Pulse Engineering (GRAPE) algorithm. We show and explain that next to the known optimal bias point of this model, there are optimal shapes which refocus unwanted terms in the Hamiltonian. We study the limitations of controls set by the decoherence properties. This can lead to a significant improvement of quantum operations in hostile environments.Comment: 5 pages, 3 figures, improved pulse shape

Optimal control of a leaking qubit

Physical implementations of quantum bits can contain coherent transitions to energetically close non-qubit states. In particular, for anharmonic oscillator systems such as the superconducting phase qubit and the transmon a two-level approximation is insufficient. We apply optimal control theory to the envelope of a resonant Rabi pulse in a qubit in the presence of a single, weakly off-resonant leakage level. The gate error of a spin flip operation reduces by orders of magnitude compared to simple pulse shapes. Near-perfect gates can be achieved for any pulse duration longer than an intrinsic limit given by the nonlinearity. The pulses can be understood as composite sequences that refocus the leakage transition. We also discuss ways to improve the pulse shapes.Comment: 4 pages, 2 figure

Quantum algorithm for robust optimization via stochastic-gradient online learning

Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings has catered to a rich source of research problems. Robust convex optimization is a branch of optimization theory in which the variables or parameters involved have a certain level of uncertainty. In this work, we consider the online robust optimization meta-algorithm by Ben-Tal et al. and show that for a large range of stochastic subgradients, this algorithm has the same guarantee as the original non-stochastic version. We develop a quantum version of this algorithm and show that an at most quadratic improvement in terms of the dimension can be achieved. The speedup is due to the use of quantum state preparation, quantum norm estimation, and quantum multi-sampling. We apply our quantum meta-algorithm to examples such as robust linear programs and robust semidefinite programs and give applications of these robust optimization problems in finance and engineering.Comment: 21 page

Nonadiabatic transitions in the exit channel of atom-molecule collisions: Fine-structure branching in Na+N[sub 2]

We study Na+N₂collisions by laser excitation of the collision complex in a differential scattering experiment. The measured relative population of the Na(3p) fine-structure levels reflects the nonadiabatic transitions occuring in the exit channel of the collision.Theoretical results obtained with a classical-path formalism and accurate quantum chemical data for NaN₂ are found to be in good agreement. The presence of a conical intersection for the T-shaped geometry has a profound influence on the observed fine-structure branching.Support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged

Quantum algorithm for stochastic optimal stopping problems with applications in finance

The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on quantum access to a stochastic process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo. For this algorithm, we elucidate the intricate interplay of function approximation and quantum algorithms for Monte Carlo. Our algorithm achieves a nearly quadratic speedup in the runtime compared to the LSM algorithm under some mild assumptions. Specifically, our quantum algorithm can be applied to American option pricing and we analyze a case study for the common situation of Brownian motion and geometric Brownian motion processes.Comment: 45 pages; v2: title slightly changed, typos fixed, references adde

Collision photography: polarization imaging of atom-molecule collisions

We report differential scattering experiments on the laser excitation of Na+Mcollision pairs with M=N₂, CO, C₂H₂, and CO₂. The collision event is probed by the laser polarization revealing geometric and electronic properties of the collision pair. The experimental data are compared to the results of a Monte Carlo trajectory simulation using ab initio quantum chemical data.Financial support from the Deutsche Forschungsgemeinschaft and the Schweizerischer Nationalfond (Project No. 20- 065290.01) is gratefully acknowledged

Optimal number of pigments in photosynthetic complexes

We study excitation energy transfer in a simple model of photosynthetic complex. The model, described by Lindblad equation, consists of pigments interacting via dipole-dipole interaction. Overlapping of pigments induces an on-site energy disorder, providing a mechanism for blocking the excitation transfer. Based on the average efficiency as well as robustness of random configurations of pigments, we calculate the optimal number of pigments that should be enclosed in a pigment-protein complex of a given size. The results suggest that a large fraction of pigment configurations are efficient as well as robust if the number of pigments is properly chosen. We compare optimal results of the model to the structure of pigment-protein complexes as found in nature, finding good agreement.Comment: 20 pages, 7 figures; v2.: new appendix, published versio

Vibration-enhanced quantum transport

In this paper, we study the role of collective vibrational motion in the phenomenon of electronic energy transfer (EET) along a chain of coupled electronic dipoles with varying excitation frequencies. Previous experimental work on EET in conjugated polymer samples has suggested that the common structural framework of the macromolecule introduces correlations in the energy gap fluctuations which cause coherent EET. Inspired by these results, we present a simple model in which a driven nanomechanical resonator mode modulates the excitation energy of coupled quantum dots and find that this can indeed lead to an enhancement in the transport of excitations across the quantum network. Disorder of the on-site energies is a key requirement for this to occur. We also show that in this solid state system phase information is partially retained in the transfer process, as experimentally demonstrated in conjugated polymer samples. Consequently, this mechanism of vibration enhanced quantum transport might find applications in quantum information transfer of qubit states or entanglement.Comment: 7 pages, 6 figures, new material, included references, final published versio