Publications

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We present an expression for the spectral gap, opening up new possibilities for performing and accelerating spectral calculations of quantum many-body systems. We develop and demonstrate one such possibility in the context of tensor network simulations. Our approach requires only minor modifications of the widely used simple update method and is computationally lightweight relative to other approaches. We validate it by computing spectral gaps of the 2D and 3D transverse-field Ising models and find strong agreement with previously reported perturbation theory results.

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The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on inverting the underlying dynamical equations governing the controlled observables. In this paper, we generalize the ideas in [Phys. Rev. A 98, 043429 (2018)2469-992610.1103/PhysRevA.98.043429] to the task of orienting symmetric top molecules in three dimensions. To this end, we derive equations for the control fields capable of directly tracking the expected value of the three-dimensional dipole orientation vector along a desired path in time. We show this framework can be utilized for tracking the orientation of linear molecules as well, and present numerical illustrations of these principles for symmetric-top tracking control problems.

We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state through an adaptively constructed quantum circuit, where each adaptive step is informed by feedback from gradient measurements in which the associated tangent space directions are randomized. We provide theoretical arguments and numerical evidence that convergence to the target state can be achieved for almost all initial states. We investigate different randomization procedures and develop lower bounds on the expected cost function change, which allows for drawing connections to barren plateaus and for assessing the applicability of the algorithm to large-scale problems.

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It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to constructively assign values to quantum circuit parameters. We show that this procedure results in an estimate of the combinatorial optimization problem solution that improves monotonically with the depth of the quantum circuit. Importantly, the measurement-based feedback enables approximate solutions to the combinatorial optimization problem without the need for any classical optimization effort, as would be required for the quantum approximate optimization algorithm. We demonstrate this feedback-based protocol on a superconducting quantum processor for the graph-partitioning problem MaxCut, and present a series of numerical analyses that further investigate the protocol's performance.

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The characterization of mixtures of non-interacting, spectroscopically similar quantum components has important applications in chemistry, biology, and materials science. We introduce an approach based on quantum tracking control that allows for determining the relative concentrations of constituents in a quantum mixture, using a single pulse which enhances the distinguishability of components of the mixture and has a length that scales linearly with the number of mixture constituents. To illustrate the method, we consider two very distinct model systems: mixtures of diatomic molecules in the gas phase, as well as solid-state materials composed of a mixture of components. A set of numerical analyses are presented, showing strong performance in both settings.

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