Southwest Quantum Information and Technology

Sixteenth Annual Meeting, February 20-22, 2014
Santa Fe, New Mexico

Full Program | Thursday | Friday | Saturday | All Sessions

SESSION 11: Quantum Tomography
10:15am - 10:45am	John Gamble, Sandia National Laboratories
	Quantum gate set tomography
	Abstract. In this talk, I will discuss a recently-proposed framework called "gate set tomography" (GST) for self-consistently characterizing an entire set of quantum logic gates on a black-box quantum device. Until recently, protocols for quantum tomography relied on a pre-existing and perfectly calibrated reference frame for the measurements used to characterize a device. GST eschews this artificial separation entirely, instead characterizing quantum processes, preparations, and measurements concurrently. I will then describe an explicit closed-form protocol for linear-inversion GST, whose reliability is independent of pathologies such as local maxima of the likelihood function. This initial estimate can then be refined using standard likelihood maximization techniques. Finally, I discuss recent experimental implementations of GST for single qubits in both ion traps and electrostatically defined quantum dot systems. This work was supported in part by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
10:45am - 11:15am	Carlos Riofrio, Freie Universität Berlin
	Tomography of Quantum Fields
	Abstract. Understanding the fundamental interactions in many-body physical systems is of great interest in current theoretical and experimental efforts. In particular, continuous many-body systems or fields are exciting because they offer the tools for performing quantum simulations of processes of non-equilibrium, equilibration and thermalization. In this context, the problem of developing tools for identifying and reconstructing the state or some aspect of such systems is needed on a practical level. In this talk, I will present a first approach in that direction and possible applications for reconstructing quantum fields from low order correlation functions readily measurable in current experiments. We concentrate on one dimensional systems with spatially limited entanglement which are well described by the continuous matrix product state (cMPS) formalism.
11:15am - 11:45am	Amir Kalev, University of New Mexico
	Quantum process tomography of near-unitary maps
	Abstract. We study the problem of quantum process tomography given the prior information that the implemented map is near to a unitary map on a d-dimensional Hilbert space. In particular, we show that a perfect unitary map is completely characterized by a minimum of d^2 + d measurement outcomes. This contrasts with the d^4 measurement outcomes required in general. To achieve this lower bound, one must probe the system with a particular set of d states in a particular order. This order exploits unitarity but does not assume any other structure of the map. We further numerically study the behaviors of two of compressed sensing estimators based on correct or faulty prior information caused by noise. The results show two important features: (1) When we have accurate prior information, one can drastically reduce the required data needed; (2) Different estimators applied to the same data are sensitive to different types of noise. The estimators could, therefore, be used as indicators of particular error models and to validate the use of prior assumptions for compressed sensing quantum process tomography. Finally, we consider the more general case of noisy quantum maps, with a low level of noise. Our study indicates that transforming to the interaction picture, where the noiseless map is represented by a diagonal operator, can provide a useful tool to identify the noise structure. This, in turn, can lead to a substantial reduction in the numerical resources needed to estimate the noisy map.
11:45am - 12:15pm	Scott Glancy, National Institute of Standards and Technology
	Practical and Fast Gaussian State Estimation
	Abstract. Many experiments on quantum systems involve the preparation and measurement of Gaussian states of a multi-system continuous variable Hilbert space. Examples include optical and microwave systems involving squeezing and linear interactions and nanomechanical resonators described with second order Hamiltonians. The state space that these systems access is much smaller than the full Hilbert space and can be fully characterized with a 2Nx2N covariance matrix and 2N means vector, where N is the number of individual modes or resonators. We describe here a very simple and fast method for estimating the covariance matrix and means vector from homodyne (or quadrature) measurement data collected at arbitrary phases. The method computes observed means of simple functions of the homodyne (phase, quadrature) pairs, which are easily related to the covariance matrix and means vector. We characterize uncertainty through a parametric bootstrap strategy. Our method is particularly useful for the analysis of large data sets.