Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session B26: Focus Session: Quantum Characterization, Verification, and Validation I |
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Sponsoring Units: GQI Chair: Charles Tahan, Laboratory for Physical Sciences Room: 328 |
Monday, March 18, 2013 11:15AM - 11:51AM |
B26.00001: Using Compressed Sensing for Quantum Tomography Invited Speaker: Steve Flammia |
Monday, March 18, 2013 11:51AM - 12:03PM |
B26.00002: Analyzing quantum simulators efficiently: Scalable state tomography and quantifying entanglement with routine measurements Marcus Cramer, Tillmann Baumgratz, Oliver Marty, David Gross, Martin Plenio Conventional full state tomography reaches its limit already for a few qubits and hence novel methods for the verification and benchmarking of quantum devices are called for. We show how the complete reconstruction of density matrices is possible even if one relies only on local information about the state. This results in an experimental effort that is linear in the number of qubits and efficient post-processing -- in stark contrast to the exponential scaling of standard tomography. Whenever full tomography is not needed but instead less information required, one would expect that even fewer measurements suffice. Taking entanglement content of solid state samples and bosons in lattices as an example, we show how it may be quantified unconditionally using already routinely performed measurements only.\\ {\em Scalable reconstruction of density matrices}, T. Baumgratz, D. Gross, M. Cramer, and M.B. Plenio, arXiv:1207.0358.\\ {\em Efficient quantum state tomography}, M. Cramer, M.B. Plenio, S.T. Flammia, R. Somma, D. Gross, S.D. Bartlett, O. Landon-Cardinal, D. Poulin, and Y.-K. Liu, Nat. Commun. 1, 149 (2010).\\ {\em Measuring entanglement in condensed matter systems}, M. Cramer, M.B. Plenio, and H. Wunderlich, Phys. Rev. Lett. 106, 020401 (2011). [Preview Abstract] |
Monday, March 18, 2013 12:03PM - 12:15PM |
B26.00003: Quantum Estimation, meet Computational Statistics; Computational Statistics, meet Quantum Estimation Chris Ferrie, Chris Granade, Joshua Combes Quantum estimation, that is, post processing data to obtain classical descriptions of quantum states and processes, is an intractable problem---scaling exponentially with the number of interacting systems. Thankfully there is an entire field, Computational Statistics, devoted to designing algorithms to estimate probabilities for seemingly intractable problems. So, why not look to the most advanced machine learning algorithms for quantum estimation tasks? We did. I'll describe how we adapted and combined machine learning methodologies to obtain an online learning algorithm designed to estimate quantum states and processes. [Preview Abstract] |
Monday, March 18, 2013 12:15PM - 12:27PM |
B26.00004: Direct characterization of any linear photonic device Alessandro Fedrizzi, Matthew Broome, Andrew White, Robert Fickler, Saleh Rahimi-Keshari, Timothy Ralph Linear photonic devices comprised of simple beamsplitters and phase shifters can implement any unitary operator for quantum information processing. The significant practical challenge is to characterize such an interferometric device once it is built. Performing quantum process tomography requires the full suite of quantum tools such as N-mode quantum state preparation and measurement, and is, despite progress on more efficient methods, slow and impractical for large interferometric devices. Here we introduce a simple technique to characterize the unitary matrix of a linear photonic device using standard laser sources and photodetectors, without the requirement for active locking or single-photon sources. Our method is precise and efficient, requiring only 2N-1 measurement configurations for a N-path network. We use it experimentally to characterise an integrated 3x3 fused-fibre coupler and highlight its precision by comparing measured quantum interference patterns with those predicted using the classically-estimated unitary. We observe excellent agreement between the two experimental methods. [Preview Abstract] |
Monday, March 18, 2013 12:27PM - 12:39PM |
B26.00005: Ultrafast Quantum Process Tomography via Continuous Measurement and Convex Optimization Charles Baldwin, Carlos Riofrio, Ivan Deutsch Quantum process tomography (QPT) is an essential tool to diagnose the implementation of a dynamical map. However, the standard protocol is extremely resource intensive. For a Hilbert space of dimension $d$, it requires $d^2$ different input preparations followed by state tomography via the estimation of the expectation values of $d^2-1$ orthogonal observables. We show that when the process is nearly unitary, we can dramatically improve the efficiency and robustness of QPT through a collective continuous measurement protocol on an ensemble of identically prepared systems. Given the measurement history we obtain the process matrix via a convex program that optimizes a desired cost function. We study two estimators: least-squares and compressive sensing. Both allow rapid QPT due to the condition of complete positivity of the map; this is a powerful constraint to force the process to be physical and consistent with the data. We apply the method to a real experimental implementation, where optimal control is used to perform a unitary map on a $d=8$ dimensional system of hyperfine levels in cesium atoms, and obtain the measurement record via Faraday spectroscopy of a laser probe. [Preview Abstract] |
Monday, March 18, 2013 12:39PM - 1:15PM |
B26.00006: Finding systematic errors in tomographic data: Characterising ion-trap quantum computers Invited Speaker: Thomas Monz Quantum state tomography has become a standard tool in quantum information processing to extract information about an unknown state. Several recipes exist to post-process the data and obtain a density matrix; for instance using maximum-likelihood estimation. These evaluations, and all conclusions taken from the density matrices, however, rely on valid data - meaning data that agrees both with the measurement model and a quantum model within statistical uncertainties. Given the wide span of possible discrepancies between laboratory and theory model, data ought to be tested for its validity prior to any subsequent evaluation. The presented talk will provide an overview of such tests which are easily implemented. These will then be applied onto tomographic data from an ion-trap quantum computer. [Preview Abstract] |
Monday, March 18, 2013 1:15PM - 1:27PM |
B26.00007: Adaptive quantum gate-set tomography Robin Blume-Kohout Quantum information hardware needs to be characterized and calibrated. This is the job of quantum state and process tomography, but standard tomographic methods have an Achilles heel: to characterize an unknown process, they rely on a set of absolutely calibrated measurements. But many technologies (e.g., solid-state qubits) admit only a single native measurement basis, and other bases are measured using unitary control. So tomography becomes circular -- tomographic protocols are using gates to calibrate themselves! Gate-set tomography confronts this problem head-on and resolves it by treating gates relationally. We abandon all assumptions about what a given gate operation does, and characterize entire universal gate sets from the ground up using only the observed statistics of an [unknown] 2-outcome measurement after various strings of [unknown] gate operations. The accuracy and reliability of the resulting estimate depends critically on which gate strings are used, and benefits greatly from adaptivity. [Preview Abstract] |
Monday, March 18, 2013 1:27PM - 1:39PM |
B26.00008: Quadratically faster state tomography using single-step adaptation Dylan Mahler, Lee Rozema, Ardavan Darabi, Christopher Ferrie, Robin Blume-Kohout, Aephraim Steinberg In quantum state tomography, an informationally complete set of measurements is made on N identically prepared quantum systems and from these measurements the quantum state can be determined. In the limit as $N\rightarrow\infty$ the estimate of the state converges on the true state. The rate at which this convergence occurs depends on both the state and the measurements used to probe the state. On the one hand, since nothing is known a priori about the state being probed, a set of maximally unbiased measurements should be made. On the other hand, if something was known about the state being measured a set of biased measurements would yield a more accurate estimate. It has been shown[1,2] that by adaptively choosing measurements optimal accuracy in the state estimate can be obtained regardless of the state being measured. Here we present an experimental demonstration of one-qubit adaptive tomography that achieves a rate of convergence of $1-O(\frac{1}{N})$ in the quantum state fidelity with only a single adaptive step and local measurements, as compared to $1-O(\frac{1}{\sqrt(N)})$ for standard tomography. Furthermore, we show how this protocol generalizes to arbitrarily entangled two-qubit systems. [1] Phys. Rev. Lett. 97, 130501 (2006) [2] Phys. Rev. A 85, 052120 (2012) [Preview Abstract] |
Monday, March 18, 2013 1:39PM - 1:51PM |
B26.00009: Quantum process tomography of energy and phase relaxation through adaptive measurements Markku Stenberg, Frank Wilhelm Quantum process tomography tends to be very time consuming when multiple degrees of freedom are studied simultaneously. We propose a method of efficient quantum process tomography to estimate the energy and phase relaxation rates in qubits. The method applies Bayesian inference to adaptively choose measurements based on the previously obtained measurement outcomes. We adopt sequential Monte-Carlo approach to perform the Bayesian updates and make use of a fast numerical implementation of the algorithm. We compare the performance of our method to conventional offline (implemented after experimental data collection) strategies and illustrate how our method can speed up quantum process tomography. [Preview Abstract] |
Monday, March 18, 2013 1:51PM - 2:03PM |
B26.00010: A quantum neural network computes its own relative phase Elizabeth Behrman Complete characterization of the state of a quantum system made up of subsystems requires determination of relative phase, because of interference effects between the subsystems. For a system of qubits used as a quantum computer this is especially vital, because the entanglement, which is the basis for the quantum advantage in computing, depends intricately on phase. We present here a first step towards that determination, in which we use a two-qubit quantum system as a quantum neural network, which is trained to compute and output its own relative phase. [Preview Abstract] |
Monday, March 18, 2013 2:03PM - 2:15PM |
B26.00011: Modeling quantum noise for efficient testing of fault-tolerant circuits Easwar Magesan, Daniel Puzzuoli, Christopher E. Granade, David G. Cory Simulating fault-tolerant properties of quantum circuits is important for the design of large-scale quantum information processors. For general circuits and noise models, these simulations quickly become intractable in the size of the encoded circuit. We introduce methods for approximating a noise process by one which allows for efficient Monte Carlo simulation of properties of encoded circuits. The approximations are as close to the original process as possible without overestimating their ability to preserve quantum information, a key property for obtaining more honest estimates of threshold values. We numerically illustrate the method with physically relevant noise models. [Preview Abstract] |
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