Southwest Quantum Information and Technology

Thirteenth Annual Meeting, February 17-20, 2011
Boulder, Colorado

Full Program | Thursday | Friday | Saturday | Sunday | All Sessions

SESSION 10a: Breakout A -- Quantum Tomography, Estimation, Optimization
Session Chair:
4:00pm-4:30pm	Robin Blume-Kohout, Los Alamos National Lab
	Confidence intervals for quantum state estimation
	Abstract. Quantum state and process tomography -- widely used to validate quantum devices -- typically yield a point estimate. The final result is a single "best guess" for the system's density matrix or process matrix. A point estimator cannot enable reliable fault-tolerant design, for the best that can be said is "The estimate is probably close to the true state." Interval estimators, on the other hand, report a convex region that contains the true state with (guaranteed) high probability. They support rigorous logical statements about the state (or process), which in turn enable fault tolerant designs. In this talk, I'll demonstrate how to design a confidence region estimator with guaranteed success probability, how to describe the result concisely, and how to derive a useful point estimator from it.
4:30pm-5:00pm	Mike Mullan, National Institute of Standards and Technology
	Improving Quantum Clocks via Semidefinite Programming
	Abstract. The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, as before and after clock queries, we are able to apply arbitrary unitary operations and measurements. Here, we take advantage of this freedom and present a numerical technique designed to increase the accuracy of these clocks by optimizing over these choices of quantum operations. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after a single interrogation step; we do not optimize over sequences of interrogations nor over the time of each step. In contrast to prior work, which derived asymptotically optimal strategies under the assumption that all classical oscillator states are equiprobable, we are able to consider the more realistic situation where we have some prior knowledge of the frequency of this oscillator, either from experimental considerations or previous measurements. Additionally, we are able to compare clocks with varying numbers of ions and those subject to multiple, coherent queries. Our technique is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small. While we can only simulate small systems, many quantum logic clocks, like the highly accurate Al+ optical clock at NIST, use relatively few ions and are therefore natural candidates for the techniques developed here. This work is in collaboration with Manny Knill and Till Rosenband.
5:00pm-5:30pm	Joshua Combes, Center for Quantum Information and Control, University of New Mexico, USA
	Efficient methods for the characterisation of qbit Hamiltonian dynamics
	Abstract. We investigate schemes for Hamiltonian parameter estimation of a two-level system using fixed-basis projective measurements. To be concrete we consider two regimes of parameter estimation. Regime I: the coupling of qbit to the environment is negligible. However, due to manufacturing imperfections the strength ω of the Hamiltonian, H=ω σ_x/2, is unknown. Regime II: the second and more realistic case is when the qbit is weakly coupled, with strength κ, to a Markovian environment. In this situation both κ and ω must be estimated. We show that it is possible to reduce the total number of measurements required for characterisation in both cases by using measurements that are not uniformly spaced in time.
5:30pm-6:00pm	Yu Tomita, Georgia Institute of Technology
	Multi-qubit compensation sequences
	Abstract. We discuss our recent work on the multi-qubit compensation sequences [Tomita et al., New J. Phys. 12, 015002 (2010)]. The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n-qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantum computers based on the XY interaction, single-qubit composite pulse sequences naturally correct systematic errors. For quantum computers based on the Heisenberg or exchange interaction, the composite pulse sequences reduce the logical single-qubit gate errors but increase the errors for logical two-qubit gates.