Multi-qubit compensation sequences

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.Comment: 9 pages, 5 figures; corrected reference formattin

Are 'unbiased' forecasts really unbiased? Another look at the Fed forecasts

This paper reconciles contradictory findings obtained from forecast evaluations: the existence of systematic errors and the failure to reject rationality in the presence of such errors. Systematic errors in one economic state may offset the opposite types of errors in the other state such that the null of rationality is not rejected. A modified test applied to the Fed forecasts shows that the forecasts were ex post biased.Greenbook Forecasts, forecast evaluation, systematic errors

Systematic Errors in Cosmic Microwave Background Interferometry

Cosmic microwave background (CMB) polarization observations will require superb control of systematic errors in order to achieve their full scientific potential, particularly in the case of attempts to detect the B modes that may provide a window on inflation. Interferometry may be a promising way to achieve these goals. This paper presents a formalism for characterizing the effects of a variety of systematic errors on interferometric CMB polarization observations, with particular emphasis on estimates of the B-mode power spectrum. The most severe errors are those that couple the temperature anisotropy signal to polarization; such errors include cross-talk within detectors, misalignment of polarizers, and cross-polarization. In a B mode experiment, the next most serious category of errors are those that mix E and B modes, such as gain fluctuations, pointing errors, and beam shape errors. The paper also indicates which sources of error may cause circular polarization (e.g., from foregrounds) to contaminate the cosmologically interesting linear polarization channels, and conversely whether monitoring of the circular polarization channels may yield useful information about the errors themselves. For all the sources of error considered, estimates of the level of control that will be required for both E and B mode experiments are provided. Both experiments that interfere linear polarizations and those that interfere circular polarizations are considered. The fact that circular experiments simultaneously measure both linear polarization Stokes parameters in each baseline mitigates some sources of error.Comment: 19 pages, 9 figures, submitted to Phys. Rev.

Treating Systematic Errors in Multiple Sclerosis Data

Multiple sclerosis (MS) is characterized by high variability between patients and, more importantly here, within an individual over time. This makes categorization and prognosis difficult. Moreover, it is unclear to what degree this intra-individual variation reflects the long-term course of irreversible disability and what is attributable to short-term processes such as relapses, to interrater variability and to measurement error. Any investigation and prediction of the medium or long term evolution of irreversible disability in individual patients is therefore confronted with the problem of systematic error in addition to random fluctuations. The approach described in this article aims to assist in detecting relapses in disease curves and in identifying the underlying disease course. To this end neurological knowledge was transformed into simple rules which were then implemented into computer algorithms for pre-editing disease curves. Based on simulations it is shown that pre-editing time series of disability measured with the Expanded Disability Status Scale (EDSS) can lead to more robust and less biased estimates for important disease characteristics, such as baseline EDSS and time to reach certain EDSS levels or sustained progression

Can the Fed Predict the State of the Economy?

Recent research has documented that the Federal Reserve produces systematic errors in forecasting inflation, real GDP growth, and the unemployment rate, even though these forecasts are unbiased. We show that these systematic errors reveal that the Fed is “surprised” by real and inflationary cycles. Using a modified Mincer-Zarnowitz regression, we show that the Fed knows the state of the economy for the current quarter, but cannot predict it one quarter ahead.Forecast Evaluation; Federal Reserve; Systematic Errors; Recessions