6,068 research outputs found
Reliable channel-adapted error correction: Bacon-Shor code recovery from amplitude damping
We construct two simple error correction schemes adapted to amplitude damping
noise for Bacon-Shor codes and investigate their prospects for fault-tolerant
implementation. Both consist solely of Clifford gates and require far fewer
qubits, relative to the standard method, to achieve correction to a desired
order in the damping rate. The first, employing one-bit teleportation and
single-qubit measurements, needs only one fourth as many physical qubits, while
the second, using just stabilizer measurements and Pauli corrections, needs
only half. We show that existing fault-tolerance methods can be employed for
the latter, while the former can be made to avoid potential catastrophic errors
and can easily cope with damping faults in ancilla qubits.Comment: 8 pages, 1 figur
Information-Theoretic Analysis of Serial Dependence and Cointegration
This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the existence of a cointegrating relationship in a nonlinear context. This new framework represents a natural extension of the linear-memory concepts based on correlations. Finally, we show that our testing devices seem promising for exploratory analysis with nonlinearly cointegrated time series.Publicad
Cointegration tests based on record counting statistics
This paper presents of number of cointegration tests that exploit the statistical properties of the records from the original time series variables. We prove their consistency and obtain their asymptotic null distributions. Among the advantages of this novel methodology, the new tests are invariant with respect to the individual series' variances and also with respect to monotonic transformations applied to these series. In addition, these tests are robust against the presence of level breaks as long as the number of these breaks increases slowly enough with the sample size. Finally, an alternative scheme is proposed to deal with additive outliers, which prevent them from causing size distortions
Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames
Following the introduction of the task of reference frame error correction,
we show how, by using reference frame alignment with clocks, one can add a
continuous Abelian group of transversal logical gates to any error-correcting
code. With this we further explore a way of circumventing the no-go theorem of
Eastin and Knill, which states that if local errors are correctable, the group
of transversal gates must be of finite order. We are able to do this by
introducing a small error on the decoding procedure that decreases with the
dimension of the frames used. Furthermore, we show that there is a direct
relationship between how small this error can be and how accurate quantum
clocks can be: the more accurate the clock, the smaller the error; and the
no-go theorem would be violated if time could be measured perfectly in quantum
mechanics. The asymptotic scaling of the error is studied under a number of
scenarios of reference frames and error models. The scheme is also extended to
errors at unknown locations, and we show how to achieve this by simple majority
voting related error correction schemes on the reference frames. In the
Outlook, we discuss our results in relation to the AdS/CFT correspondence and
the Page-Wooters mechanism.Comment: 10+35 pages. Also see related work uploaded to the arXiv on the same
day; arXiv:1902.0771
Range unit root tests
Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the type of "long-wave" patterns observed not only in unit root time series but also in series following more complex data generating mechanism. To this end, our testing device analyses the trend exhibit by the data, without imposing any constraint on the generating mechanism. We call our device the Range Unit Root (RUR) Test since it is constructed from running ranges of the series. These statistics allow a more general characterization of a strong serial dependence in the mean behavior, thus endowing our test with a number of desirable properties. Among these properties are the invariance to nonlinear monotonic transformations of the series and the robustness to the presence of level shifts and additive outliers. In addition, the RUR test outperforms the power of standard unit root tests on near-unit-root stationary time series
Information-Theoretic Analysis of Serial Dependence and Cointegration.
This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the existence of a cointegrating relationship in a nonlinear context. This new framework represents a natural extension of the linear-memory concepts based on correlations. Finally, we show that our testing devices seem promising for exploratory analysis with nonlinearly cointegrated time series.
Instrumental Variable Interpretation of Cointegration with Inference Results for Fractional Cointegration
In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The instrument is a delayed regressor obtained from the conditional bivariate system of nonstationary fractionally integrated processes with a weakly stationary error correction term. We prove the consistency of this estimator and derive its limiting distribution. We also show that, in the I(1) case, with a semiparametric correction simpler than the one required for the fully modified ordinary least squares (FM-OLS), our fully modified instrumental variables (FM-IV) estimator is median-unbiased, a mixture of normals, and asymptotically efficient. As a consequence, standard inference can be conducted with this new FM-IV estimator of the cointegrating parameter. We show by the use of Monte Carlo simulations that the small sample gains with the new IV estimator over OLS are remarkable.Publicad
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