I am doing research in Quantum Computing, particularly on quantum error correction and fault tolerance.
My advisor is Professor K. Birgitta Whaley (Chemistry)
I filed my dissertation at 3pm PT on May 9, 2008, completing my Ph.D.
Some recent papers:
J. Fern. An upper bound on quantum fault tolerant thresholds arXiv:0801.2608
In this paper we calculate upper bounds on fault tolerance, without restrictions on the overhead involved. Optimally adaptive recovery operators are used, and the Shannon entropy is used to estimate the thresholds. By allowing for unrealistically high levels of overhead, we find a quantum fault tolerant threshold of 6.88% for the depolarizing noise used by Knill, which compares well to "above 3%" evidenced by Knill. We conjecture that the optimal threshold is 6.90%, based upon the hashing rate. We also perform threshold calculations for types of noise other than that discussed by Knill.
J. Fern, K.B. Whaley. New lower bounds on the non-zero capacity of Pauli Channels arXiv:0708.1597
We look at constructive encodings that give the best known thresholds for the non-zero capacity of quantum channels, i.e. the upper bound for correctable noise. We find that Pauli noise is correctable up to the hashing bound. For a depolarizing channel, we establish a constructive method of obtaining a non-zero capacity for a fidelity (probability of no error) of f=0.80870.
J. Fern. Correctable noise of Quantum Error Correcting Codes under adaptive concatenation. Phys. Rev. A 77, 010301(R) (2008). quant-ph/0703258 PDF
We examine the transformation of noise under a quantum error correcting code (QECC) concatenated repeatedly with itself, by analyzing the effects of a quantum channel after each level of concatenation using recovery operators that are optimally adapted to use error syndrome information from the previous levels of the code. We use the Shannon entropy of these channels to estimate the thresholds of correctable noise for QECCs and find considerable improvements under this adaptive concatenation. Similar methods could be used to increase quantum fault tolerant thresholds.
J. Fern, J. Kempe, S. Simic, S.Sastry. Generalized Performance of Concatenated Quantum Codes -- A Dynamical Systems Approach. IEEE Trans. on Automatic Control 51:448-459 (March 2006). quant-ph/0409084 PDF
We apply a dynamical systems approach to concatenation of quantum error correcting codes, extending and generalizing the results of Rahn et al. [1] to both diagonal and nondiagonal channels. Our point of view is global: instead of focusing on particular types of noise channels, we study the geometry of the coding map as a discrete-time dynamical system on the entire space of noise channels. In the case of diagonal channels, we show that any code with distance at least three corrects (in the infinite concatenation limit) an open set of errors. For Calderbank-Shor-Steane (CSS) codes, we give a more precise characterization of that set. We show how to incorporate noise in the gates, thus completing the framework. We derive some general bounds for noise channels, which allows us to analyze several codes in detail.
My ArXiv papers on different mirrors UC Davis ArXiv E-Print Web
Email me at jesse at math dot berkeley dot edu