Effect of ancilla's structure on quantum error correction using the 7-qubit Calderbank-Shor-Steane code

In this work we discuss the ability of different types of ancillas to control the decoherence of a qubit interacting with an environment. The error is introduced into the numerical simulation via a depolarizing isotropic channel. After the correction we calculate the fidelity as a quality criterion for the qubit recovered. We observe that a recovery method with a three-qubit ancilla provides reasonable good results bearing in mind its economy. If we want to go further, we have to use fault-tolerant ancillas with a high degree of parallelism, even if this condition implies introducing new ancilla verification qubits.Comment: 24 pages, 10 Figures included. Accepted in Phys. Rev. A 200

Good Quantum Error-Correcting Codes Exist

A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n = 1 - 2H(2t/n) where H(p) is the binary entropy function -p log p - (1-p) log (1-p). Upper bounds on this asymptotic rate are given.Comment: Latex, 23 pages, 1 figure. Revised April 1996 to give more intuition and an example. Submitted to Phys. Rev.

Integrated software package STAMP for minor planets

The integrated software package STAMP allowed for rapid and exact reproduction of the tables of the year-book 'Ephemerides of Minor Planets.' Additionally, STAMP solved the typical problems connected with the use of the year-book. STAMP is described. The year-book 'Ephemerides of Minor Planets' (EMP) is a publication used in many astronomical institutions around the world. It contains all the necessary information on the orbits of the numbered minor planets. Also, the astronomical coordinates are provided for each planet during its suitable observation period

An Universal Quantum Network - Quantum CPU

An universal quantum network which can implement a general quantum computing is proposed. In this sense, it can be called the quantum central processing unit (QCPU). For a given quantum computing, its realization of QCPU is just its quantum network. QCPU is standard and easy-assemble because it only has two kinds of basic elements and two auxiliary elements. QCPU and its realizations are scalable, that is, they can be connected together, and so they can construct the whole quantum network to implement the general quantum algorithm and quantum simulating procedure.Comment: 8 pages, Revised versio

Quantum Error Correction and Orthogonal Geometry

A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.Comment: RevTex, 4 pages, no figures, submitted to Phys. Rev. Letters. We have changed the statement of Theorem 2 to correct it -- we now get worse rates than we previously claimed for our quantum codes. Minor changes have been made to the rest of the pape

Quantum Error Correction via Codes over GF(4)

The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.Comment: Latex, 46 pages. To appear in IEEE Transactions on Information Theory. Replaced Sept. 24, 1996, to correct a number of minor errors. Replaced Sept. 10, 1997. The second section has been completely rewritten, and should hopefully be much clearer. We have also added a new section discussing the developments of the past year. Finally, we again corrected a number of minor error

Topological Quantum Error Correction with Optimal Encoding Rate

We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of arbitrary genus. We find a class of regular toric codes that are optimal. For physical implementations, we present planar topological codes.Comment: REVTEX4 file, 5 figure

Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State

We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the Fractional Quantum Hall Effect state at Landau level filling fraction nu=5/2. Since the braid group representation describing statistics of these anyons is not computationally universal, one cannot directly apply the standard TQC technique. We propose to use very noisy non-topological operations such as direct short-range interaction between anyons to simulate a universal set of gates. Assuming that all TQC operations are implemented perfectly, we prove that the threshold error rate for non-topological operations is above 14%. The total number of non-topological computational elements that one needs to simulate a quantum circuit with $L$ gates scales as $L(\log L)^3$.Comment: 17 pages, 12 eps figure