Fault-Tolerant Quantum Computation with Local Gates

I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor gates are available, and present explicit constructions. In two or three dimensions, I also show how nearest-neighbor gates can give a threshold result. In all cases, I simply demonstrate that a threshold exists, and do not attempt to optimize the error correction circuit or determine the exact value of the threshold. The additional overhead due to the fault-tolerance in both space and time is polylogarithmic in the error rate per logical gate.Comment: 14 pages, LaTe

Improvement of stabilizer based entanglement distillation protocols by encoding operators

This paper presents a method for enumerating all encoding operators in the Clifford group for a given stabilizer. Furthermore, we classify encoding operators into the equivalence classes such that EDPs (Entanglement Distillation Protocol) constructed from encoding operators in the same equivalence class have the same performance. By this classification, for a given parameter, the number of candidates for good EDPs is significantly reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]] stabilizer codes. This EDP has a better performance than previously known EDPs over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding operators in the Clifford group, and fix the wrong classification of encoding operators in version

A Note on Linear Optics Gates by Post-Selection

Recently it was realized that linear optics and photo-detectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation (eLOQC) was to design a simple non-deterministic gate, which upon post-selection based on a measurement result implements a non-linear phase shift on one mode. Here a computational strategy is given for finding non-deterministic gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained.Comment: 14 pages. Minor changes for clarit

Toward fault-tolerant quantum computation without concatenation

It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own attractive features-improved accuracy threshold, local operations-have also been studied. By iteratively distilling a certain two-qubit entangled state it is shown how to perform an encoded Toffoli gate, important for universal computation, on CSS codes that are either unconcatenated or, for a range of very large block sizes, singly concatenated.Comment: 12 pages, 2 figures, replaced: new stuff on error models, numerical example for concatenation criteri

Encoding a qubit in an oscillator

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested by Phys. Rev. A, minor correction

A simple proof of the unconditional security of quantum key distribution

Quantum key distribution is the most well-known application of quantum cryptography. Previous proposed proofs of security of quantum key distribution contain various technical subtleties. Here, a conceptually simpler proof of security of quantum key distribution is presented. The new insight is the invariance of the error rate of a teleportation channel: We show that the error rate of a teleportation channel is independent of the signals being transmitted. This is because the non-trivial error patterns are permuted under teleportation. This new insight is combined with the recently proposed quantum to classical reduction theorem. Our result shows that assuming that Alice and Bob have fault-tolerant quantum computers, quantum key distribution can be made unconditionally secure over arbitrarily long distances even against the most general type of eavesdropping attacks and in the presence of all types of noises.Comment: 13 pages, extended abstract. Comments will be appreciate

Inorganic phosphate, arsenate, and vanadate enhance exonuclease transcript cleavage by RNA polymerase by 2000-fold

Inorganic Pi is involved in all major biochemical pathways. Here we describe a previously unreported activity of Pi. We show that Pi and its structural mimics, vanadate and arsenate, enhance nascent transcript cleavage by RNA polymerase (RNAP). They engage an Mg2+ ion in catalysis and activate an attacking water molecule. Pi, vanadate, and arsenate stimulate the intrinsic exonuclease activity of the enzyme nearly 2,000-fold at saturating concentrations of the reactant anions and Mg2+. This enhancement is comparable to that of specialized transcript cleavage protein factors Gre and TFIIS (3,000- to 4,000-fold). Unlike these protein factors, Pi and its analogs do not stimulate endonuclease transcript cleavage. Conversely, the protein factors only marginally enhance exonucleolytic cleavage. Pi thus complements cellular protein factors in assisting hydrolytic RNA cleavage by extending the repertoire of RNAP transcript degradation modes

Quantum Teleportation is a Universal Computational Primitive

We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell measurements, and GHZ states. We also present straightforward constructions of a wide variety of fault-tolerant quantum gates.Comment: 6 pages, REVTeX, 6 epsf figure

Efficient classical simulation of slightly entangled quantum computations

We present a scheme to efficiently simulate, with a classical computer, the dynamics of multipartite quantum systems on which the amount of entanglement (or of correlations in the case of mixed-state dynamics) is conveniently restricted. The evolution of a pure state of n qubits can be simulated by using computational resources that grow linearly in n and exponentially in the entanglement. We show that a pure-state quantum computation can only yield an exponential speed-up with respect to classical computations if the entanglement increases with the size n of the computation, and gives a lower bound on the required growth.Comment: 4 pages. Major changes. Significantly improved simulation schem

The extent of NGC 6822 revealed by its C stars population

Using the CFH12K camera, we apply the four band photometric technique to identify 904 carbon stars in an area 28' x 42' centered on NGC 6822. A few C stars, outside of this area were also discovered with the Las Campanas Swope Telescope. The NGC 6822 C star population has an average I of 19.26 mag leading to an average absolute I magnitude of -4.70 mag, a value essentially identical to the mean magnitude obtained for the C stars in IC 1613. Contrary to stars highlighting the optical image of NGC 6822, C stars are seen at large radial distances and trace a huge slightly elliptical halo which do not coincide with the huge HI cloud surrounding NGC6822. The previously unknown stellar component of NGC 6822 has a exponential scale length of 3.0' +/- 0.1' and can be traced to five scale lengths. The C/M ratio of NGC 6822 is evaluated to br 1.0 +/- 0.2.Comment: accepted, to be published in A