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

Error Analysis For Encoding A Qubit In An Oscillator

In the paper titled "Encoding A Qubit In An Oscillator" Gottesman, Kitaev, and Preskill [quant-ph/0008040] described a method to encode a qubit in the continuous Hilbert space of an oscillator's position and momentum variables. This encoding provides a natural error correction scheme that can correct errors due to small shifts of the position or momentum wave functions (i.e., use of the displacement operator). We present bounds on the size of correctable shift errors when both qubit and ancilla states may contain errors. We then use these bounds to constrain the quality of input qubit and ancilla states.Comment: 5 pages, 8 figures, submitted to Physical Review

Optical pumping of quantum dot nuclear spins

An all-optical scheme to polarize nuclear spins in a single quantum dot is analyzed. The hyperfine interaction with randomly oriented nuclear spins presents a fundamental limit for electron spin coherence in a quantum dot; by cooling the nuclear spins, this decoherence mechanism could be suppressed. The proposed scheme is inspired by laser cooling methods of atomic physics and implements a "controlled Overhauser effect" in a zero-dimensional structure

Experimental magic state distillation for fault-tolerant quantum computing

Any physical quantum device for quantum information processing is subject to errors in implementation. In order to be reliable and efficient, quantum computers will need error correcting or error avoiding methods. Fault-tolerance achieved through quantum error correction will be an integral part of quantum computers. Of the many methods that have been discovered to implement it, a highly successful approach has been to use transversal gates and specific initial states. A critical element for its implementation is the availability of high-fidelity initial states such as |0> and the Magic State. Here we report an experiment, performed in a nuclear magnetic resonance (NMR) quantum processor, showing sufficient quantum control to improve the fidelity of imperfect initial magic states by distilling five of them into one with higher fidelity

Quantum Computing with Very Noisy Devices

In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices called ``gates'' that tend to destroy the fragile quantum states needed for computation. The goal of fault-tolerant quantum computing is to compute accurately even when gates have a high probability of error each time they are used. Here we give evidence that accurate quantum computing is possible with error probabilities above 3% per gate, which is significantly higher than what was previously thought possible. However, the resources required for computing at such high error probabilities are excessive. Fortunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today's digital computers, we could implement non-trivial quantum computations at error probabilities as high as 1% per gate.Comment: 47 page

Comparison of LOQC C-sign gates with ancilla inefficiency and an improvement to functionality under these conditions

We compare three proposals for non-deterministic C-sign gates implemented using linear optics and conditional measurements with non-ideal ancilla mode production and detection. The simplified KLM gate [Ralph et al, Phys.Rev.A {\bf 65}, 012314 (2001)] appears to be the most resilient under these conditions. We also find that the operation of this gate can be improved by adjusting the beamsplitter ratios to compensate to some extent for the effects of the imperfect ancilla.Comment: to appear in PR

Upper bounds on success probabilities in linear optics

We develop an abstract way of defining linear-optics networks designed to perform quantum information tasks such as quantum gates. We will be mainly concerned with the nonlinear sign shift gate, but it will become obvious that all other gates can be treated in a similar manner. The abstract scheme is extremely well suited for analytical as well as numerical investigations since it reduces the number of parameters for a general setting. With that we show numerically and partially analytically for a wide class of states that the success probability of generating a nonlinear sign shift gate does not exceed 1/4 which to our knowledge is the strongest bound to date.Comment: 8 pages, typeset using RevTex4, 5 EPS figure

Introduction to Quantum Error Correction

In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied for fault tolerance. Considering the capabilities of currently available quantum technology, the requirements appear daunting. But the idea of ``subsystems'' shows that these requirements can be met in many different, and often unexpected ways.Comment: 44 pages, to appear in LA Science. Hyperlinked PDF at http://www.c3.lanl.gov/~knill/qip/ecprhtml/ecprpdf.pdf, HTML at http://www.c3.lanl.gov/~knill/qip/ecprhtm