Stabilizing distinguishable qubits against spontaneous decay by detected-jump correcting quantum codes

A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an embedded quantum code and exploiting the classical information available about which qubit has been affected by the environment. They are immediately relevant for quantum computation and information processing using arrays of trapped ions or nuclear spins. Interesting relations between these quantum codes and basic notions of design theory are established

Automatic Quantum Error Correction

Criteria are given by which dissipative evolution can transfer populations and coherences between quantum subspaces, without a loss of coherence. This results in a form of quantum error correction that is implemented by the joint evolution of a system and a cold bath. It requires no external intervention and, in principal, no ancilla. An example of a system that protects a qubit against spin-flip errors is proposed. It consists of three spin 1/2 magnetic particles and three modes of a resonator. The qubit is the triple quantum coherence of the spins, and the photons act as ancilla.Comment: 16 pages 12 fig LaTex uses multicol, graphicx expanded version of letter submitted to Phys Rev Let

Quantum Logical States and Operators for Josephson-like Systems

We give a formal algebraic description of Josephson-type quantum dynamical systems, i.e., Hamiltonian systems with a cos theta-like potential term. The two-boson Heisenberg algebra plays for such systems the role that the h(1) algebra does for the harmonic oscillator. A single Josephson junction is selected as a representative of Josephson systems. We construct both logical states (codewords) and logical (gate) operators in the superconductive regime. The codewords are the even and odd coherent states of the two-boson algebra: they are shift-resistant and robust, due to squeezing. The logical operators acting on the qubit codewords are expressed in terms of operators in the enveloping of the two-boson algebra. Such a scheme appears to be relevant for quantum information applications.Comment: 12 pages in RevTex. In press, Journal of Physics A/Letter

Approximate quantum error correction for generalized amplitude damping errors

We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes. The performance of such error-correcting schemes is quantified by means of the entanglement fidelity as a function of the damping probability and the non-zero environmental temperature. The recovery scheme employed throughout our work applies, in principle, to arbitrary quantum codes and is the analogue of the perfect Knill-Laflamme recovery scheme adapted to the approximate quantum error correction framework for the GAD error model. We also analytically recover and/or clarify some previously known numerical results in the limiting case of vanishing temperature of the environment, the well-known traditional amplitude damping channel. In addition, our study suggests that degenerate stabilizer codes and self-complementary nonadditive codes are especially suitable for the error correction of the GAD noise model. Finally, comparing the properly normalized entanglement fidelities of the best performant stabilizer and nonadditive codes characterized by the same length, we show that nonadditive codes outperform stabilizer codes not only in terms of encoded dimension but also in terms of entanglement fidelity.Comment: 44 pages, 8 figures, improved v