Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information

The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hope for eventually realizing practical quantum computers. In principle, a system that implements QEC can actually pass a "break-even" point and preserve quantum information for longer than the lifetime of its constituent parts. Reaching the break-even point, however, has thus far remained an outstanding and challenging goal. Several previous works have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers, photons, and superconducting transmons. However, these works primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to extend the lifetime of quantum information over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of coherent states, or cat states of a superconducting resonator. Moreover, the experiment implements a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode, and correct. As measured by full process tomography, the enhanced lifetime of the encoded information is 320 microseconds without any post-selection. This is 20 times greater than that of the system's transmon, over twice as long as an uncorrected logical encoding, and 10% longer than the highest quality element of the system (the resonator's 0, 1 Fock states). Our results illustrate the power of novel, hardware efficient qubit encodings over traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming the basic concepts to exploring the metrics that drive system performance and the challenges in implementing a fault-tolerant system

Performance and structure of single-mode bosonic codes

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce new codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat/binomial/GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multi-qubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a new multi-qudit code.Comment: 34 pages, 11 figures, 4 tables. v3: published version. See related talk at https://absuploads.aps.org/presentation.cfm?pid=1351

Resonant Transfer and Excitation in Li-Like F Colliding with H₂

We have measured coincidences between x rays and projectiles that have captured one electron in F6+ + H2 collisions at projectile energies between 15 and 33 MeV. The cross sections for capture and simultaneous x-ray emission as a function of projectile energy show clear structures. Indications of an unexpectedly high population of high-n states predominantly formed by resonant transfer and excitation (RTE) were found. Above the Kln (n\u3e1) RTE resonance energies another maximum was observed

Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling

We present the effective low-energy theory for interacting 1D quantum wires subject to Rashba spin-orbit coupling. Under a one-loop renormalization group scheme including all allowed interaction processes for not too weak Rashba coupling, we show that electron-electron backscattering is an irrelevant perturbation. Therefore no gap arises and electronic transport is described by a modified Luttinger liquid theory. As an application of the theory, we discuss the RKKY interaction between two magnetic impurities. Interactions are shown to induce a slower power-law decay of the RKKY range function than the usual 1D noninteracting $\cos(2k_F x)/|x|$ law. Moreover, in the noninteracting Rashba wire, the spin-orbit coupling causes a twisted (anisotropic) range function with several different spatial oscillation periods. In the interacting case, we show that one special oscillation period leads to the slowest decay, and therefore dominates the RKKY interaction for large separation.Comment: 11 pages, 1 figure; v2: minor changes, published versio

Analysis of the construction of the hightemperature gas infrared radiator with the use of virtual prototyping

Method of virtual prototyping with the following mathematical modeling was used to simulate the heat-mass exchange and combustion during the operation of high-temperature gas infrared radiators, and to find optimal technical solutions for its design. The most authoritative and approved software product Ansys Multiphysics was used. The results of the mathematical modeling of heat and mass transfer in a turbulent reaction medium with combustion reproduce the experimental data produced by a measurement in real operating conditions of the gas-fired infrared heat emitter. The temperature distribution along the height of the ceramic nozzle was established. Obtained results enable estimation of the ignition and combustion zones