Density-matrix simulation of small surface codes under current and projected experimental noise

We present a full density-matrix simulation of the quantum memory and computing performance of the distance-3 logical qubit Surface-17, following a recently proposed quantum circuit and using experimental error parameters for transmon qubits in a planar circuit QED architecture. We use this simulation to optimize components of the QEC scheme (e.g., trading off stabilizer measurement infidelity for reduced cycle time) and to investigate the benefits of feedback harnessing the fundamental asymmetry of relaxation-dominated error in the constituent transmons. A lower-order approximate calculation extends these predictions to the distance-$5$ Surface-49. These results clearly indicate error rates below the fault-tolerance threshold of surface code, and the potential for Surface-17 to perform beyond the break-even point of quantum memory. At state-of-the-art qubit relaxation times and readout speeds, Surface-49 could surpass the break-even point of computation.Comment: 10 pages + 8 pages appendix, 12 figure

Majorana-based fermionic quantum computation

Because Majorana zero modes store quantum information non-locally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majoranas to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majoranas for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, and the simulation of Trotterized Hubbard Hamiltonian in $\mathcal{O}(1)$ time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates.Comment: 4 pages + 4 page appendix, 4 figures, 2 table

Adaptive weight estimator for quantum error correction

Quantum error correction of a surface code or repetition code requires the pairwise matching of error events in a space-time graph of qubit measurements, such that the total weight of the matching is minimized. The input weights follow from a physical model of the error processes that affect the qubits. This approach becomes problematic if the system has sources of error that change over time. Here we show how the weights can be determined from the measured data in the absence of an error model. The resulting adaptive decoder performs well in a time-dependent environment, provided that the characteristic time scale $\tau_{\mathrm{env}}$ of the variations is greater than $\delta t/\bar{p}$, with $\delta t$ the duration of one error-correction cycle and $\bar{p}$ the typical error probability per qubit in one cycle.Comment: 5 pages, 4 figure

Low-cost error mitigation by symmetry verification

We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a zero-cost post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost their mitigation against different error channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen molecule (using a classical density-matrix simulator), finding up to an order of magnitude reduction of the error in obtaining the ground state dissociation curve.Comment: Published versio

Twisted Fermi surface of a thin-film Weyl semimetal

The Fermi surface of a conventional two-dimensional electron gas is equivalent to a circle, up to smooth deformations that preserve the orientation of the equi-energy contour. Here we show that a Weyl semimetal confined to a thin film with an in-plane magnetization and broken spatial inversion symmetry can have a topologically distinct Fermi surface that is twisted into a \mbox{figure-8} $-$ opposite orientations are coupled at a crossing which is protected up to an exponentially small gap. The twisted spectral response to a perpendicular magnetic field $B$ is distinct from that of a deformed Fermi circle, because the two lobes of a \mbox{figure-8} cyclotron orbit give opposite contributions to the Aharonov-Bohm phase. The magnetic edge channels come in two counterpropagating types, a wide channel of width $\beta l_m^2\propto 1/B$ and a narrow channel of width $l_m\propto 1/\sqrt B$ (with $l_m=\sqrt{\hbar/eB}$ the magnetic length and $\beta$ the momentum separation of the Weyl points). Only one of the two is transmitted into a metallic contact, providing unique magnetotransport signatures.Comment: V4: 10 pages, 14 figures. Added figure and discussion about "uncrossing deformations" of oriented contours, plus minor corrections. Published in NJ

A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe

Swift observations of the 2006 outburst of the recurrent nova RS Ophiuchi: II. 1D hydrodynamical models of wind driven shocks

Following the early Swift X-ray observations of the latest outburst of the recurrent nova RS Ophiuchi in February 2006 (Paper I), we present new 1D hydrodynamical models of the system which take into account all three phases of the remnant evolution. The models suggest a novel way of modelling the system by treating the outburst as a sudden increase then decrease in wind mass-loss rate and velocity. The differences between this wind model and previous Primakoff-type simulations are described. A more complex structure, even in 1D, is revealed through the presence of both forward and reverse shocks, with a separating contact discontinuity. The effects of radiative cooling are investigated and key outburst parameters such as mass-loss rate, ejecta velocity and mass are varied. The shock velocities as a function of time are compared to the ones derived in Paper I. We show how the manner in which the matter is ejected controls the evolution of the shock and that for a well-cooled remnant, the shock deceleration rate depends on the amount of energy that is radiated away.Comment: 9 pages, 5 figure

An Atlas of Computed Equivalent Widths of Quasar Broad Emission Lines

We present graphically the results of several thousand photoionization calculations of broad emission line clouds in quasars, spanning seven orders of magnitude in hydrogen ionizing flux and particle density. The equivalent widths of 42 quasar emission lines are presented as contours in the particle density - ionizing flux plane for a typical incident continuum shape, solar chemical abundances, and cloud column density of $N(H) = 10^{23} cm^{-2}$. Results are similarly given for a small subset of emission lines for two other column densities ($10^{22} cm^{-2}$ and $10^{24} cm^{-2}$), five other incident continuum shapes, and a gas metallicity of 5 \Zsun. These graphs should prove useful in the analysis of quasar emission line data and in the detailed modeling of quasar broad emission line regions. The digital results of these emission line grids and many more are available over the Internet.Comment: 16 pages, LaTeX (AASTeX aaspp4.sty); to appear in the 1997 ApJS: full contents of the 9 photoionization grids presented in this paper may be found at http://www.pa.uky.edu/~korista/grids/grids.htm