Ultrahigh Error Threshold for Surface Codes with Biased Noise

We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing dominates, is ubiquitous in many quantum architectures. In the limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor network decoder proposed by Bravyi, Suchara and Vargo. The threshold remains surprisingly large in the regime of realistic noise bias ratios, for example 28.2(2)% at a bias of 10. The performance is in fact at or near the hashing bound for all values of the bias. The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome bits associated with the dominant Z errors. Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes.Comment: 6 pages, 5 figures, comments welcome; v2 includes minor improvements to the numerical results, additional references, and an extended discussion; v3 published version (incorporating supplementary material into main body of paper

Some Remarks on the Question of Charge Densities in Stationary-Current-Carrying Conductors

Recently, some discussions arose as to the definition of charge and the value of the density of charge in stationary-current-carrying conductors. We stress that the problem of charge definition comes from a misunderstanding of the usual definition. We provide some theoretical elements which suggest that positive and negative charge densities are equal in the frame of the positive ions.Comment: 14 pages, TeX, macro newsym.tex include

Tailoring surface codes for highly biased noise

The surface code, with a simple modification, exhibits ultra-high error correction thresholds when the noise is biased towards dephasing. Here, we identify features of the surface code responsible for these ultra-high thresholds. We provide strong evidence that the threshold error rate of the surface code tracks the hashing bound exactly for all biases, and show how to exploit these features to achieve significant improvement in logical failure rate. First, we consider the infinite bias limit, meaning pure dephasing. We prove that the error threshold of the modified surface code for pure dephasing noise is $50\%$, i.e., that all qubits are fully dephased, and this threshold can be achieved by a polynomial time decoding algorithm. We demonstrate that the sub-threshold behavior of the code depends critically on the precise shape and boundary conditions of the code. That is, for rectangular surface codes with standard rough/smooth open boundaries, it is controlled by the parameter $g=\gcd(j,k)$, where $j$ and $k$ are dimensions of the surface code lattice. We demonstrate a significant improvement in logical failure rate with pure dephasing for co-prime codes that have $g=1$, and closely-related rotated codes, which have a modified boundary. The effect is dramatic: the same logical failure rate achievable with a square surface code and $n$ physical qubits can be obtained with a co-prime or rotated surface code using only $O(\sqrt{n})$ physical qubits. Finally, we use approximate maximum likelihood decoding to demonstrate that this improvement persists for a general Pauli noise biased towards dephasing. In particular, comparing with a square surface code, we observe a significant improvement in logical failure rate against biased noise using a rotated surface code with approximately half the number of physical qubits.Comment: 18+4 pages, 24 figures; v2 includes additional coauthor (ASD) and new results on the performance of surface codes in the finite-bias regime, obtained with beveled surface codes and an improved tensor network decoder; v3 published versio

A molecular perspective on the limits of life: Enzymes under pressure

From a purely operational standpoint, the existence of microbes that can grow under extreme conditions, or "extremophiles", leads to the question of how the molecules making up these microbes can maintain both their structure and function. While microbes that live under extremes of temperature have been heavily studied, those that live under extremes of pressure have been neglected, in part due to the difficulty of collecting samples and performing experiments under the ambient conditions of the microbe. However, thermodynamic arguments imply that the effects of pressure might lead to different organismal solutions than from the effects of temperature. Observationally, some of these solutions might be in the condensed matter properties of the intracellular milieu in addition to genetic modifications of the macromolecules or repair mechanisms for the macromolecules. Here, the effects of pressure on enzymes, which are proteins essential for the growth and reproduction of an organism, and some adaptations against these effects are reviewed and amplified by the results from molecular dynamics simulations. The aim is to provide biological background for soft matter studies of these systems under pressure.Comment: 16 pages, 8 figure

Measurement-based quantum computation in a 2D phase of matter

Recently it has been shown that the non-local correlations needed for measurement based quantum computation (MBQC) can be revealed in the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model involving nearest neighbor spin-3/2 interactions on a honeycomb lattice. This state is not singular but resides in the disordered phase of ground states of a large family of Hamiltonians characterized by short-range-correlated valence bond solid states. By applying local filtering and adaptive single particle measurements we show that most states in the disordered phase can be reduced to a graph of correlated qubits that is a scalable resource for MBQC. At the transition between the disordered and Neel ordered phases we find a transition from universal to non-universal states as witnessed by the scaling of percolation in the reduced graph state.Comment: 8 pages, 6 figures, comments welcome. v2: published versio

Entanglement Measures for Single- and Multi-Reference Correlation Effects

Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multi-reference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.Comment: 14 pages, 4 figure

Coupled cluster calculations of ground and excited states of nuclei

The standard and renormalized coupled cluster methods with singles, doubles, and noniterative triples and their generalizations to excited states, based on the equation of motion coupled cluster approach, are applied to the He-4 and O-16 nuclei. A comparison of coupled cluster results with the results of the exact diagonalization of the Hamiltonian in the same model space shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei. The bulk of the correlation effects is obtained at the coupled cluster singles and doubles level. Triples, treated noniteratively, provide the virtually exact description

p75 Neurotrophin receptor expression defines a population of BDNF-responsive neurogenic precursor cells

Although our understanding of adult neurogenesis has increased dramatically over the last decade, confusion still exists regarding both the identity of the stem cell responsible for neuron production and the mechanisms that regulate its activity. Here we show, using flow cytometry, that a small population of cells (0.3%) within the stem cell niche of the rat subventricular zone (SVZ) expresses the p75 neurotrophin receptor (p75(NTR)) and that these cells are responsible for neuron production in both newborn and adult animals. In the adult, the p75(NTR)-positive population contains all of the neurosphere-producing precursor cells, whereas in the newborn many of the precursor cells are p75(NTR) negative. However, at both ages, only the neurospheres derived from p75(NTR)-positive cells are neurogenic. We also show that neuron production from p75(NTR)-positive but not p75(NTR)-negative precursors is greatly enhanced after treatment with brain-derived neurotrophic factor (BDNF) or nerve growth factor. This effect appears to be mediated specifically by p75(NTR), because precursor cells from p75(NTR)-deficient mice show a 70% reduction in their neurogenic potential in vitro and fail to respond to BDNF treatment. Furthermore, adult p75(NTR)-deficient mice have significantly reduced numbers of PSA-NCAM ( polysialylated neural cell adhesion molecule)-positive SVZ neuroblasts in vivo and a lower olfactory bulb weight. Thus, p75(NTR) defines a discrete population of highly proliferative SVZ precursor cells that are able to respond to neurotrophin activation by increasing neuroblast generation, making this pathway the most likely mechanism for the increased neurogenesis that accompanies raised BDNF levels in a variety of disease and behavioral situations

A Classical Bound on Quantum Entropy

A classical upper bound for quantum entropy is identified and illustrated, $0\leq S_q \leq \ln (e \sigma^2 / 2\hbar)$, involving the variance $\sigma^2$ in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Renyi.Comment: Latex2e, 7 pages, publication versio

Dzyaloshinskii-Moriya interaction and spin re-orientation transition in the frustrated kagome lattice antiferromagnet

Magnetization, specific heat, and neutron scattering measurements were performed to study a magnetic transition in jarosite, a spin-5/2 kagome lattice antiferromagnet. When a magnetic field is applied perpendicular to the kagome plane, magnetizations in the ordered state show a sudden increase at a critical field H_c, indicative of the transition from antiferromagnetic to ferromagnetic states. This sudden increase arises as the spins on alternate kagome planes rotate 180 degrees to ferromagnetically align the canted moments along the field direction. The canted moment on a single kagome plane is a result of the Dzyaloshinskii-Moriya interaction. For H < H_c, the weak ferromagnetic interlayer coupling forces the spins to align in such an arrangement that the canted components on any two adjacent layers are equal and opposite, yielding a zero net magnetic moment. For H > H_c, the Zeeman energy overcomes the interlayer coupling causing the spins on the alternate layers to rotate, aligning the canted moments along the field direction. Neutron scattering measurements provide the first direct evidence of this 180-degree spin rotation at the transition.Comment: 13 pages, 15 figure