Anisotropic Landau-Lifshitz-Gilbert models of dissipation in qubits

We derive a microscopic model for dissipative dynamics in a system of mutually interacting qubits coupled to a thermal bath that generalizes the dissipative model of Landau-Lifshitz-Gilbert to the case of anisotropic bath couplings. We show that the dissipation acts to bias the quantum trajectories towards a reduced phase space. This model applies to a system of superconducting flux qubits whose coupling to the environment is necessarily anisotropic. We study the model in the context of the D-Wave computing device and show that the form of environmental coupling in this case produces dynamics that are closely related to several models proposed on phenomenological grounds

Trajectory-resolved Weiss fields for quantum spin dynamics

We explore the dynamics of quantum spin systems in two and three dimensions using an exact mapping to classical stochastic processes. In recent work, we explored the effectiveness of sampling around the mean-field evolution as determined by a stochastically averaged Weiss field. Here, we show that this approach can be significantly extended by sampling around the instantaneous Weiss field associated with each stochastic trajectory taken separately. This trajectory-resolved approach incorporates sample to sample fluctuations and allows for longer simulation times. We demonstrate the utility of this approach for quenches in the two-dimensional and three-dimensional quantum Ising model. We show that the method is particularly advantageous in situations where the average Weiss field vanishes, but the trajectory-resolved Weiss fields are nonzero. We discuss the connection to the gauge-P phase-space approach, where the trajectory-resolved Weiss field can be interpreted as a gauge degree of freedom

Phase transitions in the classical simulability of open quantum systems

We introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling to the environment. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. This is the Hamiltonian open system counterpart of the saturation in entanglement found in random circuits with projective or weak measurements. If a system is open, there is a limit to the advantage in simulating its behaviour on a quantum computer, even when that evolution harbours important quantum effects. Moreover, if a quantum simulator is in this phase, it cannot simulate with quantum advantage

Magnetic hard-direction ordering in anisotropic Kondo systems

We present a generic mechanism that explains why many Kondo materials show magnetic ordering along directions that are not favoured by the crystal-field anisotropy. Using a renormalization-group (RG) analysis of single impurity Kondo models with single-ion anisotropy, we demonstrate that strong fluctuations above the Kondo temperature drive a moment re-orientation over a wide range of parameters, e.g. for different spin values $S$ and number of Kondo channels $N$. In tetragonal systems this can happen for both easy-plane or easy axis anisotropy. The characteristic crossing of magnetic susceptibilities is not an artefact of the weak-coupling RG treatment but can be reproduced in brute-force perturbation theory. Employing numerical renormalization group (NRG), we show that for an under-screened moment ($S=1$, $N=1$) with easy-plane anisotropy, a crossing of magnetic susceptibilities can also occur in the strong-coupling regime (below the Kondo temperature). This suggests that collective magnetic ordering of such under-screened moments would develop along the magnetic hard axis

Compact neural networks based on the multiscale entanglement renormalization Ansatz

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for the fully connected layers in a convolutional neural network and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA layers with 14000 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers, scaling like O(N)

Deletions of the derivative chromosome 9 occur at the time of the Philadelphia translocation and provide a powerful and independent prognostic indicator in chronic myeloid leukemia

Chronic myeloid leukemia (CML) is characterized by formation of the BCR-ABL fusion gene, usually as a consequence of the Philadelphia (Ph) translocation between chromosomes 9 and 22. Large deletions on the derivative chromosome 9 have recently been reported, but it was unclear whether deletions arose during disease progression or at the time of the Ph translocation. Fluorescence in situ hybridization (FISH) analysis was used to assess the deletion status of 253 patients with CML. The strength of deletion status as a prognostic indicator was then compared to the Sokal and Hasford scoring systems. The frequency of deletions was similar at diagnosis and after disease progression but was significantly increased in patients with variant Ph translocations. In patients with a deletion, all Ph+ metaphases carried the deletion. The median survival of patients with and without deletions was 38 months and 88 months, respectively (P = .0001). By contrast the survival difference between Sokal or Hasford high-risk and non-high-risk patients was of only borderline significance (P = .057 and P = .034). The results indicate that deletions occur at the time of the Ph translocation. An apparently simple reciprocal translocation may therefore result in considerable genetic heterogeneity ab initio, a concept that is likely to apply to other malignancies associated with translocations. Deletion status is also a powerful and independent prognostic factor for patients with CML. The prognostic significance of deletion status should now be studied prospectively and, if confirmed, should be incorporated into management decisions and the analysis of clinical trials. (C) 2001 by The American Society of Hematology

Non-linear quantum critical transport and the Schwinger Mechanism

Scaling arguments imply that quantum critical points exhibit universal non-linear responses to external probes. We investigate the origins of such non-linearities in transport, which is especially problematic since the system is necessarily driven far from equilibrium. We argue that for a wide class of systems the new ingredient that enters is the Schwinger mechanism--the production of carriers from the vacuum by the applied field-- which is then balanced against a scattering rate which is itself set by the field. We show by explicit computation how this works for the case of the symmetric superfluid-Mott insulator transition of bosons

Nonlinear quantum critical transport and the Schwinger mechanism for a superfluid-Mott-insulator transition of bosons

Scaling arguments imply that quantum-critical points exhibit universal nonlinear responses to external probes. We investigate the origins of such nonlinearities in transport, which is especially problematic since the system is necessarily driven far from equilibrium. We argue that for a wide class of systems the new ingredient that enters is the Schwinger mechanism-the production of carriers from the vacuum by the applied field-which is then balanced against a scattering rate that is itself set by the field. We show by explicit computation how this works for the case of the symmetric superfluid-Mott insulator transition of bosons