Related papers: Fractalizing quantum codes
We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for…
Motivated by the inadequacy of conducting atomistic simulations of crack propagation using static boundary conditions that do not reflect the movement of the crack tip, we extend Sinclair's flexible boundary condition algorithm [Philos.…
A self-correcting quantum memory is a type of quantum error correcting code that can correct errors passively through cooling. A major open question in the field is whether self-correcting quantum memories can exist in 3D. In this work, we…
We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which cloning offers an advantage which cannot be matched by any approach that does not resort to it. In these quantum computations, we need…
In this paper, a new framework for one-dimensional contour extraction from discrete two-dimensional data sets is presented. Contour extraction is important in many scientific fields such as digital image processing, computer vision, pattern…
Simulation has become the evaluation method of choice for many areas of distributing computing research. However, most existing simulation packages have several limitations on the size and complexity of the system being modeled. Fine…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
In the presence of dynamic insertions and deletions into a partially reconfigurable FPGA, fragmentation is unavoidable. This poses the challenge of developing efficient approaches to dynamic defragmentation and reallocation. One key aspect…
The field of quantum computing is at an exciting time where we are constructing novel hardware, evaluating algorithms, and finding out what works best. As qubit technology grows and matures, we need to be ready to design and program larger…
Quantum entanglement, crucial for understanding quantum many-body systems and quantum gravity, is commonly assessed through various measures such as von Neumann entropy, mutual information, and entanglement contour, each with its inherent…
We study quantum-fluctuation-driven fractionalized phases in the vicinity of altermagnetic order. First, the long-range magnetic orders in the vicinity of collinear altermagnetism are identified; these feature a non-coplanar "orbital…
This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated…
We construct explicit examples of microscopic models that stabilize a variety of fractionalized phases of strongly correlated systems in spatial dimension bigger than one, and in zero external magnetic field. These include models of charge…
Exploiting quantum properties to outperform classical ways of information-processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
We discussed hierarchies and rescaling rule of the self similar transformations in Ising models, and define a fractal dimension of an ordered cluster, which minimum corresponds to a fixed point of the transformations. By the fractal…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
An algorithm for calculating generalized fractal dimension of a time series using the general information function is presented. The algorithm is based on a strings sort technique and requires $O(N \log_2 N)$ computations. A rough estimate…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…