Related papers: Minimum quantum degrees with Maya diagrams
Graph partitioning has many applications in powersystems from decentralized state estimation to parallel simulation. Focusing on parallel simulation, optimal grid partitioning minimizes the idle time caused by different simulation times for…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…
In this article, we discuss the effect of the zero point quantum fluctuations to improve the results of the minimal field theory which has been applied to study %SMG the skyrmions in the quantum Hall systems. Our calculation which is based…
Several mathematical problems can be modeled as a search in a database. An example is the problem of finding the minimum of a function. Quantum algorithms for solving this problem have been proposed and all of them use the quantum search…
Understanding and predicting the properties of solid-state materials from first-principles has been a great challenge for decades. Owing to the recent advances in quantum technologies, quantum computations offer a promising way to achieve…
We provide a simple proof for the necessity of conditions for discriminating with minimum error between a known set of quantum states.
Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum…
We obtain sufficient conditions for conservativity of minimal quantum dynamical semigroup by modifying and extending the method used in [Chebotarev and Fagnola, J. Funct. Anal. 153(1998), 382-404]. Our criterion for conservativity can be…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein {\it et al.} [Phys. Rev. A \textbf{73}, 012320 (2006)]. The conjecture states…
QMA and QCMA are possible quantum analogues of the complexity class NP. In QCMA the verifier is a quantum program and the proof is classical. In contrast, in QMA the proof is also a quantum state. We show that two known QMA-complete…
Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much…
One of the most severe bottlenecks to reach high-precision predictions in QFT is the calculation of multiloop multileg Feynman integrals. Several new strategies have been proposed in the last years, allowing impressive results with deep…
We conducted quantum simulations of strongly correlated systems using the quantum flow (QFlow) approach, which enables sampling large sub-spaces of the Hilbert space through coupled eigenvalue problems in reduced dimensionality active…
We introduce diagrammatic differentiation for tensor calculus by generalising the dual number construction from rigs to monoidal categories. Applying this to ZX diagrams, we show how to calculate diagrammatically the gradient of a linear…
We give a realization of crystal graphs for basic representations of the quantum affine algebra U_q(C_n^{(1)}) using combinatorics of Young walls. The notion of splitting blocks plays a crucial role in the construction of crystal graphs.
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…