Related papers: Is there a problem with our Hamiltonians for quant…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to…
The first quantum technologies to solve computational problems that are beyond the capabilities of classical computers are likely to be devices that exploit characteristics inherent to a particular physical system, to tackle a bespoke…
The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum…
We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results…
A central task in quantum information processing is to characterize quantum processes. In the realm of optical quantum information processing, this amounts to characterizing the transformations of the mode creation and annihilation…
Linear oscillators contribute to most branches of contemporary quantum science. They have already successfully served as quantum sensors and memories, found applications in quantum communication, and hold promise for cluster-state-based…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
It is argued that the existing schemes of fault-tolerant quantum computation designed for discrete-time models and based on quantum error correction fail for continuous-time Hamiltonian models even with Markovian noise.
Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…
We analyze how complicated a linear optical component has to be if it is to perform one of a range of functions. Specifically, we devise an approach to evaluating the number of real parameters that must be specified in the device design or…
There is a pressing need for more accurate computational simulations of the opto-electronic properties of defects in materials to aid in the development of quantum sensing platforms. In this work, we explore how quantum computers could be…
We argue that the analog nature of quantum computing makes the usual design approach of constructing complicated logical operations from many simple gates inappropriate. Instead, we propose to design multi-spin quantum gates in which the…
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…
A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occur in a pairwise fashion. It is also…
BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this…