相关论文: On the uncomputability of the spectral gap

The aim of this article is to study (additively) indecomposable algebraic integers $\mathcal O_K$ of biquadratic number fields $K$ and universal totally positive quadratic forms with coefficients in $\mathcal O_K$. There are given…

We present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic…

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…

Quantum resources outperform classical ones for certain communication and computational tasks. Remarkably, in some cases, the quantum advantage cannot be improved using hypothetical postquantum resources. A class of tasks with this property…

Past studies of fractional quantum Hall systems have found that the charge gap dominates the neutral gap for all relevant parameter choices. We report a wide-ranging proof that this domination is in fact a universal property of any…

We classify holomorphic Pfaff systems (possibly non locally decomposable) on certain Hopf manifolds. As consequence, we prove some integrability results. We also prove that any holomorphic distribution on a general (non-resonance) Hopf…

We present a scheme to study non-abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error…

While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…

Demonstrating a quantum computational speedup is a crucial milestone for near-term quantum technology. Recently, quantum simulation architectures have been proposed that have the potential to show such a quantum advantage, based on commonly…

In 2001 all-optical quantum computing became feasible with the discovery that scalable quantum computing is possible using only single photon sources, linear optical elements, and single photon detectors. Although it was in principle…

We review the paper 'Integrability of the S-Matrix vs Integrability of the Hamiltonian' by C. Jung and T.H. Seligman (Phys. Rep. 285, 77-141 (1997)). This paper deals with the connection between the integrability of the scattering matrix…

In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of…

In relativistic field theories, the mass spectrum is given by the difference between the energy of the vacuum and the excited states. Near the continuum limit, the cancellation between these two values leads to loss of precision. We propose…

We show that the universal theory of the hyperfinite II$_1$ factor is not computable. The proof uses the recent result that MIP*=RE. Combined with an earlier observation of the authors, this yields a proof that the Connes Embedding Problem…

A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.

The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…

The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better…

This paper shows that universal quantum computers possess decoherent histories in which complex adaptive systems evolve with high probability.

For all convex co-compact hyperbolic surfaces, we prove the existence of an essential spectral gap, that is a strip beyond the unitarity axis in which the Selberg zeta function has only finitely many zeroes. We make no assumption on the…

A four-wave mixing Hamiltonian system on the classical as well as on the quantum level is investigated. In the classical case, if one assumes the frequency resonance condition of the form $\omega_0 -\omega_1 +\omega_2 -\omega_3=0$, this…