Related papers: Quantum Period Query Proves NP in BQP
Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.
We propose a new method for evaluating NISQ devices. This paper has three distinct parts. First, we present a new quantum algorithm that solves a two hundred year old problem of finding quadratic nonresidues (QNR) in polynomial time. We…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…
We study the non equilibrium time evolution of an integrable field theory in 1+1 dimensions after a sudden variation of a global parameter of the Hamiltonian. For a class of quenches defined in the text, we compute the long times limit of…
We show that combining two different hypothetical enhancements to quantum computation---namely, quantum advice and non-collapsing measurements---would let a quantum computer solve any decision problem whatsoever in polynomial time, even…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
We show how conformal invariance predicts the functional form of two-point correlators in one-dimensional periodic quantum systems. Numerical evidence for this functional form in a wide class of models --- including long-ranged ones --- is…
We study quantum period finding algorithms such as Simon and Shor (and its variants Eker{\aa}-H{\aa}stad and Mosca-Ekert). For a periodic function $f$ these algorithms produce -- via some quantum embedding of $f$ -- a quantum superposition…
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…
This paper is withdrawn due to some gaps in the proof
Quantum mechanical wave functions have phases. These phases either initial or acquired during time evolution usually do not enter the final expressions for observable physical quantities. Nevertheless in many cases the observable physical…
We review the implementation of two QKD protocols (BB84 and B92) keeping in mind that their implementations do not easily satisfy the requirement of use of single photons. We argue that current models do not take into account issues raised…
Quantum no-Hiding theorem, first proposed by Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)], was verified experimentally by Samal et al. [Phys. Rev. Lett. 186, 080401 (2011)] using NMR quantum processor. Till then, this…
Perturbative quantum field theories frequently feature rational linear combinations of multiple zeta values (periods). In massless \phi^4-theory we show that the periods originate from certain `primitive' vacuum graphs. Graphs with vertex…
In this paper we consider the Hardy-Lorentz spaces $H^{p,q}(R^n)$, with $0<p\le 1$, $0<q\le \infty$. We discuss the atomic decomposition of the elements in these spaces, their interpolation properties, and the behavior of singular integrals…
A wave function of the $N$-component KP Hierarchy with continuous flows determined by an invertible matrix $H$ is constructed from the choice of an $MN$-dimensional space of finitely-supported vector distributions. This wave function is…
Possible interpretations of the HERA large-Q^2 data are reviewed briefly. The possibility of statistical fluctuations cannot be ruled out, and it seems premature to argue that the H1 and ZEUS anomalies are incompatible. The data cannot be…
In the recent breakthrough paper by Barbulescu, Gaudry, Joux and Thom{\'e}, a quasi-polynomial time algorithm (QPA) is proposed for the discrete logarithm problem over finite fields of small characteristic. The time complexity analysis of…
A cosmological model with two global internal times shows that time reparameterization invariance, and therefore covariance, is not guaranteed by deparameterization. In particular, it is impossible to derive proper-time effective equations…