相关论文: Complexity of multivariate Feynman-Kac path integr…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
Quantum measurement problem is still unconsensus since it has existed many years and inspired a large of literature in physics and philosophy. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
A (Quantum) Random Access Code ((Q)RAC) is a scheme that encodes $n$ bits into $m$ (qu)bits such that any of the $n$ bits can be recovered with a worst case probability $p>\frac{1}{2}$. Such a code is denoted by the triple $(n,m,p)$. It is…
We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \log^{2 +…
In this work, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware. In particular, some steps of the implementation,…
While quantum computers hold the promise of significant computational speedups, the limited size of early quantum machines motivates the study of space-bounded quantum computation. We relate the quantum space complexity of computing a…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain and Monrad [Ann. Probab. 11 (1983)…
We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…
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…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
For a long time it is well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grows polynomially both in the dimension and in the…
The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport…
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems…
In this paper we study the quantum learnability of constant-depth classical circuits under the uniform distribution and in the distribution-independent framework of PAC learning. In order to attain our results, we establish connections…
I consider the case of two interacting scalar fields, \phi and \psi, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…