Quantum Measurement, Complexity and Discrete Physics

Quantum Discrete Fourier Transform with Classical Output for Signal Processing

Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms with classical output (1D QDFT and 2D QDFT) are presented in this paper. And quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, QDFT has two advantages at least. One of advantages is that 1D and 2D QDFT has time complexity O(sqrt(N)) and O(N) respectively. The other advantage is that QDFT can process very long sign…

Short Proofs of Linear Growth of Quantum Circuit Complexity

The complexity of a quantum gate, defined as the minimal number of elementary gates to build it, is an important concept in quantum information and computation. It is shown recently that the complexity of quantum gates built from random quantum circuits almost surely grows linearly with the number of building blocks. In this article, we provide two short proofs of this fact. We also discuss a discrete version of quantum circuit complexity growth.

Discrete logarithm and Diffie-Hellman problems in identity black-box groups

We investigate the computational complexity of the discrete logarithm, the computational Diffie-Hellman and the decisional Diffie-Hellman problems in some identity black-box groups G_{p,t}, where p is a prime number and t is a positive integer. These are defined as quotient groups of vector space Z_p^{t+1} by a hyperplane H given through an identity oracle. While in general black-box groups with unique encoding these computational problems are classically all hard and quantumly all easy, we find that in the groups G_{p,t} the situation is more contrasted. We prove that while there is a polynom…

Principles and symmetries of complexity in quantum field theory

Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the complexity in continuous systems. Due to fundamental symmetries of quantum field theories, the Finsler metric is more constrained and consequently, the complexity of SU($n$) operators is uniquely determined as a length of a geodesic in the Finsler geometry. Our Finsler metric is bi-invariant contrary to the right-invariance of discrete qubit systems. We clarify …

非可逆电路复杂度来自融合操作

Non-invertible circuit complexity from fusion operations

本文提出了一种基于融合操作的非可逆电路复杂度框架，结合连续几何与离散扇区跳跃，应用于共形场理论并探讨了AdS₃解释。

波函数的自发坍缩：一种由离散物理学启发的可检验方案

Spontaneous Collapse of the Wavefunction: A Testable Proposal Motivated by Discrete Physics

本研究提出一种含全新波函数坍缩机制的修正量子力学，可解决量子测量问题，其能从全离散物理学自然衍生，且相比既有自发坍缩理论更适配波函数的实在论诠释。

The information-theoretical viewpoint on the physical complexity of classical and quantum objects and their dynamical evolution

Charles Bennett's measure of physical complexity for classical objects, namely logical-depth, is used in order to prove that a chaotic classical dynamical system is not physical complex. The natural measure of physical complexity for quantum objects, quantum logical-depth, is then introduced in order to prove that a chaotic quantum dynamical system is not physical complex too.

量子离散事件系统的监督控制

Supervisory Control of Quantum Discrete Event Systems

针对经典离散事件系统状态复杂度难题，本文以量子有限自动机为建模工具建立量子离散事件系统框架，证明其监督控制定理，提出可控性判定多项式算法，并验证其状态复杂度优势。