Phase Space Formulation of Filtering. Insight into the Wave-Particle Duality

Quadratic unconstrained binary optimization formulation for rectified-linear-unit-type functions

We propose a quadratic unconstrained binary optimization (QUBO) formulation of rectified linear unit (ReLU) type functions. Different from the q-loss function proposed by Denchev et al. (2012), a simple discussion based on the Legendre duality is not sufficient to obtain the QUBO formulation of the ReLU-type functions. In addition to the Legendre duality, we employ the Wolfe duality, and the QUBO formulation of the ReLU-type is derived. The QUBO formulation is available in Ising-type annealing methods, including quantum annealing machines.

量子力学路径积分表述中的幂对偶性

Power-Duality in Path Integral Formulation of Quantum Mechanics

本文研究费曼路径积分表述下的幂对偶性，发现修改后的promotor在经典角动量下形式不变，角动量量子化后对偶性破坏，进而提出准幂对偶性概念并给出由已知格林函数确定对偶系统格林函数的公式。

宇宙作为探测器：Diósi-Penrose模型的量子滤波 formulation

The Universe as a Detector: A Quantum Filtering Formulation of the Diósi-Penrose Model

本文提出将宇宙视为探测器，通过量子滤波方法重新诠释Diósi-Penrose模型，探讨量子连续时间塌缩与开放量子随机模型的关系。

Duality and Conditional Expectations in the Nakajima-Mori-Zwanzig Formulation

We develop a new operator algebraic formulation of the Nakajima-Mori-Zwanzig (NMZ) method of projections. The new theory is built upon rigorous mathematical foundations, and it can be applied to both classical and quantum systems. We show that a duality principle between the NMZ formulation in the space of observables and in the state space can be established, analogous to the Heisenberg and Schrödinger pictures in quantum mechanics. Based on this duality we prove that, under natural assumptions, the projection operators appearing in the NMZ equation must be conditional expectations. The propo…

Gauss's Law, Duality, and the Hamiltonian Formulation of U(1) Lattice Gauge Theory

Quantum computers have the potential to explore the vast Hilbert space of entangled states that play an important role in the behavior of strongly interacting matter. This opportunity motivates reconsidering the Hamiltonian formulation of gauge theories, with a suitable truncation scheme to render the Hilbert space finite-dimensional. Conventional formulations lead to a Hilbert space largely spanned by unphysical states; given the current inability to perform large scale quantum computations, we examine here how one might restrict wave function evolution entirely or mostly to the physical subs…

Quantitative duality and neutral kaon interferometry in CPLEAR experiments

A quantitative formulation of Bohr's complementarity principle and interferometric duality is discussed and applied to the neutral kaon system. Recent measurements by the CPLEAR Collaboration can be easily interpreted in terms of ``neutral kaon interferometry'' illustrating and confirming those basic principles of quantum mechanics.