arXiv subjects

Zujin Wen

Publications and source records attributed to Zujin Wen.

3 recordsLinked to original sources

arXiv2026

$\mathcal{O}(n)$ alternative to Quantum Fourier Transform with efficient neural net classical post-processing

The Quantum Fourier Transform (QFT) is employed by hidden subgroup problem (HSP) algorithms, including Shor's algorithm for factoring. The circuit depth of the QFT remains challenging for near-term hardware. To find shallower alternatives we identify two properties that are exploited by the QFT to enable HSP. Firstly, the shift invariance of the QFT allows for the removal of a random overall shift. Secondly, the QFT retains information about the hidden subgroup generator accessible in the measurement outcomes. We quantify that information via the discrete Fisher information. We construct a family of shallow circuits using Hadamards and controlled-Phase gates, HP-$L$ circuits, that we prove preserve shift invariance. Numerical analysis shows these circuits retain exponentially growing Fisher information. The $\mathcal{O}(n)$ HP-$1$ is employed in place of the $\mathcal{O}(n^2)$ QFT in our numerical implementation of Shor's algorithm. An efficient neural network is used for the corresponding classical post-processing.

quant-ph↗

arXiv2026

Generalised Probabilistic Theories

We give an introduction to research associated with the generalised probabilistic theories framework, also known as the convex framework. States are real vectors representing lists of probabilities of measurement outcomes. Convex combinations of the vectors represent probabilistic combinations of different state preparations. Transformations are real matrices. Measurement outcomes are represented by functionals of the states, inner products of the state with a real vector, whose values are the probability of the measurement outcome in question. The framework generalises quantum theory. We describe the operational meaning of the framework, and how the concepts can be defined in terms of cones of states and measurement outcome vectors. We describe how the classical and quantum probability theories are represented in the framework. We describe Bell non-locality and the theory with super-quantum non-locality known as box world. We discuss generalised Hamiltonian mechanics in the discrete case and in continuous phase space, including the role of negativity of the phase space density in contextuality and tunnelling.

quant-ph↗

arXiv2025

Quantum Sinusoidal Neural Networks

We design a quantum version of neural networks with sinusoidal activation functions and compare its performance to the classical case. We create a general quantum sine circuit implementing a discretised sinusoidal activation function. Along the way, we define a classical discrete sinusoidal neural network. We build a quantum optimization algorithm around the quantum sine circuit, combining quantum search and phase estimation. This algorithm is guaranteed to find the weights with global minimum loss on the training data. We give a computational complexity analysis and demonstrate the algorithm in an example. We compare the performance with that of the standard gradient descent training method for classical sinusoidal neural networks. We show that (i) the standard classical training method typically leads to bad local minima in terms of mean squared error on test data and (ii) the weights that perform best on the training data generalise well to the test data. Points (i) and (ii) motivate using the quantum training algorithm, which is guaranteed to find the best weights on the training data.

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