arXiv subjects

Tianen Chen

Publications and source records attributed to Tianen Chen.

3 recordsLinked to original sources

arXiv2026

Beyond Single Trajectories: Optimal Control and Jordan-Lie Algebra in Hybrid Quantum Walks for Combinatorial Optimization

The Quantum Approximate Optimization Algorithm (QAOA) follows a single, fixed evolution path, overlooking the potential computational advantage of coherently superposing multiple trajectories. Here we overcome this limitation with a hybrid quantum walk (HQW) ansatz that super poses multiple Hamiltonian-driven paths coherently within each circuit layer via a dynamical coin operator. QAOA emerges as a special case of this framework with a static Pauli-X coin. Using Pontryagin's minimum principle, we derive the optimal form of the coin operator, demonstrating that it generally differs from a constant gate. A dynamical Lie algebra analysis reveals that HQW generates a strictly larger Jordan-Lie algebra, providing an algebraic foundation for its enhanced expressivity. Especially, we reveal the connection between the unique Jordan product negativity in HQW's DLA and its performance advantages. Numerical experiments on Max-Cut and Maximum Independent Set problems show that HQW systematically outperforms QAOA in convergence speed, solution accuracy, and robustness. Our work establishes a path-superposition paradigm for quantum optimization, combining optimal control theory with algebraic structure to guide the design of advanced quantum algorithms.

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arXiv2025

A hybrid quantum walk model unifying discrete and continuous quantum walks

Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with the Hamiltonian-driven time evolution of continuous walks. Through systematic analysis of probability distributions, standard deviations, and entanglement entropy on fundamental graph structures (2-vertex circles, stars, and lines), we reveal distinctive dynamical characteristics that differentiate our model from conventional quantum walk paradigms. The proposed framework demonstrates unifying capabilities by naturally encompassing existing quantum walk models as special cases. Two significant applications emerge from this hybrid architecture: (1) We develop a novel protocol for perfect state transfer(PST) in general connected graphs, overcoming the limitations of previous graph-specific approaches. A PST on a tree graph has been implemented on a quantum superconducting processor. (2) We devise a quantum algorithm for multiplying $K$ adjacency matrices of $n$-vertex regular graphs with time complexity $O(n^2d_1\cdots d_K)$, outperforming classical matrix multiplication $(O(n^{2.371552}))$ when vertex degrees $d_i$ are bounded. The algorithm's efficacy for triangle counting is experimentally validated through the quantum simulation on PennyLane. These results establish the hybrid quantum walk as a versatile framework bridging discrete and continuous paradigms while enabling practical quantum advantage in graph computation tasks.

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arXiv2025

Entanglement distribution based on quantum walk in arbitrary quantum networks

In large-scale quantum networks, quantum repeaters provide an efficient method to distribute entangled states among selected nodes for realizing long-distance and complicated quantum communications. However, extending quantum repeater protocols to high-dimensional quantum states in existing experiments is not easy. Owing to the feasible physical implementations of quantum walks, we proposed various basic modules applicable to quantum repeaters for distributing high-dimensional entangled states via quantum walks, including $d$-dimensional Bell states and multi-particle $d$-dimensional GHZ states. Furthermore, based on the above schemes, we provided a high-dimensional entanglement distribution scheme for arbitrary quantum tree networks. By searching for a Steiner tree in a quantum network, we can achieve high-dimensional entanglement distributions over an arbitrary quantum network. We constructed a quantum fractal network based on $d$-dimensional GHZ states and analyzed the quantum transport properties of continuous quantum walks in the network. Compared with the continuous quantum walk on the Sierpinski gasket, the quantum walk on the new fractal network spreads more widely within the same time frame. Finally, we conducted five experiments to implement various basic modules of 2-party or 3-party entanglement distribution schemes in a superconducting quantum processor. Our study can serve as a building block for constructing large and complex quantum networks.

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