Algebraic structure of path-independent quantum control

An algebraically independent generating set of the algebra of local unitary invariants

We show that the inverse limit of the graded algebras of local unitary invariant polynomials of finite dimensional k-partite quantum systems is free, and give an algebraically independent generating set. The number of degree 2d invariants in the generating set is equal to the number of conjugacy classes of index d subgroups of a free group on k-1 generators.

Algebraic solution of the Lindblad equation for a collection of multilevel systems coupled to independent environments

We consider the Lindblad equation for a collection of multilevel systems coupled to independent environments. The equation is symmetric under the exchange of the labels associated with each system and thus the open-system dynamics takes place in the permutation-symmetric subspace of the operator space. The dimension of this space grows polynomially with the number of systems. We construct a basis of this space and a set of superoperators whose action on this basis is easily specified. For a given number of levels, $M$, these superoperators are written in terms of a bosonic realization of the g…

Creating path entanglement and violating Bell inequalities by independent photon sources

We demonstrate a novel approach of violating position dependent Bell inequalities by photons emitted via independent photon sources in free space. We trace this violation back to path entanglement created a posteriori by the selection of modes due to the process of detection.

Path-Independent Quantum Gates with Noisy Ancilla

Ancilla systems are often indispensable to universal control of a nearly isolated quantum system. However, ancilla systems are typically more vulnerable to environmental noise, which limits the performance of such ancilla-assisted quantum control. To address this challenge of ancilla-induced decoherence, we propose a general framework that integrates quantum control and quantum error correction, so that we can achieve robust quantum gates resilient to ancilla noise. We introduce the path independence criterion for fault-tolerant quantum gates against ancilla errors. As an example, a path-indep…

Qutrit电路与代数关系：通往高效自旋-1哈密顿量模拟的路径

Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation

本文研究利用Yang-Baxter-like turnover等代数关系压缩和优化qutrit电路，以降低电路深度并提升高保真实现效率，并探索其向高维量子电路及一维自旋-1 Heisenberg模型的推广。

驱动瑞利德堡原子系统中局部关联的代数规律

Algebraic law of local correlations in a driven Rydberg atomic system

研究驱动瑞利德堡原子系统中反铁磁关联的代数规律，通过Magnus展开验证其叠加原理的鲁棒性。