Introduces forward-assisted purification via a new spatiotemporal framework that outperforms conventional static purification by up to 50x in copy efficiency and circumvents no-purification theorems for Bell states.
Tensor networks and graphical calculus for open quantum systems
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abstract
We describe a graphical calculus for completely positive maps and in doing so review the theory of open quantum systems and other fundamental primitives of quantum information theory using the language of tensor networks. In particular we demonstrate the construction of tensor networks to pictographically represent the Liouville-superoperator, Choi-matrix, process-matrix, Kraus, and system-environment representations for the evolution of quantum states, review how these representations interrelate, and illustrate how graphical manipulations of the tensor networks may be used to concisely transform between them. To further demonstrate the utility of the presented graphical calculus we include several examples where we provide arguably simpler graphical proofs of several useful quantities in quantum information theory including the composition and contraction of multipartite channels, a condition for whether an arbitrary bipartite state may be used for ancilla assisted process tomography, and the derivation of expressions for the average gate fidelity and entanglement fidelity of a channel in terms of each of the different representations of the channel.
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2026 5representative citing papers
A new step size rule lets boosted stochastic Frank-Wolfe match ordinary stochastic Frank-Wolfe rates on nonconvex and quasar-convex problems and deliver faster empirical convergence on sparse logistic regression and quantum tomography.
A systematic analysis of 59 quantum software testing empirical studies reveals highly diverse designs, inconsistent reporting, and open methodological challenges, leading to recommendations for future work.
A fully general open quantum system description of arbitrarily complex oscillating and decaying neutrino systems is developed and shown to be implementable via Lindblad equations, Liouvillian superoperators, and Kraus operators.
QnRL is a distributional quantum RL framework that distills conditional action policies from moments of quantum generative models in Hilbert space via the QuAK algorithm, reporting higher scores and fewer parameters than baselines.
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A Methodological Analysis of Empirical Studies in Quantum Software Testing
A systematic analysis of 59 quantum software testing empirical studies reveals highly diverse designs, inconsistent reporting, and open methodological challenges, leading to recommendations for future work.