Efficient Algorithms for Causal Order Discovery in Quantum Networks

Abstract

Given black-box access to the input and output systems, we develop the first efficient quantum causal order discovery algorithm with polynomial query complexity with respect to the number of systems. We model the causal order with quantum combs, and our algorithm outputs the order of inputs and outputs that the given process is compatible with. Our algorithm searches for the last input and the last output in the causal order, removes them, and iteratively repeats the above procedure until we get the order of all inputs and outputs. Our method guarantees a polynomial running time for quantum combs with a low Kraus rank, namely processes with low noise and little information loss. For special cases where the causal order can be inferred from local observations, we also propose algorithms that have lower query complexity and only require local state preparation and local measurements. Our algorithms will provide efficient ways to detect and optimize available transmission paths in quantum communication networks, as well as methods to verify quantum circuits and to discover the latent structure of multipartite quantum systems.

Quantum Accelerated Causal Tomography: Circuit Considerations For Applications In Bioinformatics and AGI

“…Quantum information enables a richer spectrum of causal relations that is not possible to access via classical statistics. Most research in this direction is towards exploring causality in the quantum context [16][17][18][19][20][21]. Our focus in this work is specifically using the quantum formulation to provide a computational advantage with respect to a classical technique on classical data.…”

Experimentally adjudicating between different causal accounts of Bell inequality violations via statistical model selection

“…[40] also considered a quantum generalization of the notion of causal discovery, but only for the special case of distinguishing a cause-effect relation from a commoncause relation and only device-dependently. Several other works [15,19,20] have focussed on the problem of determining the causal structure based on interventionist data. 7 That is, rather than making inferences about causal structure based on a probability distribution over the observed classical variables, as we do here, they do so based on a tomographic characterization of each process in a circuit that describes the causal relations.…”

“…Our proposal is an example of causal discovery using purely observational data. Its relation to past work on causal discovery, both classical [17,18] and quantum [19,20] is discussed in Appendix B 1.…”