Quantum compression of tensor network states

Bai, Guoqiang; Yang, Yuxiang; Chiribella, Giulio

doi:10.1088/1367-2630/ab7a34

Cited by 10 publications

(3 citation statements)

References 63 publications

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“…Based on the causal structure and tomography data, we may model the underlying physical process by finding the smallest quantum model that reproduces the observed data [35][36][37]. More generally, characterizing the causal structure of a multipartite process as a tensor network enables the use of efficient protocols that exploits the tensor network structure, including simulation protocols [34,38,39] and compression protocols [40].…”

Section: Discussionmentioning

confidence: 99%

Quantum Causal Unravelling

Bai,

Wu,

Zhu

et al. 2021

Preprint

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Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process, using only access to its input and output systems. Our method is based on a quantum algorithm whose complexity scales polynomially for all processes with bounded information loss. Under additional assumptions, we also provide a second algorithm that has lower complexity and requires only local state preparation and local measurements. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography. Similarly, they can be used to identify useful communication channels in a quantum networks, and to test the structure of uncharacterized quantum circuits.

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Section: Discussionmentioning

confidence: 99%

Quantum Causal Unravelling

Bai,

Wu,

Zhu

et al. 2021

Preprint

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“…Causal order discovery can be also used to detect the latent structure of quantum systems, by applying the causal order discovery algorithms to detect the correlations in multipartite states. Knowing the causal structure of the system may allow us to ignore unnecessary correlations and represent states efficiently with, for example, tensor networks [31,32], which allow efficient tomography [33], simulation [32,34,35] and compression [36] of multipartite states. .…”

Section: Discussionmentioning

confidence: 99%

Efficient Algorithms for Causal Order Discovery in Quantum Networks

Bai,

Wu,

Zhu

et al. 2020

Preprint

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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.

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“…In this paper we join this effort and implement quantum compression algorithm introduced in 28 and further developed in [29][30][31][32][33][34] . This algorithm is used to compress n identical copies of an arbitrary pure qubit state into roughly log(n) qubits.…”

Section: Introductionmentioning

confidence: 99%

Implementation of quantum compression on IBM quantum computers

Pivoluska¹,

Plesch²

2022

Preprint

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Advances in development of quantum computing processors brought ample opportunities to test the performance of various quantum algorithms with practical implementations. In this paper we report on implementations of quantum compression algorithm that can efficiently compress unknown quantum information. We restricted ourselves to compression of three pure qubits into two qubits, as the complexity of even such a simple implementation is barely within the reach of today's quantum processors. We implemented the algorithm on IBM quantum processors with two different topological layouts-a fully connected triangle processor and a partially connected line processor. It turns out that the incomplete connectivity of the line processor affects the performance only minimally. On the other hand, it turns out that the transpilation, i.e. compilation of the circuit into gates physically available to the quantum processor, crucially influences the result. We also have seen that the compression followed by immediate decompression is, even for such a simple case, on the edge or even beyond the capabilities of currently available quantum processors.

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Quantum compression of tensor network states

Cited by 10 publications

References 63 publications

Quantum Causal Unravelling

Quantum Causal Unravelling

Efficient Algorithms for Causal Order Discovery in Quantum Networks

Implementation of quantum compression on IBM quantum computers

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