Complexity Phase Transitions Generated by Entanglement

Ghosh, Soumik; Deshpande, Abhinav V.; Hangleiter, Dominik; Gorshkov, Alexey V.; Fefferman, Bill

doi:10.1103/physrevlett.131.030601

Cited by 4 publications

(1 citation statement)

References 48 publications

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“…It is a reasonable assertion that the edge structure of algorithm-specific graphs that implements a quantum circuit upper-bounds the entanglement required for the computation. It is an open question whether this intuition can be quantified and if further connections exist between graph properties and the computational complexity of the algorithm being implemented similar to those known for regular universal cluster states [42]. If such connections exist, graph compilation could be used for classification and characterisation of different quantum algorithms-for example do classes of algorithm share common compiled graph properties?…”

Section: Applications and Open Questionsmentioning

confidence: 99%

Compilation of algorithm-specific graph states for quantum circuits

Krishnan Vijayan,

Paler,

Gavriel

et al. 2024

Quantum Sci. Technol.

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We present a quantum circuit compiler that prepares an algorithm-speciﬁc graph state from quantum circuits described in high level languages, such as Cirq and Q#. The computation can then be implemented using a series of non-Pauli measurements on this graph state. By compiling the graph state directly instead of starting with a standard lattice cluster state and preparing it over the course of the computation, we are able to better understand the resource costs involved and eliminate wasteful Pauli measurements on the actual quantum device. Access to this algorithm-speciﬁc graph state also allows for optimisation over locally equivalent graph states to implement the same quantum circuit. The compiler presented here ﬁnds ready application in measurement based quantum computing, NISQ devices and logical level compilation for fault tolereant implementations.

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Section: Applications and Open Questionsmentioning

confidence: 99%

Compilation of algorithm-specific graph states for quantum circuits

Krishnan Vijayan,

Paler,

Gavriel

et al. 2024

Quantum Sci. Technol.

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Benchmarking highly entangled states on a 60-atom analogue quantum simulator

Shaw,

Chen,

Choi

et al. 2024

Nature

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Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices2–5, and it remains unsolved how to estimate the actual entanglement content of experiments6. Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement6, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution2–5. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

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Error-Resilience Phase Transitions in Encoding-Decoding Quantum Circuits

Turkeshi,

Sierant

2024

Phys. Rev. Lett.

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Complexity Phase Transitions Generated by Entanglement

Cited by 4 publications

References 48 publications

Compilation of algorithm-specific graph states for quantum circuits

Compilation of algorithm-specific graph states for quantum circuits

Benchmarking highly entangled states on a 60-atom analogue quantum simulator

Error-Resilience Phase Transitions in Encoding-Decoding Quantum Circuits

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