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Random circuits have no shortcuts

Nature Physics volume 18, pages 482–483 (2022)Cite this article

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Theoretical physicists studying black holes have produced a conjecture that random quantum circuits cannot be simplified. Now, a minimal version of this conjecture has been proven, reaching a milestone in quantum-circuit complexity theory.

Take a collection of qubits initialized in a simple state and consider applying a sequence of random two-qubit gates. One may ask whether the same output state can be prepared using a substantially shorter sequence of judiciously chosen operations. Surprisingly, this question has arisen in the holographic description of black-hole physics, in which the growth of a wormhole’s size has been proposed to correspond to the growth of complexity in quantum dynamics. This idea implies the conjecture that the answer is no, a random sequence of gates cannot be shortened unless its length approaches a value that is exponentially large in the number of qubits. Now, writing in Nature Physics, Jonas Haferkamp and collaborators report an unexpectedly simple proof of this conjecture1.

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Fig. 1: A quantum circuit made by random two-qubit gates.

References

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Authors and Affiliations

  1. Philippe Meyer Institute, Physics Department, École Normale Supérieure (ENS), Université PSL, Paris, France

    Lorenzo Piroli

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  1. Lorenzo Piroli
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Correspondence to Lorenzo Piroli.

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Piroli, L. Random circuits have no shortcuts. Nat. Phys. 18, 482–483 (2022). https://doi.org/10.1038/s41567-022-01559-2

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