Unconditional quantum magic advantage in shallow circuit computation

Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum computation resides in the specific resource of “magic” states—the secret sauce to establish universal quantum computation. However, it is still qu...

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Bibliographic Details
Published in:Nature communications Vol. 15; no. 1; pp. 10513 - 10
Main Authors: Zhang, Xingjian, Pan, Zhaokai, Liu, Guoding
Format: Journal Article
Language:English
Published: London Nature Publishing Group UK 03.12.2024
Nature Publishing Group
Nature Portfolio
Subjects:
639/705/1041
639/705/117
639/766/259
639/766/483/481
Algorithms
Black boxes
Circuits
Computer applications
Constraints
Group communication
Humanities and Social Sciences
multidisciplinary
Quantum computing
Quantum theory
Science
Science (multidisciplinary)
Separation
Statistical analysis
Statistics
Task complexity
Telepathy
ISSN:2041-1723, 2041-1723
Online Access:Get full text
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Summary:Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum computation resides in the specific resource of “magic” states—the secret sauce to establish universal quantum computation. However, it is still questionable whether magic indeed brings the believed quantum advantage, ridding unproven complexity assumptions or black-box oracles. In this work, we demonstrate the first unconditional magic advantage: a separation between the power of generic constant-depth or shallow quantum circuits and magic-free counterparts. For this purpose, we link the shallow circuit computation with the strongest form of quantum nonlocality—quantum pseudo-telepathy, where distant non-communicating observers generate perfectly synchronous statistics. We prove quantum magic is indispensable for such correlated statistics in a specific nonlocal game inspired by the linear binary constraint system. Then, we translate generating quantum pseudo-telepathy into computational tasks, where magic is necessary for a shallow circuit to meet the target. As a by-product, we provide an efficient algorithm to solve a general linear binary constraint system over the Pauli group, in contrast to the broad undecidability in constraint systems. We anticipate our results will enlighten the final establishment of the unconditional advantage of universal quantum computation. "Magic” is a resource in quantum computation that is believed to be important for quantum speedup, but the proofs of this have involved complexity assumptions or invoking a black-box oracle. Here, by constructing magic-required quantum pseudo-telepathy and converting it into a relation problem, the authors show an unconditional separation between constant-depth quantum circuits and magic-free ones.
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ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-024-54864-0