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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Vydáno v:	Nature communications Ročník 15; číslo 1; s. 10513 - 10
Hlavní autoři:	Zhang, Xingjian, Pan, Zhaokai, Liu, Guoding
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	London Nature Publishing Group UK 03.12.2024 Nature Publishing Group Nature Portfolio
Témata:	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
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Abstract	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.
AbstractList	Abstract 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. 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.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. 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. 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. 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.
ArticleNumber	10513
Author	Pan, Zhaokai Liu, Guoding Zhang, Xingjian
Author_xml	– sequence: 1 givenname: Xingjian orcidid: 0000-0003-0677-6996 surname: Zhang fullname: Zhang, Xingjian email: zxj24@hku.hk organization: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong – sequence: 2 givenname: Zhaokai orcidid: 0009-0000-8940-990X surname: Pan fullname: Pan, Zhaokai email: panzk24@mails.tsinghua.edu.cn organization: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University – sequence: 3 givenname: Guoding orcidid: 0000-0003-3288-1394 surname: Liu fullname: Liu, Guoding email: lgd22@mails.tsinghua.edu.cn organization: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University
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Cites_doi	10.1007/BF01645779 10.22331/q-2020-09-30-337 10.1007/978-3-662-43948-7_27 10.1103/RevModPhys.81.865 10.1038/nature15759 10.1016/S0019-9958(85)80041-3 10.1103/PhysRevLett.129.200401 10.22331/q-2024-05-21-1351 10.1016/0375-9601(90)90172-K 10.1103/PhysRevLett.127.180501 10.1109/SFCS.1979.29 10.1103/PhysRevLett.118.090501 10.1103/PhysRevLett.79.325 10.1103/RevModPhys.86.419 10.1017/fmp.2018.3 10.1103/PhysRevA.73.012301 10.1090/jams/929 10.1063/1.4973422 10.1038/s41586-023-05784-4 10.1103/PhysRevA.68.022312 10.1126/science.aar3106 10.1007/3-540-36494-3_22 10.1137/S0097539795293172 10.1126/science.270.5242.1633 10.22331/q-2019-09-02-181 10.1088/1367-2630/16/1/013009 10.1090/gsm/047 10.1038/s41586-023-05782-6 10.1007/s10701-005-7353-4 10.1088/1367-2630/ab451d 10.1103/PhysRevLett.86.5188 10.1103/PhysRevResearch.2.033420 10.1103/PRXQuantum.2.010345 10.1103/PhysRevLett.80.3891 10.1201/9781003358817-7 10.1017/CBO9780511804090 10.4086/toc.2005.v001a005 10.1007/s00023-023-01378-y 10.1103/PhysRevLett.65.3373 10.1103/PRXQuantum.3.020333 10.1038/s41586-019-1666-5 10.1038/s41586-023-06927-3 10.1007/BF02650179 10.1038/s41567-020-0948-z 10.1103/PhysRevA.70.052328 10.1103/PhysRevA.71.022316 10.1103/PhysRevA.75.012103
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Snippet	Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum... Abstract Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of...
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SubjectTerms	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
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Title	Unconditional quantum magic advantage in shallow circuit computation
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