Conformal field theories are magical
"Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large m...
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| Veröffentlicht in: | Physical review. B 2021-02, Vol.103 (7), p.1, Article 075145 |
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| container_title | Physical review. B |
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| creator | White, Christopher David Cao, ChunJun Swingle, Brian |
| description | "Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the three-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer and constrain tensor network models of AdS-CFT. |
| doi_str_mv | 10.1103/PhysRevB.103.075145 |
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We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the three-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer and constrain tensor network models of AdS-CFT.</description><identifier>ISSN: 2469-9950</identifier><identifier>EISSN: 2469-9969</identifier><identifier>DOI: 10.1103/PhysRevB.103.075145</identifier><language>eng</language><publisher>College Park: American Physical Society</publisher><subject>1-dimensional spin chains ; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY ; Conformal field theory ; Critical phenomena ; Critical point ; Density matrix renormalization group ; Error correction ; Field theory ; Ground state ; Materials science ; Mathematical analysis ; Physics ; Quantum computers ; Quantum correlations in quantum information ; Quantum phase transitions ; Quantum simulation ; Tensors</subject><ispartof>Physical review. 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B</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>White, Christopher David</au><au>Cao, ChunJun</au><au>Swingle, Brian</au><aucorp>Univ. of California, Oakland, CA (United States)</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Conformal field theories are magical</atitle><jtitle>Physical review. B</jtitle><date>2021-02-25</date><risdate>2021</risdate><volume>103</volume><issue>7</issue><spage>1</spage><pages>1-</pages><artnum>075145</artnum><issn>2469-9950</issn><eissn>2469-9969</eissn><abstract>"Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. 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| subjects | 1-dimensional spin chains CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY Conformal field theory Critical phenomena Critical point Density matrix renormalization group Error correction Field theory Ground state Materials science Mathematical analysis Physics Quantum computers Quantum correlations in quantum information Quantum phase transitions Quantum simulation Tensors |
| title | Conformal field theories are magical |
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