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The clifford group forms a unitary 3-design

WebThe Clifford Group of Companies Construction Scarborough, Ontario 666 followers The Clifford Group of Companies operates within the construction industry specializing in … WebMay 19, 2016 · As an immediate consequence, any orbit of pure states of the multiqubit Clifford group forms a complex projective 3-design; in particular, the set of stabilizer …

[1510.02619] Multiqubit Clifford groups are unitary 3-designs - arXiv.org

Webforming a subgroup of the Clifford group. When represented as symplectic matrices, this subgroup is isomorphic to the projective special linear group PSL(2,N). We show that this automorphism group acts transitively on the Pauli matrices, which implies that the ensemble is Pauli mixing and hence forms a unitary 2-design. WebAug 28, 2024 · In this article, we study a weaker form of approximate unitary designs motivated by operations on isolated quantum systems. We show that approximate unitary designs of much smaller size exist in this ... Zak Webb ``The Clifford group forms a unitary 3-design'' Quantum Information and Computation 16, 1379–1400 (2016). basman tenenbaum https://sarahkhider.com

[1510.02769] The Clifford group forms a unitary 3-design

WebNov 1, 2016 · We prove that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected. Our proof strategy … WebJul 6, 2024 · A main collective conclusion is that the Rényi entanglement entropies averaged over designs of the same order are almost maximal. This links the orders of entropy and design, and therefore suggests Rényi entanglement entropies as diagnostics of the randomness complexity of corresponding designs. WebTHE CLIFFORD GROUP FORMS A UNITARY 3-DESIGN 3 the Hermitian conjugate of U and IX is the identity operator on X. Additionally, the completely-positive, trace-preserving, linear operators acting on L(X), denoted by C(X), are the quantum channels taking X to X. For any two operators A,B ∈ L(X), their inner product is defined as hA,Bi = Tr(A ... tajuana davis

Representations of the multi-qubit Clifford group Request PDF

Category:Approximate unitary 3-designs from transvection Markov chains

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The clifford group forms a unitary 3-design

Multiqubit Clifford groups are unitary 3-designs - ResearchGate

WebContact Us. Headquartered in Upper Saddle River, NJ with sales offices throughout North America. read more..... WebSep 26, 2016 · In fact, the Clifford group is singled out among the finite subgroups of the unitary group by being a 3-design [38]. ... Efficient Unitary Designs with a System-Size Independent Number...

The clifford group forms a unitary 3-design

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WebMay 19, 2016 · As an immediate consequence, any orbit of pure states of the multiqubit Clifford group forms a complex projective 3-design; in particular, the set of stabilizer states forms a 3-design. By contrast, the Clifford group in any odd prime power dimension is only a unitary 2-design. WebJul 15, 2024 · Definition of the Pauli group and the Clifford group. There seem to be two definitions of the Pauli group. In Nielsen and Chuang, the Pauli group on 1 qubit is defined as. P 1 = { ± I, ± i I, ± X, ± i X, ± Y, ± i Y, ± Z, ± i Z } = X, Y, Z . P 1 = { ± I, ± X, ± i Y, ± Z } = X, Z . The second definition makes more sense in the ...

WebSep 26, 2016 · The Clifford operators are an important and well-studied subset of quantum operations, in both the qubit and higher-dimensional qudit cases. While there are many … WebApr 20, 2024 · We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame poten-tial,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. ... The Clifford group forms a …

WebOct 9, 2015 · We prove that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected. Our proof strategy … WebClifford definition, U.S. lawyer and government official. See more.

WebWe describe an efficient construction for an exact unitary 2-design based on the Clifford group, and then develop a method for generating an ϵ -approximate unitary 2-design that requires only O(nlog(1/ϵ)) gates, where n is the number of qubits and ϵ is an appropriate measure of precision.

WebOct 9, 2015 · Multiqubit Clifford groups are unitary 3-designs. Unitary -designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum … tajuana brooks laneWebMay 31, 2024 · The clifford group f orms a unitary 3-design. Quantum Info. Com put., 16(15-16):1379–1400, November 2016. ... The Clifford group forms a unitary 3-design. Article. Oct 2015; QUANTUM INF COMPUT; basma punjabWebSep 8, 2024 · Schur–Weyl duality for the Clifford group with applications: Property testing, a robust Hudson theorem, and de Finetti representations. Communications in Mathematical Physics, 385(3):1325–1393, 2024. doi:10.1007/ s00220-021-04118-7. bas marketing groupWebJun 2009 - Sep 20112 years 4 months. Shanghai, China. Studio assistant internship for three consecutive summers (June through Sept of 2009 - 2011) at an international architectural … tajuana davis indianapolisWebThe Clifford group is defined as the group of unitaries that normalize the Pauli group: The Clifford gates are then defined as elements in the Clifford group. Some authors choose to define the Clifford group as the quotient group , which counts elements in that differ only by an overall phase factor as the same element. taj uaebas mariaWebimal unitary 3-design except for dimension 4, in which case it has a unique proper subgroup that is a unitary 3-design. Remark 2. In dimension 4, C=D’Sp(4;2) ’S 6 con-tains a unique subgroup that is isomorphic to A 6 [54], where S m and A m denote the symmetric group and al-ternatinggroupon mletters. Thepreimageof A 6 in C isaunitary3 ... bas mariage