The clifford group forms a unitary 3-design
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 … http://export.arxiv.org/abs/1510.02769
The clifford group forms a unitary 3-design
Did you know?
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...
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 … 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.
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 … WebThe 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.
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.
WebThe uniform distribution over the Clifford group on n qubits is a unitary 2-design with D=2n. As is known, the Clifford group C n on n qubits can be implemented by quantum circuits of size O n2 2,15 . This general result allows us to immediately deduce that, for ex-ample, the Clifford group gives a more efficient solution to containerization of applicationsWebSep 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. containerization of appsWebNov 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 … effectiveness of tongue cleanersWebJun 15, 2024 · Equation implies that twirling any quantum channel over U2D is equivalent to twirling over a Haar-measure unitary group. The multi-qubit Clifford group for n qubits forms a U2D [37, 48]. Though not explicitly stated, the multi-qudit Clifford group evidently forms a U2D based on Webb's analysis of Pauli-mixing Clifford ensembles . effectiveness of training and development pdfcontainerization of microservicesWebOct 9, 2015 · Multiqubit Clifford groups are unitary 3-designs. Unitary -designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum … effectiveness of total gymWebJul 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 ... containerization on aws