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
[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