![]() Finally, we study computational quantum advantage where a classical reversible linear circuit can be implemented more efficiently using Clifford gates, and show an explicit example where such an advantage takes place. The variants of the canonical form, one with a short Hadamard-free part and one allowing a circuit depth $9n$ implementation of arbitrary Clifford unitaries in the Linear Nearest Neighbor architecture are also discussed. A surprising connection is highlighted between random uniform Clifford operators and the Mallows distribution on the symmetric group. The number of random bits consumed by the algorithm matches the information-theoretic lower bound. ![]() We employ this canonical form to generate a random uniformly distributed $n$-qubit Clifford operator in runtime $O(n^2)$. We report a polynomial-time algorithm for computing the canonical form. Conversely, some fault-tolerant measurement-based schemes have been developed that are not expected to have a description in. Our canonical form provides a one-to-one correspondence between Clifford operators and layered quantum circuits. Much research has sought to map quantum errorcorrecting codes into measurement-based schemes (29, 39) through a system called foliation to access favorable properties of exotic quantum errorcorrecting codes. We show that any Clifford operator can be uniquely written in the canonical form $F_1HSF_2$, where $H$ is a layer of Hadamard gates, $S$ is a permutation of qubits, and $F_i$ are parameterized Hadamard-free circuits chosen from suitable subgroups of the Clifford group. Here we study the structural properties of this group. Single-qubit gates X, H and S are Clifford, and gates T and R are non-Clifford.b The task-dependent circuit frame. Download a PDF of the paper titled Hadamard-free circuits expose the structure of the Clifford group, by Sergey Bravyi and 1 other authors Download PDF Abstract:The Clifford group plays a central role in quantum randomized benchmarking, quantum tomography, and error correction protocols.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |