Matches in SemOpenAlex for { <https://semopenalex.org/work/W2920312441> ?p ?o ?g. }
Showing items 1 to 78 of
78
with 100 items per page.
- W2920312441 abstract "The Clifford hierarchy of unitary operators is a foundational concept for universal quantum computation. It was introduced to show that universal quantum computation can be realized via quantum teleportation, given access to certain standard resources. While the full structure of the hierarchy is still not understood, Cui et al. [S. X. Cui et al., Phys. Rev. A 95, 012329 (2017)] recently described the structure of diagonal unitaries in the hierarchy. They considered diagonal unitaries whose action on a computational basis qudit state is described by a ${2}^{k}mathrm{th}$ root of unity raised to some polynomial function of the state, and they established the level of such unitaries in the hierarchy as a function of $k$ and the degree of the polynomial. For qubit systems, we consider $kmathrm{th}$-level diagonal unitaries that can be described just by quadratic forms of the state over the ring ${mathbb{Z}}_{{2}^{k}}$ of integers modulo ${2}^{k}$. The quadratic forms involve symmetric matrices over ${mathbb{Z}}_{{2}^{k}}$ that can be used to efficiently describe all two-local and certain higher locality diagonal gates in the hierarchy. We also provide explicit algebraic descriptions of their action on Pauli matrices, which establishes a natural recursion to diagonal unitaries from lower levels. The result involves symplectic matrices over ${mathbb{Z}}_{{2}^{k}}$ and hence our perspective unifies a subgroup of diagonal gates in the Clifford hierarchy with the binary symplectic framework for gates in the Clifford group. We augment our description with simple examples for certain standard gates. In addition to demonstrating structure, these formulas might prove useful in applications such as (i) classical simulation of quantum circuits, especially via the stabilizer rank approach, (ii) synthesis of logical non-Clifford unitaries, specifically alternatives to expensive magic state distillation, and (iii) decomposition of arbitrary unitaries beyond the $mathrm{Clifford}+T$ set of gates, perhaps leading to shorter depth circuits. Our results suggest that some nondiagonal gates in the hierarchy might also be understood by generalizing other binary symplectic matrices to integer rings." @default.
- W2920312441 created "2019-03-11" @default.
- W2920312441 creator A5034044119 @default.
- W2920312441 creator A5037795370 @default.
- W2920312441 creator A5070430560 @default.
- W2920312441 date "2019-08-07" @default.
- W2920312441 modified "2023-09-28" @default.
- W2920312441 title "Unifying the Clifford hierarchy via symmetric matrices over rings" @default.
- W2920312441 cites W1490521149 @default.
- W2920312441 cites W1984436207 @default.
- W2920312441 cites W2009169733 @default.
- W2920312441 cites W2012760578 @default.
- W2920312441 cites W2035755047 @default.
- W2920312441 cites W2052146120 @default.
- W2920312441 cites W2079294297 @default.
- W2920312441 cites W2151462437 @default.
- W2920312441 cites W2167413626 @default.
- W2920312441 cites W2512564998 @default.
- W2920312441 cites W2586874551 @default.
- W2920312441 cites W2604467189 @default.
- W2920312441 cites W3122575146 @default.
- W2920312441 doi "https://doi.org/10.1103/physreva.100.022304" @default.
- W2920312441 hasPublicationYear "2019" @default.
- W2920312441 type Work @default.
- W2920312441 sameAs 2920312441 @default.
- W2920312441 citedByCount "13" @default.
- W2920312441 countsByYear W29203124412020 @default.
- W2920312441 countsByYear W29203124412021 @default.
- W2920312441 countsByYear W29203124412022 @default.
- W2920312441 countsByYear W29203124412023 @default.
- W2920312441 crossrefType "journal-article" @default.
- W2920312441 hasAuthorship W2920312441A5034044119 @default.
- W2920312441 hasAuthorship W2920312441A5037795370 @default.
- W2920312441 hasAuthorship W2920312441A5070430560 @default.
- W2920312441 hasBestOaLocation W29203124411 @default.
- W2920312441 hasConcept C114614502 @default.
- W2920312441 hasConcept C118615104 @default.
- W2920312441 hasConcept C130367717 @default.
- W2920312441 hasConcept C134306372 @default.
- W2920312441 hasConcept C136119220 @default.
- W2920312441 hasConcept C168619227 @default.
- W2920312441 hasConcept C202444582 @default.
- W2920312441 hasConcept C2524010 @default.
- W2920312441 hasConcept C33923547 @default.
- W2920312441 hasConcept C90119067 @default.
- W2920312441 hasConcept C9485509 @default.
- W2920312441 hasConceptScore W2920312441C114614502 @default.
- W2920312441 hasConceptScore W2920312441C118615104 @default.
- W2920312441 hasConceptScore W2920312441C130367717 @default.
- W2920312441 hasConceptScore W2920312441C134306372 @default.
- W2920312441 hasConceptScore W2920312441C136119220 @default.
- W2920312441 hasConceptScore W2920312441C168619227 @default.
- W2920312441 hasConceptScore W2920312441C202444582 @default.
- W2920312441 hasConceptScore W2920312441C2524010 @default.
- W2920312441 hasConceptScore W2920312441C33923547 @default.
- W2920312441 hasConceptScore W2920312441C90119067 @default.
- W2920312441 hasConceptScore W2920312441C9485509 @default.
- W2920312441 hasFunder F4320306076 @default.
- W2920312441 hasIssue "2" @default.
- W2920312441 hasLocation W29203124411 @default.
- W2920312441 hasLocation W29203124412 @default.
- W2920312441 hasOpenAccess W2920312441 @default.
- W2920312441 hasPrimaryLocation W29203124411 @default.
- W2920312441 hasRelatedWork W1605952097 @default.
- W2920312441 hasRelatedWork W1976174747 @default.
- W2920312441 hasRelatedWork W1981909949 @default.
- W2920312441 hasRelatedWork W1995623237 @default.
- W2920312441 hasRelatedWork W2009896212 @default.
- W2920312441 hasRelatedWork W2070661372 @default.
- W2920312441 hasRelatedWork W2951752653 @default.
- W2920312441 hasRelatedWork W2980231599 @default.
- W2920312441 hasRelatedWork W3151745658 @default.
- W2920312441 hasRelatedWork W4226371494 @default.
- W2920312441 hasVolume "100" @default.
- W2920312441 isParatext "false" @default.
- W2920312441 isRetracted "false" @default.
- W2920312441 magId "2920312441" @default.
- W2920312441 workType "article" @default.