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Universal quantum gates

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arxiv quant-ph/0108062 v1 pith:3QQNU5RZ submitted 2001-08-13 quant-ph

Universal quantum gates

Jean-Luc Brylinski , Ranee Brylinski This is my paper
classification quant-ph
keywords gatesquditcollectiondecomposablen-quditprimitiveproducesquantum
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit gates together with V produces all n-qudit gates up to arbitrary precision, or (ii) the collection of all 1-qudit gates together with V produces all n-qudit gates exactly. We show that (i) and (ii) are equivalent conditions on V, and they hold if and only if V is not a primitive gate. Here we say V is primitive if it transforms any decomposable tensor into a decomposable tensor. We discuss some applications and also relations with work of other authors.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum circuit optimization for arbitrary high-dimensional bipartite quantum computation

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    A new synthesis method constructs general quNit-quMit gates with O(n²) CINC gates and controlled quNit-quMit gates with only 2 CINC gates, improving on prior 2n requirement.

  2. Time Evolution on Hybrid Tensor Networks -- A Novel and Parallelizable Algorithm

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    Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.

  3. Characterizing quantum channels from local-unitary invariants

    quant-ph 2026-06 unverdicted novelty 6.0

    Develops moments from local-unitary invariants via Haar integrals to characterize entanglement behavior of two-qubit channels, with second-order moments yielding criteria for non-entangling and entanglement-breaking channels.