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Efficient Circuits for Exact-Universal Computations with Qudits

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arxiv quant-ph/0509161 v1 pith:N44NREBE submitted 2005-09-22 quant-ph

Gavin K. Brennen , Stephen S. Bullock , Dianne P. O'Leary This is my paper · ORCID
classification quant-ph
keywords synthesistwo-quditcircuitsgatesquditsalgorithmancillasefficient
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This paper concerns the efficient implementation of quantum circuits for qudits. We show that controlled two-qudit gates can be implemented without ancillas and prove that the gate library containing arbitrary local unitaries and one two-qudit gate, CINC, is exact-universal. A recent paper (PRL 94 230502) describes quantum circuits for qudits which require O(d^n) two-qudit gates for state synthesis and O(d^{2n}) two-qudit gates for unitary synthesis, matching the respective lower bound complexities. In this work, we present the state synthesis circuit in much greater detail and prove that it is correct. Also, the (n-2)/(d-2) ancillas required in the original algorithm may be removed without changing the asymptotics. Further, we present a new algorithm for unitary synthesis, inspired by the QR matrix decomposition, which is also asymptotically optimal.

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Cited by 3 Pith papers

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

  1. Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition

    quant-ph 2026-07 conditional novelty 7.0 of 10

    A four-copy fixed-core architecture with five local SU(3)⊗SU(3) layers is shown to be locally universal for two-qutrit gates, via an explicit Clifford core that makes the differential an exact isometry.

  2. Non-Abelian dynamics on a cube: improving quantum compilation through qudit-based simulations

    quant-ph 2025-06 conditional novelty 7.0 of 10

    A qudit-based circuit for SU(2) lattice gauge theory on a cube, with improved decompositions for uniformly-controlled rotations and new elementary-gate resource estimates.

  3. Packaged Quantum States for Gauge-Invariant Quantum Computation and Communication

    quant-ph 2025-05 conditional novelty 3.0 of 10

    A gauge-invariant quantum information framework based on packaged states is proposed, but its core content reproduces known superselection constraints and qudit circuits.

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