pith. sign in

arxiv: 1206.5236 · v4 · pith:I75L3A7Onew · submitted 2012-06-22 · 🪐 quant-ph · cs.ET

Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates

classification 🪐 quant-ph cs.ET
keywords unitariescliffordcasecircuitsefficientequivalenceexactfrac
0
0 comments X
read the original abstract

In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring $\mathbb{Z}[\frac{1}{\sqrt{2}},i]$, in the single-qubit case. We report an efficient synthesis algorithm, with an exact optimality guarantee on the number of Hadamard and T gates used. We conjecture that the equivalence of the sets of unitaries implementable by circuits over the Clifford and T library and unitaries over the ring $\mathbb{Z}[\frac{1}{\sqrt{2}},i]$ holds in the $n$-qubit case.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 4 Pith papers

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

  1. Classical State Preparation for Variational Quantum Algorithms via Reinforcement Learning

    quant-ph 2026-05 unverdicted novelty 7.0

    CRiSP uses neural-guided MCTS and curriculum learning to insert Clifford prefixes before parameterized rotations in VQAs, yielding mean 3.17x and max 45x gains in energy accuracy on 22-qubit QAOA benchmarks versus pri...

  2. Quantum Error-Corrected Computation of Molecular Energies

    quant-ph 2025-05 conditional novelty 7.0

    First end-to-end demonstration of quantum error correction integrated with quantum phase estimation to compute molecular hydrogen ground-state energy to 0.001(13) hartree accuracy on Quantinuum H2-2 hardware.

  3. Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators

    quant-ph 2026-04 unverdicted novelty 6.0

    Qudit encodings for quadratic diagonal evolutions require exponentially stronger synthesis advantages than qubits to win asymptotically in product formulas but can yield constant-factor savings in LCU at low d.

  4. Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators

    quant-ph 2026-04 unverdicted novelty 5.0

    The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.