Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates
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.
Forward citations
Cited by 8 Pith papers
-
BPBO: Blindness-Preserving Brickwork Optimization by Certified Region Resynthesis
BPBO performs certified local resynthesis on one- to three-wire regions of BFK09 brickwork to reduce pattern size while preserving UBQC blindness, demonstrated on Grover and Toffoli cases with reductions up to 3x725 to 3x98.
-
Cultivating logical catalysts for fault-tolerant dyadic phase rotations
A new cultivation protocol prepares reusable logical catalysts as eigenstates of high-period Clifford circuits to implement exact Z^{2^{-b}} phase gates with constant online depth in surface codes.
-
More efficient Clifford+T synthesis for small-angle rotations and application to Trotterization
Clifford+T synthesis for small-angle rotations reduces T-cost to ~O(θ²/δ) and makes Trotterization cost constant in the small-step limit.
-
Classical State Preparation for Variational Quantum Algorithms via Reinforcement Learning
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...
-
Quantum Error-Corrected Computation of Molecular Energies
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.
-
Geometric Algebra Quantum Gate Decomposition
Reformulates Pauli and Clifford groups in geometric algebra with a greedy rotor decomposition algorithm for Clifford operators and geometric view of Clifford+T universality.
-
Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
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.
-
Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.