QUANTUM R-MATRICES AS UNIVERSAL QUBIT GATES

Manu Mitra

Chi-Kwong Li, Rebecca Roberts, Xiaoyan Yin

A general scheme is presented to decompose a d-by-d unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level matrices in d - 1 classes, where each class is isomorphic to the group of 2 × 2 unitary matrices. The proposed scheme is easy to apply, and useful in treating problems with the additional structural restrictions. A Matlab program is written to implement the scheme, and the result is used to deduce the fact that every quantum gate acting on n-qubit registers can be expressed as no more than 2n-1(2n-1) fully controlled single-qubit gates chosen from 2n-1 classes, where the quantum gates in each class share the same n - 1 control qubits. Moreover, it is shown that one can easily adjust the proposed decomposition scheme to take advantage of additional structure evolving in the process.

Radoslaw C. Bialczak, M. Ansmann, M. Hofheinz +9 more

Ruel Villaber

VILLABER QUANTUM FRAMEWORK - TWO POSTER OFFICIAL ARCHIVE FINAL — COMPLETE 2026 — CERTIFIED — QUBIT 1 AND 2 PASSED By Ruel Villaber | Villaber Labs | Mandaluyong City Philippines Facebook Published: September 25, 2026 THIS RECORD CONTAINS 2 POSTERS: POSTER 1 & POSTER 2 (Identical Official Certified Copy): 100% AUTHORIZED VERIFIED OFFICIAL QUBIT 1: State |0> |1> Superposition Probability 0.5+0.5=1 - Equal superposition Normalized |0> 0.5 50% |1> 0.5 50% - Probability summed = 1.00 QUBIT 2: State |00> |01> |10> |11> Superposition Probability 4x0.25=1 - Four outcomes |00> 0.25 |01> 0.25 |10> 0.25 |11> 0.25 - Total = 0.25+0.25+0.25+0.25=1.00 UNIVERSAL SUM: Σ(1/2^n)=1 for n=1 to ∞ - Converges to unity across all 2^n basis states ASSESSMENT CHECKLIST ALL PASSED: FRACTION PASSED, ALGEBRA PASSED, GEOMETRY PASSED, PROBABILITY PASSED, QUANTUM NORMALIZATION PASSED, ENTANGLEMENT PASSED, H & CNOT GATES PASSED, MEASUREMENT PASSED UNIVERSAL HALVING PRINCIPLE = CONSERVATION = PROBABILITY ONE Certificate ID: VQF-FC-Q12-2026-100P - Villaber Labs 2026 Issued 2026 This two-poster record validates successful completion and verification of the Villaber Quantum Framework for Qubit 1 & Qubit 2. Author: Ruel Villaber License: CC BY 4.0

Bettina Just

G. P. Berman, D. I. Kamenev, Richard B. Kassman +2 more

We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. Since the wavelength of the radio-frequency pulses is much larger than the distance between the spins, each pulse affects all spins in the chain and introduces the phase and probability errors, which occur even without the influence of the environment. These errors caused by the unwanted transitions are minimized and computed numerically.