arXiv subjects

Mahdi Bayanifar

Publications and source records attributed to Mahdi Bayanifar.

4 recordsLinked to original sources

arXiv2026

Bounds in the Projective Unitary Group with Respect to Global Phase Invariant Metric

We consider a global phase-invariant metric in the projective unitary group PUn, relevant for universal quantum computing. We obtain the volume and measure of small metric ball in PUn and derive the Gilbert-Varshamov and Hamming bounds in PUn. In addition, we provide upper and lower bounds for the kissing radius of the codebooks in PUn as a function of the minimum distance. Using the lower bound of the kissing radius, we find a tight Hamming bound. Also, we establish bounds on the distortion-rate function for quantizing a source uniformly distributed over PUn. As example codebooks in PUn, we consider the projective Pauli and Clifford groups, as well as the projective group of diagonal gates in the Clifford hierarchy, and find their minimum distances. For any code in PUn with given cardinality we provide a lower bound of covering radius. Also, we provide expected value of the covering radius of randomly distributed points on PUn, when cardinality of code is sufficiently large. We discuss codebooks at various stages of the projective Clifford + T and projective Clifford + S constructions in PU2, and obtain their minimum distance, distortion, and covering radius. Finally, we verify the analytical results by simulation.

quant-ph↗

arXiv2025

Transversal Toffoli-gate in Hybrid-code System

We study the transversality of the Toffoli gate in a hybrid-code system that employs two quantum error correction codes with special structure. We find that a system using a triorthogonal code with its paired code supports a fully transversal implementation of the Toffoli gate. Through circuit-level analysis, we prove the transversality of the Toffoli operation in this system. Based on this hybrid-code framework, we propose a Toffoli state distillation protocol that does not rely on pre-distilled $\mathbf{T}$-gate magic states. In our approach, the Toffoli state is directly distilled layer by layer within the hybrid-code system using only transversal operations. Numerical simulations demonstrate that our method uses approximately 50\% fewer qubit resources than previously reported protocols.

quant-ph↗

arXiv2025

Low Overhead Universal Quantum Computation with Triorthogonal Codes

We study the use of triorthogonal codes for universal fault-tolerant quantum computation and propose two methods to circumvent the Eastin-Knill theorem, which prohibits any single quantum error-correcting code from supporting both universality and a transversal gate set. We show that our methods reduce the resource overhead compared with existing fault-tolerant protocols. We develop a simple fault-tolerant implementation of the logical Hadamard gate for triorthogonal codes by exploiting the fact that they have transversal controlled-Z (CZ) gates, resulting in a circuit with reduced overhead. We also introduce a procedure for generating a symmetric Calderbank-Shor-Steane code paired with a triorthogonal code, which allows CNOT and CZ gate transversality across the pair of codes. In addition, we present logical state teleportation circuits that transfer encoded states between the two codes, allowing all logical operations to be performed transversally. Our methods can be integrated into the Steane error correction framework without incurring additional resource cost. Finally, using the 15-qubit code as an example, we demonstrate that our protocols significantly reduce the gate overhead compared with other existing methods. These results highlight the potential of combining distinct code structures to achieve low-overhead, universal fault-tolerant quantum computation.

quant-ph↗

arXiv2024

On Transversality Across Two Distinct Quantum Error Correction Codes For Quantum Repeaters

In this paper, we investigate the transversality of pairs of CSS codes and their use in the second generation of quantum repeaters (QR)s. We show that different stations of quantum link can experience different errors. Considering this fact, we suggest to use different CSS codes in different stations. We also suggest to use $[[n, k]]$ codes with $k > 1$ as they are more efficient then codes with $k = 1$. We establish sufficient and necessary conditions for a pair of CSS codes to be non-local CNOT-transversal. We show that in contrast to the well known CNOT transversality which states that two CSS codes should be the same, less restrictive constraints are needed. Next, we establish sufficient and necessary conditions for a code pair to be CZ-transversal.

quant-ph↗