arXiv subjects

Harikrishnan K J

Publications and source records attributed to Harikrishnan K J.

4 recordsLinked to original sources

arXiv2026

A graph-aware bounded distance decoder for all stabilizer codes

We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph states. Using the graphical representation of the stabilizers and the syndromes, we constitute the bounded distance decoding as an adaptable generalization of maximum likelihood decoding, ensuring correction of all errors with weights upper bounded by a target weight. We show that strategic pruning associated with a feed-forward network structure of the graph can reduce the search space and subsequently the runtime of the designed decoder. We demonstrate satisfactory performance of the bounded distance decoder in the case of the optimal non-CSS codes up to distance $d=11$ subjected to the depolarizing error on all qubits, and near-optimal decoding for the color and the surface codes, both belonging to the CSS family, under the bit-flip errors on the qubits. We also develop an open-source library, QGDecoder, enabling the graph-aware bounded distance decoding of arbitrary stabilizer codes.

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arXiv2026

Scalable and deterministic Greenberger-Horne-Zeilinger state generation via graph states-assisted measurements

We propose a scalable and deterministic protocol for growing large multi-qubit states starting from two-qubit non-maximally entangled pure states, where the bipartite entanglement in the resultant state is higher than the maximum of the available entangled qubit-pairs. This is achieved via a truncation of the Hilbert space corresponding to a subsystem of qubits to a space that hosts a single qubit, brought about by a multi-qubit measurement assisted by the graph basis. We prove its equivalence to a repetitive two-qubit measurement-based protocol, and demonstrate realization of the required two-qubit measurement via a two-qubit parity measurement, thereby establishing the implementability of the protocol. We derive lower and upper bounds of the bipartite entanglement concentrated after a given number of rounds of measurements, where the entanglement of the available qubit-pairs are not-necessarily equal. We further discuss the effect of possible imperfections that may arise in the protocol, and its robustness towards such imperfections. We demonstrate the usefulness of our proposal by applying it to create generalized GHZ states on arbitrary number of qubits, thereby underlining the possibility of creating maximally entangled qubit pairs via qubit-local projection measurements.

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arXiv2026

Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries

We investigate the topological-to-non-topological quantum phase transitions (QPTs) occurring in the Kitaev code under local perturbations in the form of local magnetic field and spin-spin interactions of the Ising-type using fidelity susceptibility (FS) and entanglement as the probes. We assume the code to be embedded on the surface of a wide cylinder of height $M$ and circumference $D$ with $M\ll D$. We demonstrate a power-law divergence of FS across the QPT, and determine the quantum critical points (QCPs) via a finite-size scaling analysis. We verify these results by mapping the perturbed Kitaev code to the 2D Ising model with nearest- and next-nearest-neighbor interactions, and computing the single-site magnetization as order parameter using quantum Monte-Carlo technique. We also demonstrate a finite size odd-even dichotomy in the occurrence of the QPT in the Kitaev ladder with respect to the odd and even values of $D$, when the system is perturbed with only Ising interaction. Our results also indicate a higher robustness of the topological phase of the Kitaev code against local perturbations if the boundary is made open along one direction. We further consider a local entanglement witness operator designed specifically to capture a lower bound to the localizable entanglement on the vertical non-trivial loop of the code. We show that the first derivative of the expectation value of the witness operator exhibits a logarithmic divergence across the QPT, and perform the finite-size scaling analysis. We demonstrate similar behaviour of the expectation value of the appropriately constructed witness operator also in the case of locally perturbed color code with open boundaries.

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arXiv2026

Scaling of entanglement entropy and correlations in the variable-range extended Ising model

We study the two-point correlation functions and the bipartite entanglement in the ground state of the exactly-solvable variable-range extended Ising model of qubits in the presence of a transverse field on a one-dimensional lattice. We introduce the variation in the range of interaction by varying the coordination number, $\mathcal{Z}$, of each qubit, where the interaction strength between a pair of qubits at a distance $r$ varies as $\sim r^{-α}$. We show that the algebraic nature of the correlation functions is present only up to $r=\mathcal{Z}$, above which it exhibits short-range exponential scaling. We also show that at the critical point, the bipartite entanglement exhibits a power-law decrease ($\sim\mathcal{Z}^{-γ}$) with increasing coordination number irrespective of the partition size and the value of $α$ for $α>1$. We further consider a sudden quench of the system starting from the ground state of the infinite-field limit of the system Hamiltonian via turning on the critical Hamiltonian, and demonstrate that the long-time averaged bipartite entanglement exhibits a qualitatively similar variation ($\sim\mathcal{Z}^{-γ}$) with $\mathcal{Z}$.

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