arXiv subjects

Nirupam Basak

Publications and source records attributed to Nirupam Basak.

9 recordsLinked to original sources

arXiv2026

Noise-Resilient Quantum Evolution in Open Systems through Error-Correcting Frameworks

We analyze quantum state preservation in open quantum systems using quantum error-correcting (QEC) codes explicitly embedded in microscopic system-bath models. Rather than assuming abstract quantum channels, we consider multi-qubit registers coupled to bosonic thermal environments, derive a second-order master equation for the reduced dynamics, and use it to benchmark the five-qubit, Steane, and toric codes under local and collective noise. We compute state fidelities as functions of system-bath coupling strength, bath temperatures, and the number of correction cycles. In the low-temperature regime, repeated error correction with the five-qubit code significantly suppresses decoherence and relaxation for weak-to-moderate couplings. In the high-temperature regime, thermal excitations reduce the effectiveness of all codes, although within the parameter range studied, the five-qubit code still yields the highest fidelities among the three codes. For two-qubit Werner states, we identify a critical evolution time associated with an early-time crossover, before which the overhead of QEC does not compensate for the noise-induced degradation; this critical time increases with entanglement, reflecting the greater fragility of strongly entangled states. Overall, our results provide a microscopic master-equation-based framework for benchmarking QEC performance in realistic open-system environments and for assessing code behavior in near-term noisy quantum architectures.

quant-ph↗

arXiv2026

Faster Optimal Decoder for Graph Codes with a Single Logical Qubit

In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting the structural properties of the underlying graph states. Although distinct error patterns may yield the same syndrome, we demonstrate that the post-measurement state follows a well-defined structure determined by the projective syndrome measurement. Building on this idea, we introduce a hierarchical decoder in which each level can be solved in polynomial time. Additionally, this decoder achieves optimal decoding performance at the lower levels of the hierarchy. This strategy avoids the need for full maximum-likelihood decoding of graph codes. Numerical results illustrate the efficiency and effectiveness of the proposed approach.

quant-ph↗

arXiv2026

Hierarchical quantum decoders

Decoders are a critical component of fault-tolerant quantum computing. They must identify errors based on syndrome measurements to correct quantum states. While finding the optimal correction is NP-hard and thus extremely difficult, approximate decoders with faster runtime often rely on uncontrolled heuristics. In this work, we propose a family of hierarchical quantum decoders with a tunable trade-off between speed and accuracy while retaining guarantees of optimality. We use the Lasserre Sum-of-Squares (SOS) hierarchy from optimization theory to relax the decoding problem. This approach creates a sequence of Semidefinite Programs (SDPs). Lower levels of the hierarchy are faster but approximate, while higher levels are slower but more accurate. We demonstrate that even low levels of this hierarchy significantly outperform standard Linear Programming relaxations. Our results on rotated surface codes and honeycomb color codes show that the SOS decoder approaches the performance of exact decoding. We find that Levels 2 and 3 of our hierarchy perform nearly as well as the exact solver. We analyze the convergence using rank-loop criteria and compare the method against other relaxation schemes. This work bridges the gap between fast heuristics and rigorous optimal decoding.

quant-ph↗

arXiv2025

Evaluating Quantumness, Efficiency and Cost of Quantum Random Number Generators via Photon Statistics

This work presents two significant contributions from the perspectives of quantum random number generator (QRNG) manufacturers and users. For manufacturers, the conventional method of assessing the quantumness of single-photon-based QRNGs through mean and variance comparisons of photon counts is statistically unreliable due to finite sample sizes. Given the sub-Poissonian statistics of single photons, confirming the underlying distribution is crucial for validating a QRNG's quantumness. We propose a more efficient two-fold statistical approach to ensure the quantumness of optical sources with the desired confidence level. Additionally, we demonstrate that the output of QRNGs from exponential and uniform distributions exhibit similarity under device noise, deriving corresponding photon statistics and conditions for $ε$-randomness. From the user's perspective, the fundamental parameters of a QRNG are quantumness, efficiency (entropy and random number generation rate), and cost. Our analysis reveals that these parameters depend on three factors, namely, expected photon count per unit time, external reference cycle duration, and detection efficiency. A lower expected photon count enhances entropy but increases cost and decreases the generation rate. A shorter external reference cycle boosts entropy but must exceed a minimum threshold to minimize timing errors, with minor impacts on cost and rate. Lower detection efficiency enhances entropy and lowers cost but reduces the generation rate. Finally, to validate our results, we perform statistical tests like NIST, Dieharder, AIS-31, ENT etc. over the data simulated with different values of the above parameters. Our findings can empower manufacturers to customize QRNGs to meet user needs effectively.

quant-ph↗

arXiv2025

Approximate Dynamical Quantum Error-Correcting Codes

Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of noise types, they often require substantial resources, making them impractical for near-term quantum devices. Approximate quantum error correction provides an alternative by tailoring codes to specific noise environments, reducing resource demands while still maintaining noise-robustness. Dynamical codes, including Floquet codes, introduce a dynamic approach to quantum error correction, employing time-dependent operations to stabilize logical qubits. In this work, we combine the flexibility of dynamical codes with the versatility of approximate quantum error correction to offer a promising avenue for addressing dominant noise in quantum systems. We construct several approximate dynamical codes using the recently developed strategic code framework. As a special case, we recover the approximate static codes widely studied in the existing literature. By analyzing these approximate dynamical codes through semidefinite programming, we establish the uniqueness and robustness of the optimal encoding, decoding, and check measurements. We also develop a temporal Petz recovery map suited to approximate dynamical codes.

quant-ph↗

arXiv2025

Resource Reduction in Multiparty Quantum Secret Sharing of both Classical and Quantum Information under Noisy Scenario

Quantum secret sharing (QSS) enables secure distribution of information among multiple parties but remains vulnerable to noise. We analyze the effects of bit-flip, phase-flip, and amplitude damping noise on the multiparty QSS for classical message (QSSCM) and secret sharing of quantum information (SSQI) protocols proposed by Zhang et al. (Phys. Rev. A, 71:044301, 2005). To scale down these effects, we introduce an efficient quantum error correction (QEC) scheme based on a simplified version of Shor's code. Leveraging the specific structure of the QSS protocols, we reduce the qubit overhead from the standard 9 of Shor's code to as few as 3 while still achieving lower average error rates than existing QEC methods. Thus, our approach can also be adopted for other single-qubit-based quantum protocols. Simulations demonstrate that our approach significantly enhances the protocols' resilience, improving their practicality for real-world deployment.

quant-ph↗

arXiv2024

Improved Routing of Multiparty Entanglement over Quantum Networks

Effective routing of entanglements over a quantum network is a fundamental problem in quantum communication. Due to the fragility of quantum states, it is difficult to route entanglements at long distances. Graph states can be utilized for this purpose, reducing the need for long-distance entanglement routing by leveraging local operations. In this paper, we propose two graph state-based routing protocols for sharing GHZ states, achieving larger sizes than the existing works, for given network topologies. For this improvement, we consider tree structures connecting the users participating in the final GHZ states, as opposed to the linear configurations used in the earlier ones. For arbitrary network topologies, we show that if such a tree is balanced, it achieves a larger size than unbalanced trees. In particular, for grid networks, we show special constructions of the above-mentioned tree that achieve optimal results. Moreover, if the user nodes among whom the entanglement is to be routed are pre-specified, we propose a strategy to accomplish the required routing.

quant-ph↗

arXiv2020

Null Lagrangians in linear theories of micropolar type and few other generalizations of elasticity

In the context of linear theories of generalized elasticity including those for homogeneous micropolar media, quasicrystals, piezoelectric and piezomagnetic media, we explore the concept of null Lagrangians. For obtaining the family of null Lagrangians we employ the sufficient conditions of H. Rund. In some cases a non-zero null Lagrangian is found and the stored energy admits a split into a null Lagrangian and a remainder. However, the null Lagrangian vanishes whenever the relevant elasticity tensor obeys certain symmetry conditions which can be construed as an analogue of the Cauchy relations.

math-ph↗

arXiv2020

Null Lagrangians in Cosserat elasticity

In the framework of nonlinear theory of Cosserat elasticity, also called micropolar elasticity, we provide the complete characterization of null Lagrangians for three dimensional bodies as well as for shells. Using the Gibb's rotation vector for description of the microrotation, this task is possible by an application of a theorem stated by Olver and Sivaloganathan in `{the structure of null Lagrangians}' (Nonlinearity, {1}, 1988, pp. 389-398). A set of necessary and sufficient conditions is also provided for the elasticity tensors to correspond to a null Lagrangian in linearized micropolar theory.

math-ph↗