arXiv subjects

Garima Rajpoot

Publications and source records attributed to Garima Rajpoot.

9 recordsLinked to original sources

arXiv2026

Lax pairs and $r$-matrices for some two-dimensional isotropic oscillators

This paper concerns Lax pairs for circularly symmetric harmonic, Fock-Darwin-type and quartic anharmonic oscillators in two dimensions. Although the 2d isotropic harmonic oscillator is bi-Hamiltonian, its recursion operator does not lead to a Lax pair, nor do we obtain such a pair by taking a limit of the harmonic Calogero model. On the other hand, we show that this superintegrable harmonic oscillator admits a $4 \times 4$ block-form Lax pair with spectral parameter giving two conserved mode energies in involution and a corresponding dynamical $r$-matrix. Interestingly, we also find $2 \times 2$ Lax pairs with spectral parameter that give all three independent conserved quantities satisfying a nonabelian Poisson algebra, thereby providing a simple example of a Lax pair whose conserved quantities are not all in involution. Next, we construct a family of $su(2)$ Lax pairs and $r$-matrices for the quadratic+quartic isotropic anharmonic oscillator. This is then extended to an isotropic oscillator with a rotational energy, which may be viewed as the Fock-Darwin oscillator with a quartic potential. With a change of variables, these Lax pairs and $r$-matrices also apply to the Rajeev-Ranken model, although its noncanonical Poisson structure is distinct from that of the anharmonic oscillator.

nlin.SI↗

arXiv2025

Quantum Simulation of Collective Neutrino Oscillations in Dense Neutrino Environment

Inside dense neutrino gases, such as neutron star mergers or core-collapse supernovae, collective neutrino effects cause the transformation of one neutrino flavour into another. Due to strong neutrino self-interactions in these environments, there is prevalence of flavour swapping. Considering these environments to be isotropic and homogeneous, we present a study of collective neutrino oscillations by simulating such a system on a noisy quantum simulator (Qiskit AerSimulator) and a quantum processor (ibm\_brisbane). We model the effective Hamiltonian governing neutrino interactions and by applying the Trotter-Suzuki approximation, decompose it into a tractable form suitable for quantum circuit implementation of the time-evolution propagator. Encoding the neutrino state for a system of two- and three-neutrinos onto qubits, we compute the time evolution of the inversion probability relative to the initial product state. Furthermore, we present quantum circuits to evaluate the concurrence as a measure of entanglement between the neutrinos.

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arXiv2025

Quantum circuits for simulating neutrino propagation in matter

Quantum simulation of particle phenomena is a rapidly advancing field of research. With the widespread availability of quantum simulators, a given quantum system can be simulated in numerous ways, offering flexibility in implementation and exploration. Here, we perform quantum simulation of neutrino propagation in matter, a phenomenon that plays a crucial role in neutrino oscillations. We present quantum circuits with novel gate arrangements to simulate neutrino propagation in both constant and varying matter density profiles. The oscillation probabilities are determined by encoding and measuring the qubit states in the neutrino flavor basis, showing excellent agreement with theoretical predictions.

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arXiv2024

Controlling and engineering a quantum state in a multi-qubit system employing the quantum Zeno effect

Controlling quantum jumps is crucial for reliable quantum computing. In this work, we demonstrate how the quantum Zeno effect can be applied to a two qubit system interacting with an ancilla which is a component of surface code architecture used to control undesired transitions. Further, we show that by designing the interaction and tuning measurement frequency, the quantum Zeno effect can be used to achieve the desired target state in both single-qubit and two qubit systems.

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arXiv2023

Quantum error correction beyond the toric code: dynamical systems meet encoding

We construct surface codes corresponding to genus greater than one in the context of quantum error correction. The architecture is inspired by the topology of invariant integral surfaces of certain non-integrable classical billiards. Corresponding to the fundamental domains of rhombus and square torus billiard, surface codes of genus two and five are presented here. There is significant improvement in encoding rates and code distance, in addition to immunity against noise.

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arXiv2023

Quantum Zeno effect: a qutrit controlled by a qubit

For a three-level system monitored by an ancilla, we show that quantum Zeno effect can be employed to control quantum jump for error correction. Further, we show that we can realize cNOT gate, and effect dense coding and teleportation. We believe that this work paves the way to generalize the control of a qudit.

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arXiv2023

A Genus-two Surface Code

We construct a double-toric surface code by exploiting the planar tessellation using a rhombus-shaped tile. With n data qubits, we are able to encode at least n/3 logical qubits or quantum memories. By a suitable arrangement of the tiles, the code achieves larger distances, leading to significant error-correcting capability. We demonstrate the robustness of the logical qubits thus obtained in the presence of external noise. We believe that the optimality of the code presented here will pave the way for design of efficient scalable architectures.

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arXiv2022

The tunable 0-\texorpdfstring{$π$}{Lg} qubit: Dynamics and Relaxation

We present a systematic treatment of a 0-\texorpdfstring{$π$}{Lg} qubit in the presence of a time-dependent external flux. A gauge-invariant Lagrangian and the corresponding Hamiltonian is obtained. The effect of the flux noise on the qubit relaxation is obtained using perturbation theory. Under a time-dependent drive of sinusoidal form, the survival probability, and transition probabilities have been studied for different strengths and frequencies. The driven qubit is shown to possess coherent oscillations among two distinct states for a weak to moderate strength close to resonant frequencies of the unperturbed qubit. The parameters can be chosen to prepare the system in its ground state. This feature paves the way to prolong the lifetime by combining ideas from weak measurement and quantum Zeno effect. We believe that this is an important variation of a topologically protected qubit which is tunable.

quant-ph↗

arXiv2022

Qubit control using quantum Zeno effect: Action principle approach

We employ the stochastic path-integral formalism and action principle for continuous quantum measurements - the Chantasri-Dressel-Jordan (CDJ) action formalism [1, 2] - to understand the stages in which quantum Zeno effect helps control the states of a simple quantum system. The detailed dynamics of a driven two-level system subjected to repeated measurements unravels a myriad of phases, so to say. When the detection frequency is smaller than the Rabi frequency, the oscillations slow down, eventually coming to a halt at an interesting resonance when measurements are spaced exactly by the time of transition between the two states. On the other hand, in the limit of large number of repeated measurements, the dynamics organizes itself in a rather interesting way about two hyperbolic points in phase space whose stable and unstable directions are reversed. Thus, the phase space flow occurs from one hyperbolic point to another, in different ways organized around the separatrices. We believe that the systematic treatment presented here paves the way for a better and clearer understanding of quantum Zeno effect in the context of quantum error correction.

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