arXiv subjects

Kunal Pal

Publications and source records attributed to Kunal Pal.

At least 19 recordsLinked to original sources

arXiv2026

Loss-aware state space geometry for quantum variational algorithms

The natural gradient descent optimisation technique is an efficient optimising protocol for broad classes of classical and quantum systems that takes the underlying geometry of the parameter manifold into account by means of using either the Fisher information metric of the classical probability distribution function or the Fubini-Study tensor of the associated parametrised quantum states in the consequent update rules. Even though the natural gradient descent procedure utilises the geometry of the space of probability or states, it is, however, insensitive to the measure of parametrised distance on the space of possible outcomes when the corresponding optimising problem is considered for the expectation value of a classical or quantum observable with respect to the probability distribution or the quantum state. In this work, we introduce a generic optimising principle, where the intrinsic geometry of the space of outcomes has been taken into account suitably, either by using an ambient space construction with a base statistical manifold with the usual Fisher information metric (or the Fubini-Study tensor), where the loss hypersurface is embedded to, or by means of a first-principle construction from the overlap of nearby quantum states on the projective Hilbert space. This construction as well as a family of conformal variants yields a form of loss-aware natural gradient updates that rescale the effective step size while preserving the descent direction. We benchmark the resulting optimisers on variational quantum circuit examples and on a classical neural network task, finding that, while the standard natural gradient remains the most robust on average, the proposed conformal schemes can improve best-case convergence in favourable regimes.

quant-ph↗

arXiv2026

A phase space approach to the wavefunction spreading and operator growth in the Krylov basis

In the Wigner-Weyl phase space formulation of quantum mechanics, we analyse the problem of the spreading of an initial state or an initial operator under time evolution when described in terms of the Krylov basis. After constructing the phase space functions corresponding to the Krylov basis states generated by a Hamiltonian from a given initial state by using the Weyl transformation, we subsequently use them to cast the Krylov state complexity as an integral over the phase space in terms of the Wigner function of the time-evolved initial state, so that the contribution of the classical Liouville equation and higher-order quantum corrections to the Wigner function time evolution equation towards the Krylov state complexity can be identified. Next, we construct the double phase space functions associated with the Krylov basis for operators by using a suitable generalisation of the Weyl transformation applicable for superoperators, and use them to rewrite the Krylov operator complexity as an integral over the double phase space in terms of a generalisation of the usual Wigner function. These results, in particular, show that the complexity measures based on the expansion of a time-evolved state (or an operator) in the Krylov basis can be thought to belong to a general class of complexity measures constructed from the expansion coefficients of the time-dependent Wigner function in an orthonormal basis in the phase space, and help us to connect these complexity measures with measures of complexity of time evolved state based on harmonic expansion of the time-dependent Wigner function.

quant-ph↗

arXiv2025

Facile Salt-Assisted Hydrothermal Synthesis of Nanodiamonds from CHO Precursors: Atomic-Scale Mechanistic Insights

Hydrothermal synthesis offers an economical and scalable way to produce nanodiamonds under relatively mild, low-pressure and low-temperature conditions. However,its sustainability and the detailed mechanisms behind diamond formation in such environments are still not fully understood. In this work, we designed ten hydrothermal synthesis protocols using different CHO-based molecular precursors containing COOH and OH groups, such as organic acids, polyols, sugars, and polysaccharides.The reactions were carried out at 190 degrees Centigrade in chlorinated, strongly alkaline aqueous solutions with alkali and alkaline-earth metal ions. Using high-resolution transmission electron microscopy and X-ray photoelectron spectroscopy, we confirmed the presence of diamond-specific lattice planes and sp3-hybridized carbon structures. Our results show that the type of precursor, its molecular size, and the ionic composition of the solution play key roles in determining the defect patterns and polymorph distribution in the resulting nanodiamonds. Atomic-scale imaging showed both coherent and incoherent transitions from graphite to diamond, along with gradual lattice compression and complex twinning patterns. These observations provide direct insight into how interfacial crystallography and defect dynamics drive diamond formation in aqueous systems. Overall, the study positions hydrothermal synthesis as a sustainable, chemistry-driven, and tunable approach for creating nanodiamonds tailored for applications in quantum technologies, biomedicine, catalysis, and advanced materials.

cond-mat.mes-hall↗

arXiv2025

Exhaustive Generation of Pattern-Avoiding s-Words

The most well-known Gray code of permutations is plain changes. It was discovered in the 1600s by bell-ringers who wished to order the permutations of [n] by swaps (e.g., 123, 132, 312, 321, 231, 213 for n = 3). In other words, plain changes traces a Hamilton path in the permutohedron. In 2013 it was shown that plain changes can be generated by a greedy algorithm: swap the largest value. Algorithm J replaces the swap operation with the jump operation (which moves a larger digit past one or more smaller digits) and forms the basis of the wildly successful Combinatorial Generation via Permutation Languages series of papers. Here we further generalize this line of research to languages of s-words (i.e., multiset permutations). We generalize jumps to bumps, which moves a sequential run of the same larger digit past one or more smaller digits. Algorithm B greedily applies minimum-length bumps prioritized by largest value, then largest index, then rightward before leftward (e.g. 1122, 1221, 1212, 2112, 2121, 2211 for s = (2, 2)). We show that the algorithm works for s-word languages avoiding a wide variety of tame patterns. Specific applications include efficient algorithm for generating s-Stirling words (which avoid 121) and new Gray codes for various s-Catalan objects (which avoid 132 and 121). The former result leads to Hamilton paths in every s-permutahedron.

math.CO↗

arXiv2025

Generalised state space geometry in Hermitian and non-Hermitian quantum systems

One of the key features of information geometry in the classical setting is the existence of a metric structure and a family of connections on the space of probability distributions. The uniqueness of the Fisher--Rao metric and the duality of these connections is at the heart of classical information geometry. However, these features do not carry over straightforwardly to quantum systems, where a Hermitian inner product structure on the Hilbert space induces a metric on the complex projective space of pure states -- the Fubini-Study tensor, which is preserved under the unitary evolution. In this work, we explore how modifying the Hermitian tensor structure on the projective space may affect the geometry of pure quantum states, and whether such generalisations can be used to define dual connections with a direct correspondence to classical probability distribution functions, modified by the presence of a non-trivial phase. We show that it is indeed possible to construct a family of connections that are dual to each other in a generalised sense with respect to the real-valued sector of the Fubini--Study tensor. Using this biorthogonal formalism, we systematically classify the four types of tensors that can arise when the dynamics of a quantum system are governed by a non-Hermitian Hamiltonian, identifying both the complex-valued metric and the Berry curvature. Finally, we elucidate the role of the metric in a quantum natural gradient descent optimisation problem, generalised to the non-Hermitian case for a suitable choice of cost function.

quant-ph↗

arXiv2025

Geometry of quantum states in random matrix ensembles and the chaos-integrability transition

We consider the geometry of quantum states associated with random matrix Hamiltonians belonging to ensembles that exhibit an integrable-to-chaotic transition in terms of the nearest-neighbour energy level spacing distribution, focusing on the $\beta$-Gaussian ensembles with generic Dyson index. For the tridiagonal Gaussian $\beta$-ensemble, which shows chaos-to-integrability transition with varying Dyson index, we first calculate an analytical expression for the ensemble-averaged fidelity susceptibility for a two-by-two matrix representation of the Hamiltonian for generic values of the Dyson index, and show that it diverges as the total Hamiltonian, which is the sum of a diagonal matrix with independent elements and a tridiagonal $\beta$-matrix, goes over to the integrable phase. Next, for large-dimensional matrices, we numerically compute the fidelity susceptibility and the quantum metric tensor, respectively, for a one-parameter and a two-parameter class of Hamiltonians that we construct from the $\beta$-ensemble, and find scaling relations of these quantities for chaotic and integrable phases. We also consider variations of the $\beta$-ensemble, such as the one that preserves the rotational invariance of the ensemble, and compute the relevant ensemble-averaged fidelity susceptibility to show that it has similar features as the tridiagonal ensemble in the integrable as well as the chaotic phase, thereby establishing the universality of these properties. Finally, the presence of non-vanishing non-diagonal elements, which arises due to the rotational non-invariance of the $\beta$-ensembles, is a specific feature of the corresponding metric tensor, and we use this to illuminate the difference between the quantum state space geometry of these ensembles and the rotationally invariant ones, such as the classical Gaussian ensembles.

quant-ph↗

arXiv2024

Statistics and Complexity of Wavefunction Spreading in Quantum Dynamical Systems

We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability distribution of the results of measurements of this spreading operator at a certain instant of time, and compute the characteristic function of this distribution. We show that the moments of this characteristic function are related to the so-called generalised spread complexities, and obtain expressions for them in several cases when the Hamiltonian is an element of a Lie algebra. Furthermore, by considering a continuum limit of the Krylov basis, we show that the generalised spread complexities of higher orders have a peak in the time evolution for a random matrix Hamiltonian belonging to the Gaussian unitary ensemble. We also obtain an upper bound on the change in generalised spread complexity at an arbitrary time in terms of the operator norm of the Hamiltonian and discuss the significance of these results.

quant-ph↗

arXiv2024

Dynamical interiors of Black-Bounce spacetimes

Using the Israel-Darmois junction conditions, we obtain a class of regular dynamical interiors to the recently proposed black-bounce spacetimes which regularises the Schwarzschild singularity by introducing a regularisation parameter. We show that a regularised Friedmann-Lemaitre-Robertson-Walker like interior geometry can not be matched smoothly with the exterior black-bounce spacetime through a timelike hypersurface, as there always exists a thin shell of non-zero energy-momentum tensor at the matching hypersurface. We obtain the expressions for the energy density and pressure of the thin shell energy-momentum tensor in terms of the regularisation parameter and derive an evolution equation for the scale factor of the interior geometry by imposing physical conditions on these components of the surface energy-momentum tensor. We also discuss the formation of the event horizon inside the interior in the case when the initial conditions are such that the situation describes a collapsing matter cloud. We elaborate upon the physical implications of these results.

gr-qc↗

arXiv2024

Quantum nonlinear effects in the number-conserving analogue gravity of Bose-Einstein condensates

We consider the quantum dynamics of Bose-Einstein condensates at absolute zero, and demonstrate that an analogue gravity model going beyond the standard linearized analogue gravity paradigm \`a la Unruh must take into account the backreaction of quasiparticle excitations onto the condensate background. This requires that one expands to second order in perturbation amplitude and thus takes the intrinsic nonlinearity of the theory into account. It is shown that, as a result, significant modifications of the standard paradigm occur. In particular, to obtain a fully Lorentz-covariant equation in curved spacetime for second-order perturbations, we demonstrate that it is necessary to introduce, to leading order in powers of the formal mean-field expansion parameter $N^{-1/2}$ (where $N$ is total particle number), a quantum-fluctuation-renormalized spacetime metric which substantially differs from the Unruh acoustic spacetime metric and, to subleading order $1/N$, two emergent vector fields and a mass term. Both the renormalized metric as well as the vector fields and the mass then keep track of the backreaction of the quasiparticles onto the condensate up to the order in powers of $N^{-1/2}$ considered. Finally, we apply our formalism to an analogue-cosmological Friedmann-Lema\^{i}tre-Robertson-Walker metric and establish its renormalized form due to the quantum many-body backreaction exerted by the excitation cloud.

gr-qc↗

arXiv2024

Time-dependent Hamiltonians and Geometry of Operators Generated by Them

We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we calculate the bi-invariant cost associated with these time-dependent Hamiltonians by suitably regularising their norms and obtain analytical expressions of the costs for several well-known time-dependent quantum mechanical systems. Specifically, we show that an equivalence exists between the total costs of obtaining an operator through time evolution generated by a unit mass harmonic oscillator whose frequency depends on time, and a harmonic oscillator whose both mass and frequency are functions of time. These results are illustrated with several examples, including a specific smooth quench protocol where the comparison of time variation of the cost with other information theoretic quantities, such as the Shannon entropy, is discussed.

quant-ph↗

arXiv2023

Complexity in two-point measurement schemes

We show that the characteristic function of the probability distribution associated with the change of an observable in a two-point measurement protocol with a perturbation can be written as an auto-correlation function between an initial state and a certain unitary evolved state by an effective unitary operator. Using this identification, we probe how the evolved state spreads in the corresponding conjugate space, by defining a notion of the complexity of the spread of this evolved state. For a sudden quench scenario, where the parameters of an initial Hamiltonian (taken as the observable measured in the two-point measurement protocol) are suddenly changed to a new set of values, we first obtain the corresponding Krylov basis vectors and the associated Lanczos coefficients for an initial pure state, and obtain the spread complexity. Interestingly, we find that in such a protocol, the Lanczos coefficients can be related to various cost functions used in the geometric formulation of circuit complexity, for example the one used to define Fubini-Study complexity. We illustrate the evolution of spread complexity both analytically, by using Lie algebraic techniques, and by performing numerical computations. This is done for cases when the Hamiltonian before and after the quench are taken as different combinations of chaotic and integrable spin chains. We show that the complexity saturates for large values of the parameter only when the pre-quench Hamiltonian is chaotic. Further, in these examples we also discuss the important role played by the initial state which is determined by the time-evolved perturbation operator.

quant-ph↗

arXiv2023

Spread complexity evolution in quenched interacting quantum systems

We analyse time evolution of spread complexity (SC) in an isolated interacting quantum many-body system when it is subjected to a sudden quench. The differences in characteristics of the time evolution of the SC for different time scales is analysed, both in integrable and chaotic models. For a short time after the quench, the SC shows universal quadratic growth, irrespective of the initial state or the nature of the Hamiltonian, with the time scale of this growth being determined by the local density of states. The characteristics of the SC in the next phase depend upon the nature of the system, and we show that depending upon whether the survival probability of an initial state is Gaussian or exponential, the SC can continue to grow quadratically, or it can show linear growth. To understand the behaviour of the SC at late times, we consider sudden quenches in two models, a full random matrix in the Gaussian orthogonal ensemble, and a spin-1/2 system with disorder. We observe that for the full random matrix model and the chaotic phase of the spin-1/2 system, the complexity shows linear growth at early times and saturation at late times. The full random matrix case shows a peak in the intermediate time region, whereas this feature is less prominent in the spin-1/2 system, as we explain.

quant-ph↗

arXiv2023

Geodesically completing regular black holes by the Simpson-Visser method

Regular black holes are often geodesically incomplete when their extensions to negative values of the radial coordinate are considered. Here, we propose to use the Simpson-Visser method of regularising a singular spacetime, and apply it to a regular solution that is geodesically incomplete, to construct a geodesically complete regular solution. Our method is generic, and can be used to cure geodesic incompleteness in any spherically symmetric static regular solution, so that the resulting solution is symmetric in the radial coordinate. As an example, we illustrate this procedure using a regular black hole solution with an asymptotic Minkowski core. We study the structure of the resulting metric, and show that it can represent a wormhole or a regular black hole with a single or double horizon per side of the throat. Further, we construct a source Lagrangian for which the geodesically complete spacetime is an exact solution of the Einstein equations, and show that this consists of a phantom scalar field and a nonlinear electromagnetic field. Finally, gravitational lensing properties of the geodesically complete spacetime are briefly studied.

gr-qc↗

arXiv2023

A rotating modified JNW spacetime as a Kerr black hole mimicker

The Event Horizon Telescope has recently observed the images and shadows of the compact objects M87$^*$ and Sgr A$^*$ at the centres of the galaxies Messier 87 and Milky Way. This has opened up a new window in observational astronomy to probe and test gravity and fundamental physics in the strong-field regime. In this paper, we consider a rotating version of a modified Janis-Newman-Winicour metric, study its shadow, and constrain the metric parameters using the observed shadows of M87$^*$ and Sgr A$^*$. Depending on parameter values, the spacetime metric represents either a naked singularity or a wormhole. We find that the naked singularity case is not consistent with observations, as it casts a shadow which is much smaller than the observed ones. On the other hand, the shadow formed by the wormhole branch, depending on the parameter values, is consistent with the observations. We put constraints on the wormhole throat radius by comparing the shadow with the observed ones of M87$^*$ and Sgr A$^*$.

gr-qc↗

arXiv2023

Time evolution of spread complexity and statistics of work done in quantum quenches

We relate the probability distribution of the work done on a statistical system under a sudden quench to the Lanczos coefficients corresponding to evolution under the post-quench Hamiltonian. Using the general relation between the moments and the cumulants of the probability distribution, we show that the Lanczos coefficients can be identified with physical quantities associated with the distribution, e.g., the average work done on the system, its variance, as well as the higher order cumulants. In a sense this gives an interpretation of the Lanczos coefficients in terms of experimentally measurable quantities. Consequently, our approach provides a way towards understanding spread complexity, a quantity that measures the spread of an initial state with time in the Krylov basis generated by the post quench Hamiltonian, from a thermodynamical perspective. We illustrate these relations with two examples. The first one involves quench done on a harmonic chain with periodic boundary conditions and with nearest neighbour interactions. As a second example, we consider mass quench in a free bosonic field theory in $d$ spatial dimensions in the limit of large system size. In both cases, we find out the time evolution of the spread complexity after the quench, and relate the Lanczos coefficients with the cumulants of the distribution of the work done on the system.

quant-ph↗

arXiv2022

Conformal Fisher information metric with torsion

We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate between probability distribution functions that otherwise have the same scalar curvature and hence define similar geometries. In the context of thermodynamic geometry, our construction gives rise to a new scalar - the torsion scalar defined on the manifold, while retaining known physical features related to other scalar quantities. We analyse this in the context of the Van der Waals and the Curie-Weiss models. In both cases, the torsion scalar has non trivial behaviour on the spinodal curve.

physics.class-ph↗

arXiv2022

Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model

We use the spread complexity of a time evolved state after a sudden quantum quench in the Lipkin-Meshkov-Glick (LMG) model prepared in the ground state as a probe of quantum phase transition when the system is quenched towards the critical point. By studying the growth of the effective number of elements of the Krylov basis, those contribute to the spread complexity more than a preassigned cut off, we show how the two phases of the LMG model can be distinguished. We also explore the time evolution of spread entropy after both non-critical and critical quenches. We show that the sum contributing to the spread entropy converges slowly in the symmetric phase of the LMG model compared to that of the broken phase, and for a critical quench, the spread entropy diverges logarithmically at late times.

hep-th↗

arXiv2022

Regularising the JNW and JMN naked singularities

We extend the method of Simpson and Visser (SV) of regularising a black hole spacetime, to cases where the initial metric represents a globally naked singularity. We choose two particular geometries, the Janis-Newman-Winicour (JNW) metric representing the solution of an Einstein-scalar field system, and the Joshi-Malafarina-Narayan (JMN) metric that represents the asymptotic equilibrium configuration of a collapsing star supported by tangential pressures as the starting configuration. We illustrate several novel features for the modified versions of the JNW and JMN spacetimes. In particular, we show that, depending on the values of the parameters involved the modified JNW metric may represents either a two way traversable wormhole or it may retain the original naked singularity. On the other hand, the SV modified JMN geometry is always a wormhole. Particle motion and observational aspects of these new geometries are investigated and are shown to posses interesting features. We also study the quasinormal modes of different branches of the regularised spacetime and explore their stability properties.

gr-qc↗