arXiv subjects

Kartiek Agarwal

Publications and source records attributed to Kartiek Agarwal.

At least 19 recordsLinked to original sources

arXiv2026

Associative Memory for Quantum Entangled States

We generalize the canonical Hopfield model of associative memory, which stores classical states of individual spins, to store entangled quantum states. The construction is based on truncated projector-sum Hamiltonian, and we explicitly consider a special case that stores dimer singlet coverings of a spin-1/2 system. We analyze the stability of the stored memories and find that the capacity -- the number of stable patterns -- scales faster with the system size than one would expect from a naive analogy with the standard Hopfield model, suggesting a possible quantum advantage.

quant-ph↗

arXiv2026

Visualizing Chiral Edge Modes in Twisted Cuprate Superconductors via Scanning-Probe Quantum Sensing

Recently, unconventional superconductivity hosted by twisted van der Waals (vdW) heterostructures has received immense interest due to the exotic pairing symmetry, electronic interactions and nontrivial topological nature that are naturally relevant to the fast-advancing quantum technologies. Here, we report scanning-probe quantum sensing of nanoscale electromagnetic behaviors of twisted vdW cuprate superconductors. Using single-spin relaxometry, we directly visualize edge modes spontaneously formed in twisted Bi2Sr2CaCu2O8+x (BSCCO). By investigating temperature dependent variations of edge-state-induced quantum spin relaxation, we experimentally evaluate the magnitude of nontrivial topological band gap opened at nodal points in twisted BSCCO and its critical temperature behaviors under different twist angles. We further observe alternating chiral domains defined by edge modes, exploring experimental signatures of in-plane magnetic field-induced topology in 45° twisted BSCCO. Our results advance the current understanding of twisted vdW nodal superconductors, presenting an appealing high-temperature topological superconducting material platform for cutting-edge quantum innovation.

cond-mat.mes-hall↗

arXiv2026

Learning shadows to predict quantum ground state correlations

We introduce a variational scheme inspired by classical shadow tomography to compute ground state correlations of quantum spin Hamiltonians. Shadow tomography allows for efficient reconstruction of expectation values of arbitrary observables from a bag of repeated, randomized measurements, called snapshots, on copies of the state $ρ$. The prescription allows one to infer expectation values of $M$ $k-$local observables to accuracy $ε$ using just $N \sim 3^k \text{log}M /ε^2$ snapshots when measurements are performed in locally random bases. Turning this around, a bag of snapshots can be considered an efficient representation of the state $ρ$, particularly for estimating low-weight observables, such as terms in a local Hamiltonian needed to estimate the energy. Inspired by this, we consider a variational scheme wherein a bag of $N$ parametrized snapshots is used to represent the putative ground state of a desired local spin Hamiltonian and optimized to lower the energy with respect to it. Additional constraints in the form of positivity of reduced density matrices, motivated by work in quantum chemistry, are employed to ensure compatibility of the predicted correlations with the underlying Hilbert space. Despite the limited set of imposed constraints, we show that the optimized ensemble of snapshots yields fairly accurate estimates of the ground state energy and other correlations, including those that do not appear in the set of constraints used in optimization.

quant-ph↗

arXiv2026

Majorana edge modes in isolated wires

Topological superconductors are believed to host exotic quasiparticle excitations known as Majorana zero-modes (MZMs), with much of the evidence based on BCS mean-field theory. The direct application of mean-field arguments is tenuous in finite, isolated systems relevant in some experiments. Here, we develop a new correlation-based method for identifying MZMs in interacting, number-conserving systems. Using DMRG, we study fermion number-conserving models with long-range interactions, which under periodic boundary conditions exhibit robust topological and non-topological superconductivity, tuned by the strength of interaction [1]. We find evidence that, on the topological side, Majorana edge modes appear in open chains, manifesting as the vanishing of the energy splitting between odd- and even-parity ground states with increasing system size. Additionally, off-diagonal two-point correlation functions show nonlocal, parity-dependent edge effects. These correlations reveal the spatial structure of Majorana modes in the many-body wavefunction. We show that the correlation diagnostic applies broadly, including to short-range interacting models, where topological superconductivity is more fragile due to the absence of a bulk excitation gap.

cond-mat.str-el↗

arXiv2026

Flat-band formation and chiral superconductivity in driven topological insulators

We demonstrate that circularly polarized light can be used to Floquet-engineer nearly flat or Mexican-hat like electronic bands on the surface of three-dimensional topological insulators (3D TIs), which under suitable conditions, can support topological superconductivity via purely repulsive Coulomb interactions. The driving acts not merely by gapping out the Dirac cone on the surface of the 3D TI, but can be used to diminish, and even flip in sign, the intrinsic curvature of the surface state dispersion away from the Dirac point. Using parameters for canonical 3D TIs, we find that the flat band limit is attained for reasonable electric fields and the bands realized by changing the strength of the driving field have a similar energetic and spatial profile to those obtained in rhombohedral graphene under varying displacement field, where the case for superconductivity with purely repulsive interactions has recently been made. We find that, with the aid of appropriately placed screening metallic gate, one can obtain $T_c \sim 7 $K in this setup while avoiding Wigner crystallization for low electron densities in the range of $10^{11}-10^{12}/\text{cm}^2$.

cond-mat.str-el↗

arXiv2026

Quantum-stabilized patterns in a vector Hopfield network

We introduce the quantum vector Hopfield network, in which patterns are formed by orientations of quantum vector spins; quantum dynamics arise intrinsically from the non-commutativity of the spin operators. We derive the equations of state and the phase diagrams for this network as well as its classical counterpart. We find that quantum fluctuations, surprisingly, stabilize the stored patterns. Both the critical retrieval temperature and the target pattern overlap are enhanced relative to the classical network. Additionally, we find that this enhancement grows with pattern loading up to network capacity. We interpret this effect as an analog of quantum order-by-disorder, a mechanism by which quantum fluctuations promote the formation of ordered phases. These findings offer a new route to quantum-enhanced associative memory.

quant-ph↗

arXiv2026

Learning quantum ground states in the space of measurement outcomes

We investigate variational learning of quantum many-body ground states directly in measurement space using autoregressive neural networks. In particular, we represent quantum states via probability distributions of outcomes over a symmetric informationally complete positive operator-valued measure (SIC-POVM). The probability distribution is encoded in the parameters of an autoregressive neural-network-based on gated recurrent units (GRUs). Ground states are obtained by gradient descent that updates the probability distribution to minimize the energy with respect to a given Hamiltonian, while enforcing positivity constraints that ensure that the distribution of measurement outcomes correspond to a physical quantum state. We analyze the role of constraint enforcement (hierarchy of positivity conditions), variety of neural network architectures (multiple layers, dilation, and modifications of input data) in determining the success of this approach. We benchmark our approach on one-dimensional transverse-field Ising model and the Heisenberg model, along with gapping fields, for system sizes up to L=128, illustrating its efficacy across a wide variety of models.

quant-ph↗

arXiv2026

Shuttling Majorana zero modes in disordered and noisy topological superconductors

The braiding of Majorana zero modes (MZMs) forms the fundamental building block for topological quantum computation. Braiding protocols which involve the physical exchange of MZMs are typically envisioned on a network of topological superconducting wires. An essential component of these protocols is the transport of MZMs, which can be performed by using electric gates to locally tune sections of the wire between topologically trivial and non-trivial phases. In this work, we numerically simulate this transport by tuning a single section of a superconducting wire which contains either disorder (uncorrelated and correlated) or noise. We focus on the impact of these additional effects on the diabatic error, which describes unwanted transitions between the ground state and excited states. We show that the behavior of the average diabatic error is predominantly controlled by the statistics of the minimum bulk energy gap which is suppressed in the presence of disorder. The increase in diabatic error can be several orders of magnitude and is most deleterious when the disorder correlation length is a finite fraction of the transport distance and negligible when these lengths are far apart. In the presence of noise, the diabatic error is significantly enhanced due to optical transitions which depend on the minimum bulk energy gap as well as the frequency modes present in the noise. The results presented here serve to further characterize the diabatic error in disordered and noisy settings, which are important considerations in practical implementations of physical braiding schemes.

cond-mat.mes-hall↗

arXiv2026

Majorana zero modes in superconductor-magnet heterostructures with d-wave order

Magnetic skyrmions in proximity to superconductors offer a route to engineering topological superconductivity due to the synthetic spin-orbit coupling engendered by the spin twist of the skyrmion texture. Previous theoretical works show that this leads to Majorana zero modes (MZMs) in skyrmion-vortex pairs for s-wave superconductors. Here we investigate this mechanism in fully gapped d+is and d+id superconductors. We find the surprising result that while stable MZMs are found in large parts of the phase diagram, strongly enhanced d-wave pairing or stronger skyrmion-induced spin twisting can in fact destroy topology unlike in s-wave superconductors. This effect can be understood from the non-trivial spatial structure of the d-wave pairing, and mixing of odd and even angular-momentum pairing channels in a rotated frame which untwists the skyrmion texture. Our results inform the feasibility of realizing MZMs with unconventional superconductors in such heterostructures.

cond-mat.supr-con↗

arXiv2025

Nanoscale defects as probes of time reversal symmetry breaking

Nanoscale defects such as Nitrogen Vacancy (NV) centers can serve as sensitive and non-invasive probes of electromagnetic fields and fluctuations from materials, which in turn can be used to characterize these systems. Here we specifically discuss how NV centers can probe time-reversal symmetry breaking (TRSB) phenomena in low-dimensional conductors. We argue that the difference in relaxation rates $Γ_{\pm \hat{z}}$ of NV centers starting from $m = \pm 1$ spin states to the ground state with $m = 0$ directly probes TRSB. The effect arises from the difference in the fluctuation spectrum of left and right-polarized electromagnetic fields emanating from such materials. In the quantum Hall setting, the NV center experiences (nearly zero) large additional contribution to its relaxation due to the presence of the material when its magnetic dipole (anti-) aligns with the external field. More generally, the difference in the relaxation rates is sensitive to the imaginary part of the wave-vector dependent Hall conductivity. We argue that this can be used to determine the Hall viscosity, which can potentially distinguish candidate fractional quantum Hall states and be used to infer the pairing angular momentum in TRSB superconductors. For the latter, we consider specifically the case of TRSB in stacked twisted Bismuth strontium calcium copper oxide (BSCCO) flakes, which have recently been investigated experimentally and are suggested to exhibit TRSB. We show that the average relaxation rate $\left[Γ_{+\hat{z}} + Γ_{-\hat{z}}\right]$ near such a system exhibits a Hebel-Slichter like enhancement below $T_c$. The difference $Γ_{+\hat{z}} - Γ_{-\hat{z}}$ also inherits this peak but is only non-zero for $T < T_c$ and only in a chiral d-wave superconductor. We provide concrete estimates for observing this effect.

cond-mat.mes-hall↗

arXiv2024

A theory of Stimulated and Spontaneous Axion Scattering

We present a theory for nonlinear, resonant excitation of dynamical axions by counter-propagating electromagnetic waves in materials that break both $\mathcal{P}$ and $\mathcal{T}$ symmetries. We show that dynamical axions can mediate an exponential growth in the amplitude of the lower frequency (Stokes) beam. We also discuss spontaneous generation of a counter-propagating Stokes mode, enabled by resonant amplification of quantum and thermal fluctuations in the presence of a single pump laser. Remarkably, the amplification can be orders of magnitude larger than that obtained via stimulated Brillouin and Raman scattering processes, and can be modulated with the application of external magnetic fields, making stimulated axion scattering promising for optoelectronics applications.

cond-mat.str-el↗

arXiv2024

Majorana braiding in superconductors with fixed total number of particles

One-dimensional topological superconductors treated at the mean-field level host zero-energy edge Majorana modes, which encode topological degeneracy of their ground states. Geometric manipulations (braiding) of multiple wires can be used to induce topologically robust transformations within the ground state subspace. The mean-field ground states do not have a definite number of particles and thus cannot describe an isolated system. Projecting such states onto fixed particle number gives a very good approximation to the true ground state of an isolated superconductor. In previous work, we showed that so projecting the prototypical Kitaev wave function of a single wire retains key features of the mean-field description, such as the zero-energy single-particle spectral peaks near the wire edges. Here we consider the case of multiple wires with conserved total charge. Again, using the projected Kitaev wave functions as the template, we identify the many-body counterparts of the mean-field topologically degenerate ground states. We then demonstrate how the quantum gates equivalent to braiding of Majorana zero modes can be implemented, albeit with reduced protection from noise and disorder.

cond-mat.str-el↗

arXiv2024

Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model

The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected topological insulator. Coupling it non-perturbatively to local thermal environments, either through the intercell or the intracell fermion tunneling elements, modifies the topological window. To understand this effect, we employ the recently developed reaction-coordinate polaron transform (RCPT) method, which allows treating system-bath interactions at arbitrary strengths. The effective system Hamiltonian, which is obtained via the RCPT, exposes the impact of the baths on the SSH chain through renormalization of tunneling elements and the generation of many-body interaction terms. By performing exact diagonalization and computing the ensemble geometric phase, a topological invariant applicable even to systems at finite temperature, we distinguish the trivial band insulator (BI) from the topological insulator (TI) phases. Furthermore, through the RCPT mapping, we are able to pinpoint the main mechanism behind the extension of the parameter space for the TI or the BI phases (depending on the coupling scheme, intracell or intercell), which is the bath-induced, dimerized, many-body interaction. We also study the effect of on-site staggered potentials on the SSH phase diagram, and discuss extensions of our method to higher dimensions.

cond-mat.mes-hall↗

arXiv2024

Spatiotemporal Quenches for Efficient Critical Ground State Preparation in Two-Dimensional Quantum Systems

Quantum simulators have the potential to shed light on the study of quantum many-body systems and materials, offering unique insights into various quantum phenomena. While adiabatic evolution has been conventionally employed for state preparation, it faces challenges when the system evolves too quickly or the coherence time is limited. In such cases, shortcuts to adiabaticity, such as spatiotemporal quenches, provide a promising alternative. This paper numerically investigates the application of spatiotemporal quenches in the two-dimensional transverse field Ising model with ferromagnetic interactions, focusing on the emergence of the ground state and its correlation properties at criticality when the gap vanishes. We demonstrate the effectiveness of these quenches in rapidly preparing ground states in critical systems. Our simulations reveal the existence of an optimal quench front velocity at the emergent speed of light, leading to minimal excitation energy density and correlation lengths of the order of finite system sizes we can simulate. These findings emphasize the potential of spatiotemporal quenches for efficient ground state preparation in quantum systems, with implications for the exploration of strongly correlated phases and programmable quantum computing.

quant-ph↗

arXiv2024

Optimal twirling depths for shadow tomography in the presence of noise

The classical shadows protocol is an efficient strategy for estimating properties of an unknown state $ρ$ using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from some ensemble and measuring the twirled state in a fixed basis. It was recently shown that for computing local properties, optimal sample complexity (copies of the state required) is remarkably achieved for unitaries drawn from shallow depth circuits composed of local entangling gates, as opposed to purely local (zero depth) or global twirling (infinite depth) ensembles. Here we consider the sample complexity as a function of the depth of the circuit, in the presence of noise. We find that this noise has important implications for determining the optimal twirling ensemble. Under fairly general conditions, we i) show that any single-site noise can be accounted for using a depolarizing noise channel with an appropriate damping parameter $f$; ii) compute thresholds $f_{\text{th}}$ at which optimal twirling reduces to local twirling for arbitrary operators and iii) $n^{\text{th}}$ order Renyi entropies ($n \ge 2$); and iv) provide a meaningful upper bound $t_{\text{max}}$ on the optimal circuit depth for any finite noise strength $f$, which applies to all operators and entanglement entropy measurements. These thresholds strongly constrain the search for optimal strategies to implement shadow tomography and can be easily tailored to the experimental system at hand.

quant-ph↗

arXiv2023

Signatures of Majorana Zero-Modes in an isolated one-dimensional superconductor

We examine properties of the mean-field wave function of the one-dimensional Kitaev model supporting Majorana Zero Modes (MZMs) \emph{when restricted} to a fixed number of particles. Such wave functions can in fact be realized as exact ground states of interacting number-conserving Hamiltonians and amount to a more realistic description of the finite isolated superconductors. Akin to their mean-field parent, the fixed-number wave functions encode a single electron spectral function at zero energy that decays exponentially away from the edges, with a localization length that agrees with the mean-field value. Based purely on the structure of the number-projected ground states, we construct the fixed particle number generalization of the MZM operators. They can be used to compute the edge tunneling conductance; however, notably the value of the zero-bias conductance remains the same as in the mean-field case, quantized to $2e^2/h$. We also compute the topological entanglement entropy for the number-projected wave functions and find that it contains a `robust' $\log(2)$ component as well as a logarithmic correction to the mean field result, which depends on the precise partitioning used to compute it. The presence of the logarithmic term in the entanglement entropy indicates the absence of a spectral gap above the ground state; as one introduces fluctuations in the number of particles, the correction vanishes smoothly.

cond-mat.supr-con↗

arXiv2023

Anomalous Electronic Transport in High Mobility Corbino Rings

We report low-temperature electronic transport measurements performed in two multi-terminal Corbino samples formed in GaAs/Al-GaAs two-dimensional electron gases (2DEG) with both ultra-high electron mobility ($\gtrsim 20\times 10^6$ $cm^2/Vs)$ and with distinct electron density of $1.7$ and $3.6\times 10^{11}~cm^{-2}$. In both Corbino samples, a non-monotonic behavior is observed in the temperature dependence of the resistance below 1~$K$. Surprisingly, a sharp {\it decrease} in resistance is observed with {\it increasing} temperature in the sample with lower electron density, whereas an opposite behavior is observed in the sample with higher density. To investigate further, transport measurements were performed in large van der Pauw samples having identical heterostructures, and as expected they exhibit resistivity that is monotonic with temperature. Finally, we discuss the results in terms of various lengthscales leading to ballistic and hydrodynamic electronic transport, as well as a possible Gurzhi effect.

cond-mat.mes-hall↗

arXiv2023

Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors

Topological quantum computing is based on the notion of braiding non-Abelian anyons, such as Majorana zero modes (MZMs), to perform gate operations. A crucial building block of these protocols is the adiabatic shuttling of MZMs through topological superconductors. Here, we consider the "piano key" approach, where MZMs are transported using local electric gates to tune sections ("keys") of a wire between topologically trivial and nontrivial phases. We numerically simulate this transport on a single wire and calculate the diabatic error corresponding to exciting the system. We find that this error is typically reduced when transport is facilitated by using multiple keys as one may expect from modeling each piano key press as an effective Landau-Zener process. However, further increasing the number of keys increases errors; thus, there exists a nontrivial optimal number of keys that minimizes the diabatic error given a fixed total shuttle time. As we show, this optimal number of keys can be explained by modeling each key press as an effective Landau-Zener process while paying careful attention to power-law corrections that arise due to the nonanalytic behavior of the time-dependent modulation of the chemical potential at the beginning and end of each key press.

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