arXiv subjects

T. S. Mahesh

Publications and source records attributed to T. S. Mahesh.

At least 19 recordsLinked to original sources

arXiv2026

Experimentally Extending Quantum Kernel Learning to Quantum Data by NMR

Quantum kernel learning (QKL) promises efficient machine learning by encoding feature maps onto exponentially large Hilbert spaces inherent in quantum systems. Using the liquid-state nuclear magnetic resonance (NMR) platform, we implement and benchmark QKL for one-dimensional regression and two-dimensional classification tasks. We then classify entangling and non-entangling operators by extending QKL to handle parametrized or non-parameterized operator inputs. We first compute the kernel numerically for a double-layered star system and then experimentally validate it on a 3-qubit NMR register. QKL provides a practical route to compare operators on native quantum hardware without expensive tomography protocols. Our results confirm the superiority of QKL over other classical methods for processing quantum data, thereby highlighting its ability to capture the inherent structure of quantum space and to extend its domain of operation beyond the training domain by exploiting symmetries in the operator space.

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arXiv2026

Noise cancellation by superposition of channels and superactivation of quantum capacity: Experimental realization by NMR

Noisy quantum channels degrade quantum resources such as coherence and entanglement and hence pose challenges for realizing quantum technologies. Coherent control of noisy channels allows us to minimize their effects on the quantum system. Here we achieve the cancellation of two noisy quantum channels by superposing their corresponding Stinespring dilation unitaries. We first arrive at conditions under which superposition of channels results in a valid quantum channel. We then consider superposing two dephasing channels and observe their destructive interference, thereby effectively recovering the quantum coherence. On superposing two zero-capacity depolarizing channels, we show superactivation of quantum capacity. We experimentally realize the cancellation of two dephasing channels using a three-qubit NMR register. Furthermore, using a five-qubit NMR register, we realize the cancellation of two depolarization channels and demonstrate superactivation of quantum capacity.

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arXiv2026

Efficient Many-Body Shadow Metrology via Clifford Lensing

Quantum probes that enable enhanced exploration and characterization of complex systems are central to modern science, spanning applications from biology to astrophysics and chemical design. In large many-body quantum systems, interactions delocalize phase information across many degrees of freedom, dispersing it away from accessible measurements and limiting the scalability of quantum metrology. Here we show that experimentally accessible Clifford operations acting jointly on quantum states and observables can refocus this distributed information. These operations implement what we term {\it Clifford lensing}--transformations that coherently localize phase information onto a reduced set of degrees of freedom, mapping optimal measurements onto observables of reduced Pauli weight. We establish a correspondence between quantum error-correcting codes and interferometric constructions that enforce deterministic phase kickback, and generalize this to circuits that concentrate many-body phase information onto a controllable subset of qubits. We further develop partial shadow tomography protocols for estimating subsystem-supported phases. We experimentally demonstrate these principles in liquid-state nuclear magnetic resonance systems of up to fifteen qubits, achieving optimal sensing with constrained resources. Our results establish a scalable route to coherent control of information flow in interacting quantum systems, enabling many-body quantum sensing and multimode interferometry across complex architectures.

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arXiv2026

Experimental prime factorization via the feedback quantum control

Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While Shor's algorithm demands high-fidelity quantum gates, Hamiltonian optimization schemes, with prime factors encoded as degenerate ground states of a problem Hamiltonian, generally require substantial classical post-processing to determine control parameters. We propose an all-quantum, measurement-based feedback approach that iteratively steers a quantum system toward the target ground state, eliminating the need for classical computation of drive parameters once the problem Hamiltonian is determined and realized. As a proof of principle, we experimentally factor the biprime 551 using a three-qubit NMR quantum register and numerically analyze the robustness of the method against control field-errors. We further demonstrate scalability by numerically implementing the FALQON factorization of larger biprimes, 9,167 and 2,106,287, using 5 and 9 qubits, respectively.

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arXiv2025

Partial Quantum Shadow Tomography for Structured Operators and its Experimental Demonstration using NMR

Quantum shadow tomography based on the classical shadow representation provides an efficient way to estimate properties of an unknown quantum state without performing a full quantum state tomography. In scenarios where estimating the expectation values for only certain classes of observables is required, obtaining information about the entire density matrix is unnecessary. We propose a partial quantum shadow tomography protocol that estimates a subset of density matrix elements relevant to the expectation values of structured observables. Specifically, we identify specific subsets of the tomographically complete set ${\mathrm{Cl}}(2)^{\otimes n}$ and a simple pseudo-inverse of the associated channel, which can be used to estimate all elements of the density matrix with the same active order. By restricting the protocol to smaller subsets of single-qubit Pauli measurements, it becomes experimentally more efficient. We demonstrate the advantage over unitary designs, such as the Clifford, full Pauli basis, and methods utilizing mutually unbiased bases, by analytically deriving error bounds and numerically evaluating the protocol on structured operators. We experimentally demonstrate the partial shadow estimation scheme for a wide class of two-qubit states (pure, entangled, and mixed) in the nuclear magnetic resonance (NMR) platform. The full density matrix, reconstructed experimentally by combining different partial estimators, achieves fidelities around 99%.

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arXiv2025

Quantum Alternating Operator Ansatz for the Preparation and Detection of Long-Lived Singlet States in NMR

Designing efficient and robust quantum control strategies is vital for developing quantum technologies. One recent strategy is the Quantum Alternating Operator Ansatz (QAOA) sequence that alternatively propagates under two noncommuting Hamiltonians, whose control parameters can be optimized to generate a gate or prepare a state. Here, we describe the design of a QAOA sequence to prepare long-lived singlet states (LLS) from the thermal state in NMR. With extraordinarily long lifetimes exceeding the spin-lattice relaxation time constant $T_1$, LLS have been of great interest for various applications, from spectroscopy to medical imaging. Accordingly, designing sequences for efficiently preparing LLS in a general spin system is crucial. Using numerical analysis, we study the efficiency and robustness of our QAOA sequence over a wide range of errors in the control parameters. Using a two-qubit NMR register, we conduct an experimental study to benchmark our QAOA sequence against other prominent methods of LLS preparation and observe superior performance, especially under noisy conditions. Finally, we numerically demonstrate the applicability of our QAOA sequence beyond two-qubit registers, specifically for polychromatic excitation of delocalized LLS in a six-proton system.

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arXiv2024

Enhanced non-macrorealism: Extreme violations of Leggett-Garg inequalities for a system evolving under superposition of unitaries

Quantum theory contravenes classical macrorealism by allowing a system to be in a superposition of two or more physically distinct states, producing physical consequences radically different from that of classical physics. We show that a system, upon subjecting to transform under superposition of unitary operators, exhibits enhanced non-macrorealistic feature - as quantified by violation of the Leggett-Garg inequality (LGI) beyond the temporal Tsirelson bound. Moreover, this superposition of unitaries also provides robustness against decoherence by allowing the system to violate LGI and thereby retain its non-macrorealistic behavior for a strikingly longer duration. Using an NMR register, we experimentally demonstrate the superposition of unitaries with the help of an ancillary qubit and verify these theoretical predictions.

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arXiv2024

Physics-informed neural network for quantum control of NMR registers

Classical and quantum machine learning are being increasingly applied to various tasks in quantum information technologies. Here, we present an experimental demonstration of quantum control using a physics-informed neural network (PINN). PINN's salient feature is how it encodes the entire control sequence in terms of its network parameters. This feature enables the control sequence to be later adopted to any hardware with optimal time discretization, which contrasts with conventional methods involving a priory time discretization. Here, we discuss two important quantum information tasks: gate synthesis and state preparation. First, we demonstrate quantum gate synthesis by designing a two-qubit CNOT gate and experimentally implementing it on a heteronuclear two-spin NMR register. Second, we demonstrate quantum state preparation by designing a control sequence to efficiently transfer the thermal state into the long-lived singlet state and experimentally implement it on a homonuclear two-spin NMR register. We present a detailed numerical analysis of the PINN control sequences regarding bandwidth, discretization levels, control field errors, and external noise.

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arXiv2023

Selective Wigner phase space tomography and its application for studying quantum chaos

The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state tomography in discrete Wigner phase space can also be implemented. We observe that for a certain class of states, such as harmonic states, the Wigner matrix is far more sparse compared to the density matrix in the computational basis. Additionally, reading only a small part of the Wigner matrix may suffice to infer certain behavior of quantum dynamics. In such cases, selective Wigner phase space tomography (SWPST) can be more efficient than the usual density matrix tomography (DMT). Employing nuclear magnetic resonance methods on a three-qubit nuclear spin register, we experimentally estimate Wigner matrices of various two-qubit quantum states. As a specific example application of SWPST, we study the evolution of spin coherent states under the quantum chaotic kicked top model and extract signatures of quantum-classical correspondence in the Wigner phase space.

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arXiv2023

NMR investigations of Dynamical Tunneling in Spin Systems

In the usual quantum tunneling, a low-energy quantum particle penetrates across a physical barrier of higher potential energy, by traversing a classically forbidden region, and finally escapes into another region. In an analogous scenario, a classical particle inside a closed regular region in the phase space is dynamically bound from escaping to other regions of the phase space. Here, the physical potential barrier is replaced by dynamical barriers which separate different regions of the phase space. However, in the quantum regime, the system can overcome such dynamical barriers and escape through them, giving rise to dynamical tunneling. In chaotic Hamiltonian systems, dynamical tunneling refers to quantum tunneling between states whose classical limit correspond to symmetry-related regular regions separated by a chaotic zone between which any classical transport is prohibited. Here, an experimental realization of dynamical tunneling in spin systems is reported using nuclear magnetic resonance (NMR) architecture. In particular, dynamical tunneling in quantum kicked tops of spin-1 and spin-3/2 systems using two- and three-qubit NMR registers is investigated. By extracting time-dependent expectation values of the angular momentum operator components, size-dependent tunneling behaviour for various initial states is systematically investigated. Further, by monitoring the adverse effects of dephasing noise on the tunneling oscillations, we assert the importance of quantum coherence in enabling dynamical tunneling.

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arXiv2022

Recommender System Expedited Quantum Control Optimization

Quantum control optimization algorithms are routinely used to generate optimal quantum gates or efficient quantum state transfers. However, there are two main challenges in designing efficient optimization algorithms, namely overcoming the sensitivity to local optima and improving the computational speed. The former challenge can be dealt with by designing hybrid algorithms, such as a combination of gradient and simulated annealing methods. Here, we propose and demonstrate the use of a machine learning method, specifically the recommender system (RS), to deal with the latter challenge of enhancing computational efficiency. We first describe ways to set up a rating matrix involving gradients or gate fidelities. We then establish that RS can rapidly and accurately predict elements of a sparse rating matrix. Using this approach, we expedite a gradient ascent based quantum control optimization, namely GRAPE and demonstrate the faster performance for up to 8 qubits. Finally, we describe and implement the enhancement of the computational speed of a hybrid algorithm, namely SAGRAPE.

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arXiv2022

Observation of quantum phase-synchronization in a nuclear spin-system

We report an experimental study of phase-synchronization in a pair of interacting nuclear spins subjected to an external drive in nuclear magnetic resonance architecture. A weak transition-selective radio-frequency field applied on one of the spins is observed to cause phase-localization, which is experimentally established by measuring the Husimi distribution function under various drive conditions. To this end, we have developed a general interferometric technique to directly extract values of the Husimi function via the transverse magnetization of the undriven nuclear spin. We further verify the robustness of synchronization to detuning in the system by studying the Arnold tongue behaviour.

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arXiv2021

Tomographic entanglement indicators from NMR experiments

In recent years, the performance of different entanglement indicators obtained directly from tomograms has been assessed in continuous-variable and hybrid quantum systems. In this paper, we carry out this task in the case of spin systems. We compute the entanglement indicators from actual experimental data obtained from three liquid-state NMR experiments, and compare them with standard entanglement measures calculated from the corresponding density matrices, both experimentally reconstructed and numerically computed. The gross features of entanglement dynamics and spin squeezing properties are found to be reproduced by these entanglement indicators. However, the extent to which these indicators and spin squeezing track the entanglement during time evolution of the multipartite systems in the NMR experiments is very sensitive to the precise nature and strength of interactions as well as the manner in which the full system is partitioned into subsystems. We also use the IBM quantum computer to implement equivalent circuits that capture the dynamics of the multipartite system in one of the NMR experiments. We compute and compare the entanglement indicators obtained from the tomograms corresponding to the experimental execution and simulation of these equivalent circuits. This exercise shows that these indicators can estimate the degree of entanglement without necessitating detailed state reconstruction procedures, establishing the advantage of the tomographic approach.

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arXiv2021

Robust Quantum Control using Hybrid Pulse Engineering

The development of efficient algorithms that generate robust quantum controls is crucial for the realization of quantum technologies. The commonly used gradient-based optimization algorithms are limited by their sensitivity to the initial guess, which affects their performance. Here we propose combining the gradient method with the simulated annealing technique to formulate a hybrid algorithm. Our numerical analysis confirms its superior convergence rate. Using the hybrid algorithm, we generate spin-selective $π$ pulses and employ them for experimental measurement of local noise-spectra in a three-qubit NMR system. Moreover, here we describe a general method to construct noise-resilient quantum controls by incorporating noisy fields within the optimization routine of the hybrid algorithm. On experimental comparison with similar sequences obtained from standard algorithms, we find remarkable robustness of the hybrid sequences against dephasing errors.

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arXiv2021

Efficient Characterization of Quantum Evolutions via a Recommender System

We demonstrate characterizing quantum evolutions via matrix factorization algorithm, a particular type of the recommender system (RS). A system undergoing a quantum evolution can be characterized in several ways. Here we choose (i) quantum correlations quantified by measures such as entropy, negativity, or discord, and (ii) state-fidelity. Using quantum registers with up to 10 qubits, we demonstrate that an RS can efficiently characterize both unitary and nonunitary evolutions. After carrying out a detailed performance analysis of the RS in two qubits, we show that it can be used to distinguish a clean database of quantum correlations from a noisy or a fake one. Moreover, we find that the RS brings about a significant computational advantage for building a large database of quantum discord, for which no simple closed-form expression exists. Also, RS can efficiently characterize systems undergoing nonunitary evolutions in terms of quantum discord reduction as well as state-fidelity. Finally, we utilize RS for the construction of discord phase space in a nonlinear quantum system.

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arXiv2021

Experimental localisation of quantum entanglement through monitored classical mediator

Quantum entanglement is a form of correlation between quantum particles that cannot be increased via local operations and classical communication. It has therefore been proposed that an increment of quantum entanglement between probes that are interacting solely via a mediator implies non-classicality of the mediator. Indeed, under certain assumptions regarding the initial state, entanglement gain between the probes indicates quantum coherence in the mediator. Going beyond such assumptions, there exist other initial states which produce entanglement between the probes via only local interactions with a classical mediator. In this process the initial entanglement between any probe and the rest of the system "flows through" the classical mediator and gets localised between the probes. Here we theoretically characterise maximal entanglement gain via classical mediator and experimentally demonstrate, using liquid-state NMR spectroscopy, the optimal growth of quantum correlations between two nuclear spin qubits interacting through a mediator qubit in a classical state. We additionally monitor, i.e., dephase, the mediator in order to emphasise its classical character. Our results indicate the necessity of verifying features of the initial state if entanglement gain between the probes is used as a figure of merit for witnessing non-classical mediator. Such methods were proposed to have exemplary applications in quantum optomechanics, quantum biology and quantum gravity.

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arXiv2021

Magnetic field-assisted spectral decomposition and imaging of charge states of NV centers in diamond

With the advent of quantum technology, nitrogen vacancy ($NV$) centers in diamond turn out to be a frontier which provides an efficient platform for quantum computation, communication and sensing applications. Due to the coupled spin-charge dynamics of the $NV$ system, knowledge about $NV$ charge state dynamics can help to formulate efficient spin control sequences strategically. Through this paper we report two spectroscopy-based deconvolution methods to create charge state mapping images of ensembles of $NV$ centers in diamond. First, relying on the fact that an off axis external magnetic field mixes the electronic spins and selectively modifies the photoluminescence (PL) of $NV^-$, we perform decomposition of the optical spectrum for an ensemble of $NV$s and extract the spectra for $NV^-$ and $NV^0$ states. Next, we introduce an optical filter based decomposition protocol and perform PL imaging for $NV^-$ and $NV^0$. Earlier obtained spectra for $NV^-$ and $NV^0$ states are used to calculate their transmissivities through a long pass optical filter. These results help us to determine the spatial distribution of the $NV$ charge states in a diamond sample.

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arXiv2021

Observation of interaction induced blockade and local spin freezing in a NMR quantum simulator

We experimentally emulate interaction induced blockade and local spin freezing in two and three qubit Nuclear Magnetic Resonance (NMR) architecture. These phenomena are identical to the Rydberg blockade and Rydberg biased freezing. In Rydberg blockade, the simultaneous excitation of two or more atoms is blocked due to the level shift induced by the strong Van der Waal's interaction. In such a strong interaction regime, one can also observe Rydberg biased freezing, wherein the dynamics is confined to a subspace, with the help of multiple drives with unequal amplitudes. Here we drive NMR qubits with specific transition-selective radio waves, while intermittently characterizing the quantum states via quantum state tomography. This not only allows us to track the population dynamics, but also helps to probe quantum correlations, by means of quantum discord, evolving under blockade and freezing phenomena. While, our work constitutes the first experimental simulations of these phenomena in the NMR platform, it is also the first experimental demonstration of Rydberg biased freezing. Moreover, these studies open up interesting quantum control perspectives in exploiting the above phenomena for entanglement generation as well as subspace manipulations.

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