arXiv subjects

Rick Mukherjee

Publications and source records attributed to Rick Mukherjee.

At least 19 recordsLinked to original sources

arXiv2026

Benchmarking Hybrid Quantum-Classical Algorithms for Power Grid Optimization Problems

Alternating Current Optimal Power Flow Unit Commitment (AC-OPF-UC) is a difficult mixed-integer nonlinear optimization problem that combines binary generator commitment decisions with nonconvex continuous AC power-flow constraints. In this work, we investigate whether hybrid quantum-classical variational algorithms can improve the solution of single-period AC-OPF-UC relative to classical approaches. To the best of our knowledge, this is the first study to directly evaluate quantum or hybrid quantum-classical algorithms for the full AC-OPF-UC problem. We consider two candidate algorithms for improving AC-OPF-UC solution quality relative to purely classical methods on ideal quantum hardware. The first applies QAOA directly to a fully discretized formulation of the problem, with equality and inequality constraints incorporated through penalty terms and slack variables. Although conceptually straightforward, this approach requires a prohibitively large number of qubits even for small instances. The second, qubit-efficient approach encodes only the binary generator status variables on a quantum computer, while optimizing the continuous power-flow variables classically for each sampled bitstring. We benchmark this method on randomly generated AC-OPF-UC instances with 5 to 13 generators and compare it against SCIP, SMAC, and uniform random sampling. Our simulations show that the qubit-efficient hybrid method does not outperform uniform sampling. These results suggest that in order to establish potential advantage of the variational hybrid strategy considered here over the best classical algorithms, if any, much larger system sizes (25+ generators) need to be tested, which is beyond our computational capacity. Alternatively, different approaches, such as quantum versions of branch-and-bound methods, may be more promising.

quant-ph↗

arXiv2026

Adaptive Tensor Network Sampling for Quantum Optimal Control

Quantum optimal control (QOC) provides a systematic framework for achieving high-fidelity operations in quantum systems and plays a central role in tasks such as gate synthesis, state transfer, and pulse design. Existing QOC methods broadly fall into two categories: gradient-based and gradient-free algorithms. The associated optimization landscape is often high-dimensional, non-convex, and populated by numerous local minima, making efficient gradient-free search strategies essential. To address this, we introduce a gradient-free matrix product state/tensor train (MPS/TT) sampling heuristic for discrete quantum optimal control. In our approach, the MPS defines a score function over the space of discrete control parameters, which in turn induces a sampling distribution over candidate control sequences. This distribution is iteratively refined through selection of better performing sequences and local tensor updates to bias the search toward high-performing sequences. We evaluate the method on a range of benchmark problems, including single-qubit state transfer, Bell-pair preparation, qutrit gate implementation, and open-system population transfer. Across these tasks, the method exhibits stable convergence behavior and competitive empirical performance relative to established gradient-free baselines. These results suggest that tensor network sampling offers a viable heuristic framework for discrete quantum control.

quant-ph↗

arXiv2026

Quantum simulation of Motzkin spin chain with Rydberg atoms

Motzkin spin chain is a well-known mathematical model with connections to symmetry-protected topological phases, such as the Haldane phase, as well as to concepts in the AdS/CFT correspondence. They exhibit highly entangled ground states that violate the area law and are exceptionally difficult to simulate with conventional numerical methods. Numerical simulations of the Motzkin ground state become further challenging at large system sizes due to their high-dimensional spin structure, rendering it a natural test bed for quantum simulation with ultra-cold systems. Here, we propose a Rydberg-atom based quantum simulation scheme that effectively realizes Motzkin spins using an experimentally accessible set of parameters. We show that the resulting effective Motzkin ground state reproduces the characteristic entanglement scaling and the block-structure properties of the reduced density matrix associated with the ideal Motzkin state. Our results establish a pathway toward a concrete experimental realization of Motzkin spins beyond purely mathematical constructions, opening avenues for exploring other similar exotic non-area-law entangled phases in programmable Rydberg simulators.

quant-ph↗

arXiv2026

Inverse Quantum Potential Reconstruction via Generalized Bertlmann-Martin Inequalities

Reconstructing a radial (1D) quantum potential, V(r), from a few bound-state energies is a long-standing inverse problem because limited spectral data must constrain an entire potential. We present a Laplace-moment reconstruction pipeline that links the Bertlmann-Martin gap bound to generalized Bertlmann-Martin (GBM) even-moment ladders, continues the Laplace transform with Pade approximants, and inverts the transform to recover rho(r) and V(r). Odd moments are supplied by a physically consistent interpolation scheme. Benchmark settings and diagnostics for Coulomb, harmonic oscillator, Hulthen, Kratzer, and hyperbolic-well cases are stated so each approximation stage can be assessed under a common empirical basis. The conclusions are therefore limited to the reported benchmark settings rather than offered as universal method claims.

math.SP↗

arXiv2026

High-fidelity non-adiabatic dark state gates for neutral atoms

Rydberg blockade gates are the most experimentally mature entangling operations in neutral-atom quantum processors, combining fast gate times with simple control, but their performance degrades at larger interatomic separations and remains sensitive to motional and technical noise. Non-blockade gate schemes, such as dark-state and geometric protocols, offer complementary robustness but typically rely on complex and experimentally demanding control. Here we show that quantum optimal control enables non-blockade gate schemes to be implemented using the experimentally established pulse-shaping techniques developed for blockade-based gates. Focusing on the dark-state gate, we construct non-adiabatic implementations that preserve the intrinsic robustness of adiabatic dark-state protocols while achieving gate times comparable to time-optimal blockade gates using only smooth, experimentally feasible pulses. The resulting gates exhibit enhanced resilience to motional coupling, laser noise, and interaction inhomogeneity, particularly near and beyond the blockade radius. This work establishes a practical route to fast, robust two-qubit gates without increased experimental complexity.

quant-ph↗

arXiv2026

Scalable Preparation of Matrix Product States with Sequential and Brick Wall Quantum Circuits

Preparing arbitrary quantum states requires exponential resources. Matrix Product States (MPS) admit more efficient constructions, particularly when accuracy is traded for circuit complexity. Existing approaches to MPS preparation mostly rely on heuristic circuits that are deterministic but quickly saturate in accuracy, or on variational optimization methods that reach high fidelities but scale poorly. This work introduces an end-to-end MPS preparation framework that combines the strengths of both strategies within a single pipeline. Heuristic staircase-like and brick wall disentangler circuits provide warm-start initializations for variational optimization, enabling high-fidelity state preparation for large systems. Target MPSs are either specified as physical quantum states or constructed from classical datasets via amplitude encoding, using step-by-step singular value decompositions or tensor cross interpolation. The framework incorporates entanglement-based qubit reordering, reformulated as a quadratic assignment problem, and low-level optimizations that reduce depths by up to 50% and CNOT counts by 33%. We evaluate the full pipeline on datasets of varying complexity across systems of 19-50 qubits and identify trade-offs between fidelity, gate count, and circuit depth. Optimized brick wall circuits typically achieve the lowest depths, while the optimized staircase-like circuits minimize gate counts. Overall, our results provide principled and scalable protocols for preparing MPSs as quantum circuits, supporting utility-scale applications on near-term quantum devices.

quant-ph↗

arXiv2025

Resource-Efficient Quantum Optimization via Higher-Order Encoding

Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and gate counts. We show that Higher-Order Unconstrained Binary Optimization (HUBO) enables a more resource-efficient formulation. Our method systematically constructs HUBO Hamiltonians and, compared to a QUBO formulation in benchmarks on Gate Assignment (GAP), Maximum k-Colorable Subgraph (MkCS), and Integer Programming (IP) problems, significantly reduces qubit requirements and decreases total CNOT gate counts by at least 89.6% for all tested instances. These results highlight HUBO as a practical alternative for quantum optimization on near-term devices. To promote adoption, we release an open-source Python library that automates HUBO model construction, extends beyond the examples presented in this work, and broadens access to resource-efficient quantum optimization.

quant-ph↗

arXiv2025

Reconfigurable Four-Photon Interference among Three Nodes on a Field Deployed Metropolitan Fiber Network

Advanced quantum networking protocols beyond bi-photon, point-to-point links rely critically on the ability to perform multi-photon interference across multiple nodes under realistic operating conditions. Yet experimental validation of such higher-order, multi-node interference effects in deployed metropolitan fiber networks remains limited. Here, we report a field demonstration of polarization-controlled reconfigurable four-photon interference over three distant nodes on a deployed metropolitan fiber network. Using a fully fiber-coupled linear-optical platform, we observe a fusion-type four-photon interference signature in presence of real-world impairments, including photon loss, polarization drift, and timing uncertainty. By performing polarization-resolved measurements on two locally retained photons, we conditionally select distinct two-photon coincidence channels that exhibit Bell-like and N00N-like behavior. Rather than pursuing multi-partite entanglement verification, this work focuses on establishing the technical feasibility of multi-photon, multi-node interference and reconfigurable conditional state preparation in the field in a deployed fiber network environment. These results serve as a systems-level validation toward future multi-photon, multi-node quantum networking architectures that require robust interference performance outside the laboratory.

quant-ph↗

arXiv2025

Qudit-based scalable quantum algorithm for solving the integer programming problem

Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It is a hard problem to solve using classical algorithms, as its complexity increases exponentially with problem size. Most quantum algorithms for solving IP are highly resource inefficient because they encode integers into qubits. In [1], the issue of resource inefficiency was addressed by mapping integer variables to qudits. However, [1] has limited practical value due to a lack of scalability to multiple qudits to encode larger problems. In this work, by extending upon the ideas of [1], a circuit-based scalable quantum algorithm is presented using multiple interacting qudits for which we show a quantum speed-up. The quantum algorithm consists of a distillation function that efficiently separates the feasible from the infeasible regions, a phase-amplitude encoding for the cost function, and a quantum phase estimation coupled with a multi-controlled single-qubit rotation for optimization. We prove that the optimal solution has the maximum probability of being measured in our algorithm. The time complexity for the quantum algorithm is shown to be $O(d^{n/2} + m\cdot n^2\cdot \log{d} + n/\epsilon_{QPE})$ for a problem with the number of variables $n$ taking $d$ integer values, satisfying $m$ constraints with a precision of $\epsilon_{QPE}$. Compared to the classical time complexity of brute force $O(d^n)$ and the best classical exact algorithm $O((\log{n})^{3n})$, it incurs a reduction of $d^{n/2}$ in the time complexity in terms of $n$ for solving a general polynomial IP problem.

quant-ph↗

arXiv2024

Ab-Initio Approach to Many-Body Quantum Spin Dynamics

A fundamental longstanding problem in studying spin models is the efficient and accurate numerical simulation of the long-time behavior of larger systems. The exponential growth of the Hilbert space and the entanglement accumulation at long times pose major challenges for current methods. To address these issues, we employ the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) framework to simulate the many-body spin dynamics of the Heisenberg model in various settings, including the Ising and XYZ limits with different interaction ranges and random couplings. Benchmarks with analytical and exact numerical approaches show that ML-MCTDH accurately captures the time evolution of one- and two-body observables in both one- and two-dimensional lattices. A comparison with the discrete truncated Wigner approximation (DTWA) highlights that ML-MCTDH is particularly well-suited for handling anisotropic models and provides more reliable results for two-point observables across all tested cases. The behavior of the corresponding entanglement dynamics is analyzed to reveal the complexity of the quantum states. Our findings indicate that the rate of entanglement growth strongly depends on the interaction range and the presence of disorder. This particular relationship is then used to examine the convergence behavior of ML-MCTDH. Our results indicate that the multilayer structure of ML-MCTDH is a promising numerical framework for handling the dynamics of generic many-body spin systems.

quant-ph↗

arXiv2024

Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks

Quadratic Unconstrained Binary Optimization (QUBO) sits at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others. These problems typically involve optimizing a large number of binary variables, which makes finding exact solutions exponentially more difficult. Consequently, most QUBO problems are classified as NP-hard. To address this challenge, we developed a powerful feedforward neural network (FNN) optimizer for arbitrary QUBO problems. In this work, we demonstrate that the FNN optimizer can provide high-quality approximate solutions for large problems, including dense 80-variable weighted MaxCut and random QUBOs, achieving an average accuracy of over 99% in less than 1.1 seconds on an 8-core CPU. Additionally, the FNN optimizer outperformed the Gurobi optimizer by 72% on 200-variable random QUBO problems within a 100-second computation time limit, exhibiting strong potential for real-time optimization tasks. Building on this model, we explored the novel approach of integrating FNNs with a quantum annealer-based activation function to create a quantum-classical encoder-decoder (QCED) optimizer, aiming to further enhance the performance of FNNs in QUBO optimization.

quant-ph↗

arXiv2024

Solving The Travelling Salesman Problem Using A Single Qubit

The travelling salesman problem (TSP) is a popular NP-hard-combinatorial optimization problem that requires finding the optimal way for a salesman to travel through different cities once and return to the initial city. The existing methods of solving TSPs on quantum systems are either gate-based or binary variable-based encoding. Both approaches are resource-expensive in terms of the number of qubits while performing worse compared to existing classical algorithms even for small-size problems. We present an algorithm that solves an arbitrary TSP using a single qubit by invoking the principle of quantum parallelism. The cities are represented as quantum states on the Bloch sphere while the preparation of superposition states allows us to traverse multiple paths at once. The underlying framework of our algorithm is a quantum version of the classical Brachistochrone approach. Optimal control methods are employed to create a selective superposition of the quantum states to find the shortest route of a given TSP. The numerical simulations solve a sample of four to nine cities for which exact solutions are obtained. The algorithm can be implemented on any quantum platform capable of efficiently rotating a qubit and allowing state tomography measurements. For the TSP problem sizes considered in this work, our algorithm is more resource-efficient and accurate than existing quantum algorithms with the potential for scalability. A potential speed-up of polynomial time over classical algorithms is discussed.

quant-ph↗

arXiv2024

Formation of Rydberg Crystals Induced by Quantum Melting in One-Dimension

Quantum fluctuations in frustrated systems can lead to the emergence of complex many-body phases. However, the role of quantum fluctuations in frustration-free lattices is less explored and could provide an interesting avenue for exploring new physics, and perhaps easier to realize compared to frustrated lattice systems. Using Rydberg atoms with tunable interactions as a platform, we leverage strong van der Waals interactions and obtain a constrained model in one dimension with non-local fluctuations given by dipolar interactions alongside local fluctuations. The combined effect of such processes leads to intrinsically quantum-ordered Rydberg crystals through the order-by-disorder mechanism. Finite-size analyses indicate that combined fluctuations drive the transition from disordered to ordered phases, contrary to the expected direction. We provide a theoretical description to understand the physics of order-by-disorder in one-dimensional systems, which are typically seen only in higher dimensions.

cond-mat.quant-gas↗

arXiv2024

Efficient prediction of attosecond two-colour pulses from an X-ray free-electron laser with machine learning

X-ray free-electron lasers are sources of coherent, high-intensity X-rays with numerous applications in ultra-fast measurements and dynamic structural imaging. Due to the stochastic nature of the self-amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two-coloured X-ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networks and decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high-repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X-ray spectroscopy using XFELs, such as in time-resolved X-ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes.

physics.acc-ph↗

arXiv2024

Bond-Order Density Wave Phases in Dimerized Extended Bose-Hubbard Models

The Bose-Hubbard model (BHM) has been widely explored to develop a profound understanding of the strongly correlated behavior of interacting bosons. Quantum simulators not only allow the exploration of the BHM but also extend it to models with interesting phenomena such as gapped phases with multiple orders and topological phases. In this work, an extended Bose-Hubbard model involving a dimerized one-dimensional model of long-range interacting hard-core bosons is studied. Bond-order density wave phases (BODW) are characterized in terms of their symmetry breaking and topological properties. At certain fillings, interactions combined with dimerized hoppings give rise to an emergent symmetry-breaking leading to BODW phases, which differs from the case of non-interacting models that require an explicit breaking of the symmetry. Specifically, the BODW phase at filling $ρ=1/3$ possesses no analogue in the non-interacting model in terms of its symmetry-breaking properties and the unit cell structure. Upon changing the dimerization pattern, the system realizes topologically trivial BODW phases. At filling $ρ=1/4$, on-site density modulations are shown to stabilize the topological BODW phase. Our work provides the bridge between interacting and non-interacting BODW phases and highlights the significance of long-range interactions in a dimerized lattice by showing unique BODW phases that do not exist in the non-interacting model.

cond-mat.quant-gas↗

arXiv2024

Quantum simulation of hadronic states with Rydberg-dressed atoms

The phenomenon of confinement is well known in high-energy physics and can also be realized for low-energy domain-wall excitations in one-dimensional quantum spin chains. A bound state consisting of two domain-walls can behave like a meson, and in a recent work of Vovrosh et al. [PRX Quantum 3, 040309 (2022)] , it was demonstrated that a pair of mesons could dynamically form a meta-stable confinement-induced bound state (consisting of four domain-walls) akin to a hadronic state. However, the protocol discussed in Vovrosh et al. [PRX Quantum 3, 040309 (2022)] involving the use of interactions with characteristically non-monotonic distance dependence is not easy to come by in nature, thus, posing a challenge for its experimental realization. In this regard, Rydberg atoms can provide the required platform for simulating confinement-related physics. We exploit the flexibility offered by interacting Rydberg-dressed atoms to engineering modified spin-spin interactions for the one-dimensional transverse field Ising model. Our numerical simulations show how Rydberg-dressed interactions can give rise to a variety of effective potentials that are suitable for hadron formation, which opens the possibility of simulating confinement physics with Rydberg platforms as a viable alternative to current trapped-ion experiments.

cond-mat.quant-gas↗

arXiv2024

Integer Programming Using A Single Atom

Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form through the use of binary variables, which is an indirect and resource-consuming way of solving it. We develop an algorithm that maps and solves an IP problem in its original form to any quantum system possessing a large number of accessible internal degrees of freedom that are controlled with sufficient accuracy. This work leverages the principle of superposition to solve the optimization problem. Using a single Rydberg atom as an example, we associate the integer values to electronic states belonging to different manifolds and implement a selective superposition of different states to solve the full IP problem. The optimal solution is found within a few microseconds for prototypical IP problems with up to eight variables and four constraints. This also includes non-linear IP problems, which are usually harder to solve with classical algorithms when compared to their linear counterparts. Our algorithm for solving IP is benchmarked by a well-known classical algorithm (branch and bound) in terms of the number of steps needed for convergence to the solution. This approach carries the potential to improve the solutions obtained for larger-size problems using hybrid quantum-classical algorithms.

quant-ph↗

arXiv2023

Quantum Phases from Competing Van der Waals and Dipole-Dipole Interactions of Rydberg Atoms

Competing short- and long-range interactions represent distinguished ingredients for the formation of complex quantum many-body phases. Their study is hard to realize with conventional quantum simulators. In this regard, Rydberg atoms provide an exception as their excited manifold of states have both density-density and exchange interactions whose strength and range can vary considerably. Focusing on one-dimensional systems, we leverage the van der Waals and dipole-dipole interactions of the Rydberg atoms to obtain the zero-temperature phase diagram for a uniform chain and a dimer model. For the uniform chain, we can influence the boundaries between ordered phases and a Luttinger liquid phase. For the dimerized case, a new type of bond-order-density-wave phase is identified. This demonstrates the versatility of the Rydberg platform in studying physics involving short- and long-ranged interactions simultaneously.

cond-mat.quant-gas↗