arXiv subjects

Khadijeh Najafi

Publications and source records attributed to Khadijeh Najafi.

At least 19 recordsLinked to original sources

arXiv2026

Order Parameter Discovery for Quantum Many-Body Systems

Quantum phase transitions reveal deep insights into the behavior of many-body quantum systems, but identifying these transitions without prior knowledge of order parameters remains a significant challenge. In this work, we introduce a method for constructing phase diagrams using the vector field of the reduced fidelity susceptibility (RFS), and demonstrate how information encoded in this vector field can be used to discover observables corresponding to order parameters. We apply our approach to well-established models: the Axial Next Nearest Neighbour Interaction (ANNNI) model, a cluster state model, and a chain of Rydberg atoms; and validate the discovered order parameters using eigendecomposition and finite-size scaling analysis, confirming the expected universality classes. Our results demonstrate that the RFS vector field offers a unified framework for phase characterization and order-parameter discovery that requires no prior knowledge of symmetry or transition type, while relying only on reduced density matrices of small subsystems.

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arXiv2026

Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States

The preparation of quantum Gibbs states at finite temperatures is a cornerstone of quantum computation, enabling applications in quantum simulation of many-body systems, machine learning via quantum Boltzmann machines, and optimization through thermal sampling techniques. In this work, we introduce a variational framework that leverages matrix product states for the efficient classical evaluation of the Helmholtz free energy, combining scalable entanglement entropy computation with a hardware efficient ansatz to accurately approximate thermal states in one- and two-dimensional systems. We conduct extensive benchmarking on key observables, including energy density, susceptibility, specific heat, and two-point correlations, comparing against exact analytical results for 1D systems and quantum Monte Carlo simulations for 2D lattices across various temperatures and ansatz configurations. Our large-scale numerical simulations demonstrate the capability to prepare high-quality Gibbs states for 1D lattice models with up to 30 sites and 2D systems with up to 6x6 sites, using up to 44 qubits. Finally, we demonstrate the framework's practical viability on a 156-qubit IBM Heron processor by preparing the approximate Gibbs state of a 30-site transverse-field Ising model. Leveraging a combination of error mitigation techniques, we reduce the relative errors in energy and susceptibility measurements by over 50% compared to unmitigated results.

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arXiv2026

Quantum critical dynamics and emergent universality in decoherent digital quantum processors

Understanding how noise influences nonequilibrium quantum critical dynamics is essential for both fundamental physics and the development of practical quantum technologies. While the quantum Kibble-Zurek (QKZ) mechanism predicts universal scaling during quenches across a critical point, real quantum systems exhibit complex decoherence that can substantially modify these behaviors, ranging from altering critical scaling to completely suppressing it. By considering a specific case of nondemolishing noise, we first show how decoherence can reshape universal scaling and verify these theoretical predictions using numerical simulations of spin chains across a wide range of noise strengths. Then, we study linear quenches in the transverse-field Ising model on IBM superconducting processors where the noise model is unknown. Using large system sizes of 80-120 qubits, we measure equal-time connected correlations, defect densities, and excess energies across various quench times. Surprisingly, unlike earlier observations where noise-induced defect production masked universal behavior at long times, we observe clear scaling relations, pointing towards persistent universal structure shaped by decoherence. The extracted scaling exponents differ from both ideal QKZ predictions and analytic results for simplified noise models, suggesting the emergence of a distinct noise-influenced universality regime. Our results, therefore, point toward the possibility of using universal dynamical scaling as a high-level descriptor of quantum hardware, complementary to conventional gate-level performance metrics.

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arXiv2026

Observing quantum many-body dynamics in emergent curved spacetime using programmable quantum processors

We digitally simulate quantum many-body dynamics in emergent curved backgrounds using 80 superconducting qubits on IBM Heron processors. By engineering spatially varying couplings in the spin-$\frac12$ XXZ chain, consistent with the low-energy description of the model in terms of an inhomogeneous Tomonaga-Luttinger liquid, we realize excitations that follow geodesics of an effective metric inherited from the underlying spatial deformation. Following quenches from Néel and few-spin-flip states, we observe curved light-cone propagation, horizon-induced freezing in the local magnetization, and position-dependent oscillation frequencies set by the engineered spatial deformation. Despite strong spatial inhomogeneity, unequal-time correlators reveal ballistic quasiparticle propagation in the spin chain. These results establish large-scale digital quantum processors as a flexible platform for detailed and controlled exploration of many-body dynamics in tunable and synthetic curved spacetimes.

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arXiv2026

QUIET-SR: Quantum Image Enhancement Transformer for Single Image Super-Resolution

Recent advancements in Single-Image Super-Resolution (SISR) using deep learning have significantly improved image restoration quality. However, the high computational cost of processing high-resolution images due to the large number of parameters in classical models, along with the scalability challenges of quantum algorithms for image processing, remains a major obstacle. In this paper, we propose the Quantum Image Enhancement Transformer for Super-Resolution (QUIET-SR), a hybrid framework that extends the Swin transformer architecture with a novel shifted quantum window attention mechanism, built upon variational quantum neural networks. QUIET-SR effectively captures complex residual mappings between low-resolution and high-resolution images, leveraging quantum attention mechanisms to enhance feature extraction and image restoration while requiring a minimal number of qubits, making it suitable for the Noisy Intermediate-Scale Quantum (NISQ) era. We evaluate our framework in MNIST (30.24 PSNR, 0.989 SSIM), FashionMNIST (29.76 PSNR, 0.976 SSIM) and the MedMNIST dataset collection, demonstrating that QUIET-SR achieves PSNR and SSIM scores comparable to state-of-the-art methods while using fewer parameters. Our efficient batching strategy directly enables massive parallelization on multiple QPU's paving the way for practical quantum-enhanced image super-resolution through coordinated QPU-GPU quantum supercomputing.

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arXiv2025

Learning topological states from randomized measurements using variational tensor network tomography

Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. While various tomographic methods such as classical shadow and MPS tomography have shown promise in characterizing a wide class of quantum states, they face unique limitations in detecting topologically ordered two-dimensional states. To address this problem, we implement and study a heuristic tomographic method that combines variational optimization on tensor networks with randomized measurement techniques. Using this approach, we demonstrate its ability to learn the ground state of the surface code Hamiltonian as well as an experimentally realizable quantum spin liquid state. In particular, we perform numerical experiments using MPS ansätze and systematically investigate the sample complexity required to achieve high fidelities for systems of sizes up to $48$ qubits. In addition, we provide theoretical insights into the scaling of our learning algorithm by analyzing the statistical properties of maximum likelihood estimation. Notably, our method is sample-efficient and experimentally friendly, only requiring snapshots of the quantum state measured randomly in the $X$ or $Z$ bases. Using this subset of measurements, our approach can effectively learn any real pure states represented by tensor networks, and we rigorously prove that random-$XZ$ measurements are tomographically complete for such states.

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arXiv2025

Dynamic parameterized quantum circuits: expressive and barren-plateau free

Classical optimization of parameterized quantum circuits is a widely studied methodology for the preparation of complex quantum states, as well as the solution of machine learning and optimization problems. However, it is well known that many proposed parameterized quantum circuit architectures suffer from drawbacks which limit their utility, such as their classical simulability or the hardness of optimization due to a problem known as "barren plateaus". We propose and study a class of dynamic parameterized quantum circuit architectures. These are parameterized circuits containing intermediate measurements and feedforward operations. In particular, we show that these architectures: 1. Provably do not suffer from barren plateaus. 2. Are expressive enough to describe arbitrarily deep unitary quantum circuits. 3. Are competitive with state of the art methods for preparing ground states and facilitating the representation of nontrivial thermal states. These features make the proposed architectures promising candidates for a variety of applications.

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arXiv2025

Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

The remarkable complexity of the vacuum state of a topologically-ordered many-body quantum system encodes the character and intricate braiding interactions of its emergent particles, the anyons.} Quintessential predictions exploiting this complexity use the Fibonacci string-net condensate (Fib-SNC) and its Fibonacci anyons to go beyond classical computing. Sampling the Fib-SNC wavefunction is expected to yield estimates of the chromatic polynomial of graph objects, a classical task that is provably hard. At the same time, exchanging anyons of Fib-SNC is expected to allow fault-tolerant universal quantum computation. Nevertheless, the physical realization of Fib-SNC and its anyons remains elusive. Here, we introduce a scalable dynamical string-net preparation (DSNP) approach, suitable even for near-term quantum processors, which dynamically prepares Fib-SNC and its anyons through reconfigurable graphs. Using a superconducting quantum processor, we couple the DSNP approach with composite error-mitigation on deep circuits to successfully create, measure, and braid anyons of Fib-SNC in a scalable manner. We certify the creation of anyons by measuring their `anyon charge', finding an average experimental accuracy of $94\%$. Furthermore, we validate that exchanging these anyons yields the { expected} golden ratio~$ϕ$ with~$98\%$ average accuracy and~$8\%$ measurement uncertainty. Finally, we sample the Fib-SNC to estimate the chromatic polynomial at~$ϕ+2$ for {several} graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and {for aiming at} a classically-hard problem.

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arXiv2024

Measuring central charge on a universal quantum processor

Central charge is a fundamental quantity in conformal field theories (CFT), and plays a crucial role in determining universality classes of critical points in two-dimensional systems. Despite its significance, the measurement of central charge has remained elusive thus far. In this work, we present the first experimental determination of the central charge using a universal quantum processor. Using a classically optimized variational quantum circuit and employing advanced error mitigation techniques, we successfully prepare ground states of various $1+1D$ quantum spin chain models at their critical point. Leveraging the heavy-hex structure of IBM quantum processors, we are able to implement periodic boundary conditions and mitigate boundary effects. We then extract the central charge from the scaling behavior of the sub-leading term of R{é}nyi generalizations of classical Shannon entropy, computed for local Pauli measurements in the conformal bases ($σ^{z}$ and $σ^x$). The experimental results are consistent with the known central charge values for the transverse field Ising (TFI) chain ($c=0.5$) and the XXZ chain ($c=1$), achieving relative errors as low as 5 percent.

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arXiv2024

Expressive Quantum Perceptrons for Quantum Neuromorphic Computing

Quantum neuromorphic computing (QNC) is a sub-field of quantum machine learning (QML) that capitalizes on inherent system dynamics. As a result, QNC can run on contemporary, noisy quantum hardware and is poised to realize challenging algorithms in the near term. One key issue in QNC is the characterization of the requisite dynamics for ensuring expressive quantum neuromorphic computation. We address this issue by proposing a building block for QNC architectures, what we call quantum perceptrons (QPs). Our proposed QPs compute based on the analog dynamics of interacting qubits with tunable coupling constants. We show that QPs are, with restricted resources, a quantum equivalent to the classical perceptron, a simple mathematical model for a neuron that is the building block of various machine learning architectures. Moreover, we show that QPs are theoretically capable of producing any unitary operation. Thus, QPs are computationally more expressive than their classical counterparts. As a result, QNC architectures built our of QPs are, theoretically, universal. We introduce a technique for mitigating barren plateaus in QPs called entanglement thinning. We demonstrate QPs' effectiveness by applying them to numerous QML problems, including calculating the inner products between quantum states, energy measurements, and time-reversal. Finally, we discuss potential implementations of QPs and how they can be used to build more complex QNC architectures.

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arXiv2024

Quantum simulation of Fermi-Hubbard model based on transmon qudit interaction

The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many qubits as the physical sites, in addition to complicated on-chip connectivities and swap gates required to simulate the physical interactions. In this work, we introduce a novel quantum simulation approach utilizing qudits to overcome such complexities. Leveraging on the symmetries of the Fermi-Hubbard model and their intrinsic relation to Clifford algebras, we first demonstrate a Qudit Fermionic Mapping (QFM) that reduces the encoding cost associated with the qubit-based approach. We then describe the unitary evolution of the mapped Hamiltonian by interpreting the resulting Majorana operators in terms of physical single- and two-qudit gates. While the QFM can be used for any quantum hardware with four accessible energy levels, we demonstrate the specific reduction in overhead resulting from utilizing the native Controlled-SUM gate (equivalent to qubit CNOT) for a fixed-frequency ququart transmon. We further transpile the resulting two transmon-qudit gates by demonstrating a qudit operator Schmidt decomposition using the Controlled-SUM gate. Finally, we demonstrate the efficacy of our proposal by numerical simulation of local observables such as the filling factor and Green's function for various Trotter steps. The compatibility of our approach with different qudit platforms paves the path for achieving quantum advantage in simulating non-trivial quantum many-body systems.

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arXiv2023

Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

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arXiv2023

Many-body localized hidden generative models

Born machines are quantum-inspired generative models that leverage the probabilistic nature of quantum states. Here, we present a new architecture called many-body localized (MBL) hidden Born machine that utilizes both MBL dynamics and hidden units as learning resources. We show that the hidden units act as an effective thermal bath that enhances the trainability of the system, while the MBL dynamics stabilize the training trajectories. We numerically demonstrate that the MBL hidden Born machine is capable of learning a variety of tasks, including a toy version of MNIST handwritten digits, quantum data obtained from quantum many-body states, and non-local parity data. Our architecture and algorithm provide novel strategies of utilizing quantum many-body systems as learning resources, and reveal a powerful connection between disorder, interaction, and learning in quantum many-body systems.

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arXiv2023

Towards quantum-enabled cell-centric therapeutics

In recent years, there has been tremendous progress in the development of quantum computing hardware, algorithms and services leading to the expectation that in the near future quantum computers will be capable of performing simulations for natural science applications, operations research, and machine learning at scales mostly inaccessible to classical computers. Whereas the impact of quantum computing has already started to be recognized in fields such as cryptanalysis, natural science simulations, and optimization among others, very little is known about the full potential of quantum computing simulations and machine learning in the realm of healthcare and life science (HCLS). Herein, we discuss the transformational changes we expect from the use of quantum computation for HCLS research, more specifically in the field of cell-centric therapeutics. Moreover, we identify and elaborate open problems in cell engineering, tissue modeling, perturbation modeling, and bio-topology while discussing candidate quantum algorithms for research on these topics and their potential advantages over classical computational approaches.

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arXiv2023

Learning quantum symmetries with interactive quantum-classical variational algorithms

A symmetry of a state $\vert ψ\rangle$ is a unitary operator of which $\vert ψ\rangle$ is an eigenvector. When $\vert ψ\rangle$ is an unknown state supplied by a black-box oracle, the state's symmetries provide key physical insight into the quantum system; symmetries also boost many crucial quantum learning techniques. In this paper, we develop a variational hybrid quantum-classical learning scheme to systematically probe for symmetries of $\vert ψ\rangle$ with no a priori assumptions about the state. This procedure can be used to learn various symmetries at the same time. In order to avoid re-learning already known symmetries, we introduce an interactive protocol with a classical deep neural net. The classical net thereby regularizes against repetitive findings and allows our algorithm to terminate empirically with all possible symmetries found. Our scheme can be implemented efficiently on average with non-local SWAP gates; we also give a less efficient algorithm with only local operations, which may be more appropriate for current noisy quantum devices. We simulate our algorithm on representative families of states, including cluster states and ground states of Rydberg and Ising Hamiltonians. We also find that the numerical query complexity scales well with qubit size.

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arXiv2023

Analytic theory for the dynamics of wide quantum neural networks

Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.

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arXiv2022

Quantum reservoir computing using arrays of Rydberg atoms

Quantum computing promises to provide machine learning with computational advantages. However, noisy intermediate-scale quantum (NISQ) devices pose engineering challenges to realizing quantum machine learning (QML) advantages. Recently, a series of QML computational models inspired by the noise-tolerant dynamics on the brain have emerged as a means to circumvent the hardware limitations of NISQ devices. In this article, we introduce a quantum version of a recurrent neural network (RNN), a well-known model for neural circuits in the brain. Our quantum RNN (qRNN) makes use of the natural Hamiltonian dynamics of an ensemble of interacting spin-1/2 particles as a means for computation. In the limit where the Hamiltonian is diagonal, the qRNN recovers the dynamics of the classical version. Beyond this limit, we observe that the quantum dynamics of the qRNN provide it quantum computational features that can aid it in computation. To this end, we study a qRNN based on arrays of Rydberg atoms, and show that the qRNN is indeed capable of replicating the learning of several cognitive tasks such as multitasking, decision making, and long-term memory by taking advantage of several key features of this platform such as interatomic species interactions, and quantum many-body scars.

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arXiv2022

Reconstructing Quantum States Using Basis-Enhanced Born Machines

Rapid improvement in quantum hardware has opened the door to complex problems, but the precise characterization of quantum systems itself remains a challenge. To address this obstacle, novel tomography schemes have been developed that employ generative machine learning models, enabling quantum state reconstruction from limited classical data. In particular, quantum-inspired Born machines provide a natural way to encode measured data into a model of a quantum state. Born machines have shown great success in learning from classical data; however, the full potential of a Born machine in learning from quantum measurement has thus far been unrealized. To this end, we devise a complex-valued basis-enhanced Born machine and show that it can reconstruct pure quantum states using projective measurements from only two Pauli measurement bases. We implement the basis-enhanced Born machine to learn the ground states across the phase diagram of a 1D chain of Rydberg atoms, reconstructing quantum states deep in ordered phases and even at critical points with quantum fidelities surpassing 99%. The model accurately predicts quantum correlations and different observables, and system sizes as large as 37 qubits are considered. Quantum states across the phase diagram of a 1D XY spin chain are also successfully reconstructed using this scheme. Our method only requires simple Pauli measurements with a sample complexity that scales quadratically with system size, making it amenable to experimental implementation.

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