Sharon Xalxo

Project Type: DST-NQM Funded Research

Status: Ongoing

Description: We present a hardware-oriented hybrid quantum-classical implementation for solving linear ordinary differential equations via the Chebyshev spectral method and the Quantum Singular Value Transformation (QSVT) framework. A central practical obstacle in QSVT is block encoding: existing schemes are predominantly oracle-based and lack concrete, transpilable gate decompositions, while oracle-free alternatives such as FABLE and its variants incur large subnormalization factors (typically ∼ 20), rendering the resulting circuit depths in- tractable. Although recent efforts have begun to address explicit circuit-level constructions, non-normal dense matrices of the type arising from Chebyshev discretization remain particu- larly challenging, as standard Hermitian-oracle constructions fail entirely for such systems. Our primary contribution is a hardware-aware LCU block encoding via Pauli decomposition that is fully transpilable, achieving subnormalization ≈2.7 through a structured SELECT oracle (ex- actly 2q two-qubit gates), a don’t-care-optimized PREPARE circuit (5 CNOTs, reduced from 15), and an ANF-minimized PHASE circuit (2 CZ gate). Combined with clean-mode re- flection operator optimization and direct numerical phase generation which yields real-valued output amplitudes, eliminating the need for state tomography or a Hadamard test. The best configuration achieves circuit depth 738 and 374 CX gates, a 284× improvement over the FA- BLE + PYQSP baseline. We validate correctness on a noiseless simulator and characterize noise-induced degradation under the ibm fez noise model. While depth 738 remains beyond reliable near-term execution, this work establishes a concrete, implementable QSVT pipeline for ODE solving and identifies clear directions for further depth reduction.

Tools Used: Qiskit, Python, NumPy

Guide: Prof. Anil Shaji, IISER TVM

Focus Area: Dissipative Quantum Dynamics

Key Topics: Lindblad equation, decoherence channels, Kraus operators, master equations

Description: This research interest centers on a collection of pedagogical simulations exploring open quantum systems with a focus on light–matter interactions in solid-state platforms. Using the QuTiP (Quantum Toolbox in Python) framework, the notebooks investigate the theoretical foundations and practical challenges of achieving strong coupling between quantum emitters and optical fields, with detailed attention to realistic noise sources and fabrication constraints. The work bridges theory and computation by reproducing established theoretical proposals from the literature while building intuition through numerical exploration. Each simulation is written incrementally in tutorial style, progressing from foundational concepts to sophisticated multi-parameter studies, making them suitable both as learning tools for newcomers and as reference implementations for researchers. Strong light–matter coupling in solid-state systems promises transformative applications in quantum information processing, quantum sensing, and nonlinear quantum optics. However, realizing these systems requires precise control over quantum coherence and careful mitigation of environmental noise. The notebooks explore three interconnected themes. First, coherent dynamics captured through the Jaynes–Cummings model and its extensions reveal the interplay between a quantum emitter and a single quantized electromagnetic mode, uncovering phenomena like vacuum Rabi splitting and the Purcell effect. Second, decoherence and noise are systematically decomposed, since real devices operate as open quantum systems where dissipation, dephasing, and spectral noise inevitably degrade quantum properties. Third, the work addresses engineering trade-offs, as achieving strong coupling demands careful optimization of multiple parameters—cavity quality factors, emitter-cavity detuning, spatial overlap, and material properties—each subject to fabrication constraints. The simulations are built upon a foundation of rigorous theory: each notebook begins with the relevant Hamiltonian and master equation, clearly stated and justified, so that theory and simulation run in parallel and readers can follow the connection between mathematical formalism and numerical result. The notebooks are structured to introduce concepts progressively, with early sections establishing baselines and later sections adding physical realism by including noise and spatial inhomogeneity. All simulations are implemented to match published theoretical predictions, with reference lists at the end of each notebook linking the work to foundational and recent literature, ensuring traceability and reproducibility. Visualizations are chosen deliberately to illuminate physics—time evolution of populations, spectroscopic signatures, parameter-space phase diagrams, and correlation functions—rather than merely displaying data. This is an active learning project. The codes originated as personal exploration tools and are being progressively rewritten in polished, pedagogical form. While the simulations reproduce established theoretical results, some implementations may contain approximations or require further refinement as understanding deepens. This iterative approach mirrors genuine scientific practice and maintains intellectual honesty about the project's scope: rigorous simulations of well-understood physics, suitable for education and as a foundation for further research, rather than novel theoretical predictions or experimental data.

Tools Used: QuTiP, Python, NumPy, SciPy

Code: Available on GitHub

Focus Area: Quantum Field Theory on Quantum Computers

Methods: Trotter-Suzuki decomposition, variational quantum eigensolvers, lattice gauge theory

Description: Quantum Lattice Model Simulations: Digital Quantum Simulation of Field Theories This research interest centers on a collection of pedagogical simulations exploring quantum lattice models (QLMs) and their application to digital quantum simulation of field theories. Using primarily Qiskit, with complementary structures from PennyLane and other frameworks, the notebooks investigate how to efficiently map field theories onto quantum hardware architectures, with particular emphasis on matching the natural symmetries and degrees of freedom of each theory to the most appropriate quantum substrate. The work bridges theoretical physics and quantum computing by implementing established proposals for digital quantum simulation while building intuition through concrete, runnable code. Each simulation is written incrementally in tutorial style, progressing from foundational concepts in lattice gauge theory to sophisticated implementations on near-term quantum processors, making them suitable both as learning tools for those new to quantum simulation and as reference implementations for researchers developing quantum algorithms for condensed matter and high-energy physics. Digital quantum simulation offers a path toward understanding strongly correlated quantum systems and gauge theories that remain intractable classically. However, efficient simulation requires careful matching between the symmetries embedded in the physical theory and the native structure of the quantum hardware. The notebooks explore this central design principle across multiple dimensions. The framework recognizes that different gauge groups naturally prefer different quantum encodings: Z₂ theories map efficiently onto qubits, Z₃ theories onto qutrits, and higher gauge groups onto systems with correspondingly richer Hilbert spaces. Rather than forcing all theories into a single qubit-based architecture, this work emphasizes identifying and exploiting the minimal quantum resource required for faithful, efficient simulation. This architectural flexibility becomes crucial on noisy near-term quantum devices where every additional qubit and two-qubit gate introduces error; matching theory to hardware reduces overhead and improves fidelity. The simulations build upon rigorous theoretical foundations: each notebook begins with the lattice Hamiltonian in its continuum limit, explains the discretization and gauge-invariant constraints, and then systematically constructs the quantum circuit encoding. Theory and implementation run in parallel so that readers understand both the physics being simulated and the concrete choices made during digitization. The notebooks progress incrementally, with early sections establishing the theoretical scaffold and later sections implementing full variational algorithms, measurement strategies, and parameter-space explorations. All simulations are benchmarked against known analytical results or classical tensor-network calculations where available, ensuring numerical reliability and providing concrete validation of the quantum implementation. Reference lists at the end of each notebook link the work to foundational lattice gauge theory literature, digital quantum simulation proposals, and recent experimental realizations, maintaining traceability and grounding the work in the broader research landscape. The foundational work in this collection focuses on the Schwinger model—quantum electrodynamics in 1+1 dimensions. A complete, self-contained Qiskit implementation explores U(1) Wilson lattice gauge theory following the theoretical framework of digital quantum simulators by Muschik et al. All circuits are designed to run on statevector simulators, but with explicit consideration of the native gate sets available in trapped-ion architectures, particularly all-to-all Mølmer–Sørensen interactions, which enable efficient implementation of the non-local Jaynes–Cummings-type gates required for gauge theory simulation. Through this example, readers gain practical experience with the full pipeline: encoding quantum states with appropriate symmetries, implementing gauge-invariant dynamics, measuring physical observables, and extracting predictions about the continuum field theory from finite lattice simulations. This is an active learning project in ongoing development. The codes originated as personal exploration tools for understanding the connections between quantum information theory and quantum field theory, and are being progressively rewritten in polished, pedagogical form. While the simulations reproduce established theoretical results from the digital quantum simulation literature, some implementations may contain approximations or require refinement as understanding deepens. This iterative approach reflects genuine scientific practice and maintains intellectual honesty about the project's scope: clear, working implementations of well-understood proposals in lattice gauge theory and their efficient encoding on quantum hardware, suitable for education and as a foundation for developing new quantum simulation algorithms, rather than novel theoretical methods or experimental results.

Tools Used: Qiskit, Python

Code: Available on GitHub

Focus Area: Algorithm Design & Analysis

Specific Interests: QSVT, block encoding, VQE, QPE, HHL, hybrid algorithms

Description:

Tools Used: Qiskit, Python