arXiv subjects

Karunya Shirali

Publications and source records attributed to Karunya Shirali.

10 recordsLinked to original sources

arXiv2026

An efficient algorithm for approximate shadow Hamiltonian simulation

We propose an efficient algorithm based on shadow Hamiltonian simulation to approximately simulate the real-time dynamics of observables under time-independent Hamiltonians. Shadow Hamiltonian simulation works at the level of the operator algebra generated by the observables through commutators with the Hamiltonian. Exactly encoding the quantum state in this picture is generally inefficient for interacting systems due to the exponential growth of the operator algebra. Our algorithm overcomes this bottleneck by systematically identifying the elements of the algebra most relevant to the target observables. This targeted approach is a controlled approximation that yields a highly efficient quantum state encoding that substantially reduces the size of the qubit register required to perform the time evolution using the shadow Hamiltonian. We propose two main pruning schemes, one based on a predefined operator basis and another on a constructed Krylov basis. We also present a hybrid scheme that builds a Krylov basis within a pruned algebra in the predefined basis. We benchmark our algorithm using lattice spin systems in one and two dimensions, for both one- and higher-point correlators as observables.

quant-ph↗

arXiv2026

Q3SAT-GPT: A Generative Model for Discovering Quantum Circuits for the 3-SAT Problem

This work introduces Q3SAT-GPT, a generative model for discovering quantum circuits for the Max-E3-SAT problem. Our method learns from high-performing QAOA-style ansätze to directly generate candidate circuits. To create high-quality supervision, we also introduce Mosaic Adaptive QAOA (MosaicADAPT-QAOA), an adaptive strategy for constructing low-depth QAOA circuits by selecting subsets of mixer operators in each step, rather than inserting operators sequentially. The resulting circuits serve as training data for the generative model, allowing it to learn effective circuit design patterns while eliminating the need for costly variational optimization at inference time. Experiments show that our framework attains strong solution quality with shallow circuits and scales significantly better than both our adaptive construction procedure and conventional variational baselines. Our results establish generative modeling as a high-performance route toward the scalable discovery of quantum optimization circuits, demonstrating that these models can effectively internalize circuit logic while providing a foundation for future, instance-aware inductive biases. Reproducibility: The source code is available at https://github.com/pratimugale/Q3SAT-GPT.

quant-ph↗

arXiv2026

TIMES-ADAPT: A Quantum algorithm for real-time evolution in low-energy subspaces using fixed-depth circuits

We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained unitary that diagonalizes the Hamiltonian in a subspace, we construct fixed-depth circuits for real-time evolution in the subspace, where time only enters as a circuit parameter. We present two versions of the algorithm depending on whether the initial state is specified in the energy eigenbasis or computational basis. We consider two important applications of our methods: wave packet evolution and energy transport in spin systems. We benchmark our algorithms using variants of the Heisenberg XXZ model.

quant-ph↗

arXiv2025

TEPID-ADAPT: Adaptive variational method for simultaneous preparation of low-temperature Gibbs and low-lying eigenstates

Preparing Gibbs states, which describe systems in equilibrium at finite temperature, is of great importance, particularly at low temperatures. In this work, we propose a new method -- TEPID-ADAPT -- that prepares the thermal Gibbs state of a given Hamiltonian at low temperatures using a variational method that is partially adaptive and uses a purification with a minimal number of ancillary qubits. We also present an alternative implementation without ancillary qubits. A key technical innovation here is to use a mixed-state ansatz where the entropy can be efficiently calculated, with no computational overhead. Our algorithm uses a truncated, parametrized eigenspectrum of the Hamiltonian. Beyond preparing Gibbs states, this approach also straightforwardly gives us access to the truncated low-energy eigenspectrum of the Hamiltonian, making it also a method that prepares excited states simultaneously. As a result of this, we are also able to prepare thermal states at any lower temperature of the same Hamiltonian without further optimization.

quant-ph↗

arXiv2025

Floquet-ADAPT-VQE: A Quantum Algorithm to Simulate Non-Equilibrium Physics in Periodically Driven Systems

Periodically driven quantum systems exhibit many fascinating phenomena absent in equilibrium systems, but their simulation is more challenging than that of static systems. Consequently, quantum simulation of these systems offers greater opportunity for achieving quantum advantage. To build the foundation for simulating time-periodic Hamiltonians, we utilize the Floquet-Hilbert space formalism to transform the Hamiltonian into a time-independent form and provide its Pauli decomposition. We propose a hybrid quantum-classical algorithm, Floquet-ADAPT-VQE, to simulate the non-equilibrium physics of periodically driven quantum systems. We define a cost function based on the square of the shifted extended Floquet Hamiltonian and show how to prepare Floquet states using Floquet-ADAPT-VQE. We also obtain a suitable auxiliary initial state whose squared Floquet energy is independent of the number of auxiliary qubits as well as the driving frequency, which leads to better convergence with fewer ADAPT iterations. Additionally, we provide a framework to calculate the time-dependent expectation value of observables in the Floquet state with fixed-depth quantum circuit. We demonstrate our algorithm by performing numerical simulations on a periodically driven XYZ model with a magnetic field. We also explore potential applications of our algorithm for studying various non-equilibrium phenomena in periodically driven systems.

quant-ph↗

arXiv2025

QAOA-GPT: Efficient Generation of Adaptive and Regular Quantum Approximate Optimization Algorithm Circuits

Quantum computing has the potential to improve our ability to solve certain optimization problems that are computationally difficult for classical computers, by offering new algorithmic approaches that may provide speedups under specific conditions. In this work, we introduce QAOA-GPT, a generative framework that leverages Generative Pretrained Transformers (GPT) to directly synthesize quantum circuits for solving quadratic unconstrained binary optimization problems, and demonstrate it on the MaxCut problem on graphs. To diversify the training circuits and ensure their quality, we have generated a synthetic dataset using the adaptive QAOA approach, a method that incrementally builds and optimizes problem-specific circuits. The experiments conducted on a curated set of graph instances demonstrate that QAOA-GPT, generates high quality quantum circuits for new problem instances unseen in the training as well as successfully parametrizes QAOA. Our results show that using QAOA-GPT to generate quantum circuits will significantly decrease both the computational overhead of classical QAOA and adaptive approaches that often use gradient evaluation to generate the circuit and the classical optimization of the circuit parameters. Our work shows that generative AI could be a promising avenue to generate compact quantum circuits in a scalable way.

quant-ph↗

arXiv2024

Surrogate Constructed Scalable Circuits ADAPT-VQE in the Schwinger model

Inspired by recent advancements of simulating periodic systems on quantum computers, we develop a new approach, (SC)$^2$-ADAPT-VQE, to further advance the simulation of these systems. Our approach extends the scalable circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable ``Surrogate Constructed'' method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC)$^2$ methodology. Our approach allows for a wider set of classical computations, on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute properties of the Schwinger model - quantum electrodynamics for a single, massive fermion in $1+1$ dimensions - and show that our method can be used to accurately extrapolate to the continuum limit.

quant-ph↗

arXiv2024

Adaptive Quantum Generative Training using an Unbounded Loss Function

We propose a generative quantum learning algorithm, Rényi-ADAPT, using the Adaptive Derivative-Assembled Problem Tailored ansatz (ADAPT) framework in which the loss function to be minimized is the maximal quantum Rényi divergence of order two, an unbounded function that mitigates barren plateaus which inhibit training variational circuits. We benchmark this method against other state-of-the-art adaptive algorithms by learning random two-local thermal states. We perform numerical experiments on systems of up to 12 qubits, comparing our method to learning algorithms that use linear objective functions, and show that Rényi-ADAPT is capable of constructing shallow quantum circuits competitive with existing methods, while the gradients remain favorable resulting from the maximal Rényi divergence loss function.

quant-ph↗

arXiv2023

Scaling adaptive quantum simulation algorithms via operator pool tiling

Adaptive variational quantum simulation algorithms use information from the quantum computer to dynamically create optimal trial wavefunctions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wavefunctions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an ADAPT-VQE calculation on a smaller instance of the problem using a large, but computationally inefficient operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems.

quant-ph↗

arXiv2022

Inter-quintuple layer coupling and topological phase transitions in the chalcogenide topological insulators

Driving quantum phase transitions in the 3D topological insulators offers pathways to tuning the topological states and their properties. We use DFT-based calculations to systematically investigate topological phase transitions in Bi$_2$Se$_3$, Sb$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$ by varying the $c/a$ ratio of lattice constants. This ensures no net hydrostatic pressure under anisotropic stress and strain and allows a clear identification of the physics leading to the transition. As a function of $c/a$, all of these materials exhibit structural and electronic stability of the quintuple layers (QLs), and quasi-linear behavior of both the inter-quintuple layer distance and the energy gap near the topological transition. Our results show that the transition is predominantly controlled by the inter-QL physics, namely by competing Coulomb and van der Waals interactions between the outer atomic sheets in neighboring quintuple layers. We discuss the implications of our results for topological tuning by alloying.

cond-mat.mes-hall↗