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ACM Transactions on Quantum Computing

Utility-scale Experimental Quantum Computation with Hardware Efficient Ansätze and Calibrated Hamiltonian

Muhammad Ahsan

Published May 9, 2026• 0 citations
Publisher

Abstract

Variational quantum algorithms often adapt the ansätze (ansatz) to the target Hamiltonian, leading to deep or hardware-incompatible circuits. In this work we demonstrate an opposite approach: choosing a hardware-efficient CNOT-ladder ansatz and calibrating the Hamiltonian to compensate for its expressibility to solve ground-state energy problem of 100+ site lattice on real quantum computer. This ansatz-calibrated Hamiltonian framework enables two key advantages: (1) it allows restructuring the algorithm into smaller sub-problems which can independently solved off-line classically, leaving quantum computer tasked with recombining partial solutions into full state-vector with fewer parameters to optimize and (2) it leverages circuit-specific error statistics to de-noise observable readouts with nominal noise-mitigation overhead. We simulate the spin-1/2 antiferromagnetic Heisenberg model over a 103-site flat Kagome lattice using IBM’s Heron r1 and r2 processors. The obtained per-site ground-state energy of \(-0.4172\,J\) , which approaches the benchmark \(-0.4386\,J\) after open boundary correction and approximate error mitigation. Our experiments reveal a peculiar distribution of bond energies when the ansatz is executed on the quantum processor, in contrast to its classical simulation, which merits further investigation.

DOI
10.1145/3815786

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Variational quantum algorithms often adapt the ansätze (ansatz) to the target Hamiltonian, leading to deep or hardware-incompatible circuits. In this work we demonstrate an opposite approach: choosing a hardware-efficient CNOT-ladder ansatz and calibrating the Hamiltonian to compensate for its expressibility to solve ground-state energy problem of 100+ site lattice on real quantum computer. This ansatz-calibrated Hamiltonian framework enables two key advantages: (1) it allows restructuring the algorithm into smaller sub-problems which can independently solved off-line classically, leaving quantum computer tasked with recombining partial solutions into full state-vector with fewer parameters to optimize and (2) it leverages circuit-specific error statistics to de-noise observable readouts with nominal noise-mitigation overhead. We simulate the spin-1/2 antiferromagnetic Heisenberg model over a 103-site flat Kagome lattice using IBM’s Heron r1 and r2 processors. The obtained per-site ground-state energy of (-0.4172,J) , which approaches the benchmark (-0.4386,J) after open boundary correction and approximate error mitigation. Our experiments reveal a peculiar distribution of bond energies when the ansatz is executed on the quantum processor, in contrast to its classical simulation, which merits further investigation.
We present experimental quantum computation of the ground-state energy in a 103-site flat Kagome lattice under the antiferromagnetic Heisenberg model (KAFH), with IBM's Heron r1 and Heron r2 quantum processors. For spin-1/2 KAFH, our per-site ground-state energy estimate is −0.417 J-0.417\,J−0.417J, which, under open-boundary corrections, matches the energy in the thermodynamic limit, i.e., −0.4386 J-0.4386\,J−0.4386J. To achieve this, we used a hybrid approach that splits the conventional Variational Quantum Eigensolver (VQE) into local (classical) and global (quantum) components for efficient hardware utilization. More importantly, we introduce a Hamiltonian engineering strategy that increases coupling on defect triangles to mimic loop-flip dynamics, allowing us to simplify the ansatz while retaining computational accuracy. Using a single-repetition, hardware-efficient ansatz, we entangle up to 103 qubits with high fidelity to determine the Hamiltonian's lowest eigenvalue. This work demonstrates the scalability of VQE for frustrated 2D systems and lays the foundation for future studies using deeper ansatz circuits and larger lattices on utility quantum processors.
molecule, emphasizing practical implementation and performance on current quantum hardware. Our research presents a comparative study of HEA and UCCSD ansätze on noiseless and noisy simulations and implements VQE on recent IBM quantum computer noise models and a real quantum computer, IBM Fez, providing a fully functional code employing Qiskit 1.2. Our experiments confirm UCCSD's reliability in ideal conditions, while the HEA demonstrates greater robustness to hardware noise, achieving chemical accuracy on state-vector simulation (SVS). The results reveal that achieving ground-state energy within chemical accuracy is feasible without error mitigation during VQE convergence. We demonstrate that current quantum devices effectively optimize circuit parameters despite misestimating simulated energies. The SVS-evaluated energies provide a more accurate representation of the solution quality compared to QPU-estimated energy values, indicating that VQE converges to the correct ground state despite quantum noise. Our study also applies noise mitigation as a postprocessing technique, using zero-noise extrapolation (ZNE) on a real quantum computer. The detailed methodologies presented in this study, including Hamiltonian construction and Fermionic-to-qubit transformations, facilitate flexible adaptation of the VQE approach for various algorithm variants and across different levels of algorithmic implementation.
Abstract Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. We compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM’s quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y -rotations on all qubits.
This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver algorithm on real quantum hardware. We demonstrate that the ground-state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation. We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubitwise readout-error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.
Variational quantum algorithms are among the most promising approaches for simulating interacting quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. However, the practical success of variational quantum eigensolvers (VQE) critically depends on the structure of the chosen variational ansatz. In this work, we investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed, symmetry-preserving variational circuits. We benchmark variational results against exact diagonalization and noiseless simulations, and subsequently validate the approach on real IQM Garnet quantum hardware. Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior when compared to hardware-efficient ansatz under identical resource constraints. These findings highlight the importance of problem specific ansatz construction for reliable quantum simulations in the NISQ era.
Establishing the nature of the ground state of the Heisenberg antiferromagnet (HAFM) on the kagome lattice is well-known to be a prohibitively difficult problem for classical computers. Here, we give a detailed proposal for a variational quantum eigensolver (VQE) intending to solve this physical problem on a quantum computer. At the same time, this VQE constitutes an explicit experimental proposal for showing a useful quantum advantage on noisy intermediate-scale quantum devices because of its natural hardware compatibility. We classically emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy, as found by the VQE, approaches the true ground-state energy exponentially as a function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective transversal noise, adding to the noise resilience of these algorithms. Nevertheless, the extent of the effects of other noise types suggests the need for error mitigation and performance targets alternative to high-fidelity ground-state preparation, even for essentially hardware-native VQEs.