We use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more – sizes at which generic quantum circuits are beyond the reach of exact state-vector simulation – thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately 5 % without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.
We use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more – sizes at which generic quantum circuits are beyond the reach of exact state-vector simulation – thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately 5 % without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.
We propose a quantum protocol that allows preparing a ground state (GS) of the honeycomb Kitaev model. Our approach efficiently uses underlying symmetries and techniques from topological error correction. It is based on the stabilization procedure, the developed centralizer ansatz, and utilizes the vortex basis description as the most advantageous for qubit-based simulations. We demonstrate the high fidelity preparation of spin liquid ground states for the original Kitaev model, getting the exact GS for N=24 spins using 230 two-qubit operations. We then extend the variational procedure to non-zero magnetic fields, studying observables and correlations that reveal the phase transition. Finally, we perform dynamical simulation, where the ground state preparation opens a route towards studies of strongly-correlated dynamics, and a potential quantum advantage.
Abstract Quantum computers promise to solve electronic structure, lattice dynamics, and strongly correlated problems beyond classical reach. However, near-term noisy intermediate scale quantum (NISQ) processors require systematic benchmarking to establish where variational algorithms with error mitigation can achieve chemical accuracy and cor rectly predict physical phenomena. Here we present 28 quantum material simula tions implemented with Qiskit, spanning molecular hydrogen (H 2 ) through the iron molybdenum cofactor (FeMoco), one-dimensional Hubbard chains, Kitaev honeycomb spin liquids, topological insulators (SSH model), BCS superconductors, and disordered Anderson insulators. Using the variational quantum eigensolver (VQE) with UCCSD ansatz, we achieve chemical accuracy (±1.6 mHa) for H 2 across the full dissociation curve and recover exact ground-state energies for H4 within 9 mHa after zero-noise extrapolation (ZNE) — reducing raw VQE errors from 152 mHa to 9 mHa. We accu rately identify the transverse-field Ising quantum critical point (h c = J) with 4 qubits, resolve Majorana Dirac dispersions in the Kitaev spin liquid, and reproduce the Mott transition in the Fermi-Hubbard model at U c = 6t. Resource estimation for FeMoco reveals O(N 2.5 ) scaling, projecting chemical accuracy with ∼200 logical qubits. Across all benchmarks, we quantify the accuracy-circuit depth tradeoff, demonstrating that depth-6 VQE ans¨atze achieve chemical accuracy for small molecules while depth-10 is required for correlated lattices. These results establish a comprehensive benchmark suite for evaluating quantum hardware, error mitigation protocols, and variational al gorithms for materials science on NISQ processors.
Periodically driven interacting quantum many-body systems can exhibit long-lived prethermal dynamics, where local observables retain coherent structure even as entanglement and operator complexity grow. Accessing this regime at the system sizes and times needed to determine physical properties of the prethermal state remains a central challenge: state-of-the-art classical methods become unreliable, while noise in quantum hardware degrades observable expectation values. Here we overcome these limitations for a Floquet Ising magnet realized on a heavy-hex lattice. Using the advanced error mitigation software QESEM on an IBM Heron r3 superconducting quantum processor, we measure magnetization dynamics with percent-level precision and resolve long-lived subharmonic prethermal oscillations in systems of up to 74 qubits. These experiments reach regimes for which leading tensor-network simulations fail to converge, while sparse Pauli-path simulations remain strongly truncation dependent despite extensive computations on advanced GPUs and the Fugaku supercomputer. Leveraging this quantum-accessible regime, we extend finite-size scaling to larger systems and find an unexpectedly slow decrease of the oscillation amplitude with system size, providing strong evidence that this oscillatory response persists in the thermodynamic limit of heavy-hex ladders. A hierarchy of mitigation and validation tests, including unbiased error mitigation, agreement between independent mitigation estimators, noise-model validation on the superconducting hardware, and cross-platform corroboration at selected Floquet cycles on Quantinuum System Model H2 and Quantinuum Helios trapped-ion hardware, supports the reliability of these findings. Our work establishes error-mitigated quantum processors as quantitative scientific instruments for discovering new physics in non-equilibrium quantum matter.
Entanglement renormalization circuits for 2d Gaussian Fermion States
The simulation of entangled ground-states of quantum materials remains challenging for classical computational methods in more than one spatial dimension, and is a prime target for quantum computational advantage. To this end, an important goal is to identify efficient quantum state preparation protocols that minimize the physical qubit number and circuit depth resources required to capture higher-dimensional quantum correlations. This work introduces a quantum circuit compression algorithm for Gaussian fermion states based on the multi-scale entanglement renormalization ansatz (MERA), which provides an exponential reduction in the circuit depth required to approximate highly-entangled ground-states relevant for quantum materials simulations. The algorithm, termed two-dimensional Gaussian MERA (2d GMERA), extends MERA techniques to compress higher-dimensional Gaussian states. Through numerical simulations of the Haldane model on a honeycomb lattice, the method is shown to accurately capture area-law entangled states including topologically trivial insulators, Chern insulators, and critical Dirac semimetals. While Gaussian states alone are classically simulable, this approach establishes empirical upper bounds on quantum resources needed to prepare free fermion states that are adiabatically connected to correlated ground states, providing guidance for implementing these protocols on near-term quantum devices and offering a foundation for simulating more complex quantum materials. Finally, we develop a novel fermion-to-qubit encoding scheme, based on an expanding 2d topological order, that enables implementing fermionic rotations via qubit Pauli rotations with constant Pauli weight independent of system size.
Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation.Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with ``little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for ``little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated.Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D gapped systems. Note that the ground-state energy of 1D gapless Hamiltonians is computationally intractable even in the presence of translational invariance.It is tempting to extend methods and tools in 1D to two and higher dimensions (2+D), e.g., matrix product states are generalized to tensor network states. Since an area law for entanglement (if formulated properly) implies efficient matrix product state representations in 1D, an interesting question is whether a similar implication holds in 2+D. Roughly speaking, we show that an area law for entanglement (in any reasonable formulation) does not always imply efficient tensor network representations of the ground states of 2+D local Hamiltonians even in the presence of translational invariance. It should be emphasized that this result does not contradict with the common sense that in practice quantum states with more entanglement usually require more space to be stored classically; rather, it demonstrates that the relationship between entanglement and efficient classical representations is still far from being well understood.Excited eigenstates participate in the dynamics of quantum systems and are particularly relevant to the phenomenon of many-body localization (absence of transport at finite temperature in strongly correlated systems). We study the entanglement of excited eigenstates in random spin chains and expect that its singularities coincide with dynamical quantum phase transitions. This expectation is confirmed in the disordered quantum Ising chain using both analytical and numerical methods.Finally, we study the problem of generating ground states (possibly with topological order) in 1D gapped systems using quantum circuits. This is an interesting problem both in theory and in practice. It not only characterizes the essential difference between the entanglement patterns that give rise to trivial and nontrivial topological order, but also quantifies the difficulty of preparing quantum states with a quantum computer (in experiments).
Quantum computers promise an exciting path to the scalable simulation of quantum matter. However, in their nascent state, the accessible gate depth of quantum computation on available hardware remains highly constrained. In this thesis, I present a suite of hybrid quantum-classical algorithms that aid Hamiltonian simulation across both the Noisy Intermediate-Scale Quantum era and future fault-tolerant architectures. By treating classical computation as an active resource to refine quantum algorithms, I develop automated, variational methods to learn hardware-efficient circuits. This work aims to overcome traditional trainability barriers, such as barren plateaus, by embedding physical symmetries directly into the circuit design. Central to the thesis is the synergistic use of tensor networks to classically pre-compute weakly entangled stages of a quantum simulation. This enables the compression of deep circuits, drastically reducing both the accumulation of gate errors on near-term physical qubits and the prohibitive overhead of operations like magic state distillation on error-corrected hardware, reserving the quantum processor strictly for the most challenging, highly entangled dynamics. These methodologies are ultimately directed toward the ab-initio simulation of subatomic physics, providing a scalable approach for the first-principles study of strongly correlated systems, including nuclear structure and lattice gauge theories.