Quantum computing holds promise for computational chemistry, but near-term quantum hardware remains limited by noise and scale, motivating classical bridging technologies such as quantum emulators. We present an application-specific systems-level benchmark of matrix product state (MPS) tensor-network emulation for real-time Hamiltonian evolution of a density matrix embedding theory (DMET)-embedded sulfonyl-fluoride pharmaceutical fragment, using state-vector simulation as reference. We evaluate runtime, accuracy, resource requirements, and entanglement growth across active spaces from 4 to 24 qubits for a one-body temporal observable used as a quantum fingerprint for reactivity prediction. The results identify a practical boundary for this workflow. At fixed bond dimension, MPS emulation retains favorable scaling, but the bond dimension required to estimate the observable within a 1.6 mHa chemical-accuracy threshold grows rapidly with active-space size. At 20-24 qubits, it approaches the maximum available MPS representation, eliminating the runtime advantage over state-vector simulation. Entanglement entropy analysis shows that increasing bipartite entanglement in the time-evolved state drives this cost growth, consistent with a mismatch between a one-dimensional MPS ansatz and the non-local correlations generated by molecular electronic dynamics. We do not claim a universal crossover across molecules, observables, mappings, or tensor-network geometries. Rather, this study measures where MPS emulation ceases to be an efficient classical surrogate for this chemically motivated Hamiltonian-simulation workflow. The results motivate entanglement-aware algorithm design, orbital-ordering and mapping optimization, alternative tensor-network geometries, and ultimately fault-tolerant quantum hardware for regimes where accurate molecular dynamics generate non-compressible entanglement.
Quantum computing holds promise for computational chemistry, but near-term quantum hardware remains limited by noise and scale, motivating classical bridging technologies such as quantum emulators. We present an application-specific systems-level benchmark of matrix product state (MPS) tensor-network emulation for real-time Hamiltonian evolution of a density matrix embedding theory (DMET)-embedded sulfonyl-fluoride pharmaceutical fragment, using state-vector simulation as reference. We evaluate runtime, accuracy, resource requirements, and entanglement growth across active spaces from 4 to 24 qubits for a one-body temporal observable used as a quantum fingerprint for reactivity prediction. The results identify a practical boundary for this workflow. At fixed bond dimension, MPS emulation retains favorable scaling, but the bond dimension required to estimate the observable within a 1.6 mHa chemical-accuracy threshold grows rapidly with active-space size. At 20-24 qubits, it approaches the maximum available MPS representation, eliminating the runtime advantage over state-vector simulation. Entanglement entropy analysis shows that increasing bipartite entanglement in the time-evolved state drives this cost growth, consistent with a mismatch between a one-dimensional MPS ansatz and the non-local correlations generated by molecular electronic dynamics. We do not claim a universal crossover across molecules, observables, mappings, or tensor-network geometries. Rather, this study measures where MPS emulation ceases to be an efficient classical surrogate for this chemically motivated Hamiltonian-simulation workflow. The results motivate entanglement-aware algorithm design, orbital-ordering and mapping optimization, alternative tensor-network geometries, and ultimately fault-tolerant quantum hardware for regimes where accurate molecular dynamics generate non-compressible entanglement.
Efficient simulation of open quantum systems is central to modeling noisy quantum hardware and many-body dynamics. In trajectory-based tensor network methods, cost is often associated with trajectory-level quantities such as entanglement growth or bond dimension. However, the total cost of a fixed-accuracy simulation also depends on statistical sampling, and the interplay between per-trajectory complexity and sampling effort remains poorly understood. Here we introduce a cost-resolved framework for matrix product state (MPS)-based quantum trajectory simulations that decomposes total cost into memory per trajectory, runtime per trajectory, and sampling effort. We show that physically equivalent stochastic unravelings of the same Lindblad dynamics do not necessarily reduce total cost, but instead redistribute cost between trajectory complexity and statistical convergence. This trade-off is quantified by two dimensionless inflation factors: a bond dimension inflation α and a sampling inflation κ, which together determine the preferred unraveling under hardware-dependent memory and parallelism constraints. We provide a practical protocol for extracting (α,κ) from modest pilot simulations and demonstrate it using benchmarks across multiple noise channels. The resulting decision maps show that the computationally favorable unraveling can change with noise strength, time-step resolution, system size, and available parallelism. These results establish unraveling choice as a hardware-aware simulation design problem rather than an intrinsic optimization of trajectory entanglement alone.
We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H2, LiH, BeH2, H2O, and NH3. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H2 and HeH+ using both STO-3G and 6-31G basis sets, and for LiH and BeH2 in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 × 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.
The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier} restricts classical simulations and, conversely, underpins the quantum advantage anticipated from future devices. Here we show that, for one-dimensional Hamiltonian dynamics, the spatio-temporal tensor network encoding the evolved wave function amplitudes can be contracted efficiently along the left-right (spatial) direction. Exploiting this structure, we develop a hybrid Tensor-Network/Monte-Carlo (TN-MC) algorithm that samples the wave function and evaluates expectation values of generic local operators with computational cost that scales only polynomially in time. The accurate contraction of the wave function amplitudes is a consequence of the favorable scaling with time of the generalised temporal entropies. We find that their real part either saturates or, at most, grows logarithmically with time, revealing new instances of continuous dynamical quantum phase transitions (DQPTs) which we characterize. Our results therefore show that, when computing expectation values of local operators, the entanglement barrier in one-dimensional Hamiltonian evolution can be bypassed with a TN-MC blend.
The strategic demand for quantum hardware currently outpaces the availability of near-term devices, necessitating high-performance software emulators to validate novel protocols. We introduce Hyperion, a massively parallel, GPU-accelerated quantum emulator architected to bypass the classical memory walls inherent in strongly correlated quantum chemistry simulations. Hyperion leverages custom-optimized Sparse Matrix-Sparse Vector (SpMspV) kernels to natively accelerate exact matrix-vector multiplications, enabling strictly accurate State-Vector (SV) ADAPT-VQE simulations for up to 32 qubits on multi-node platforms. To scale beyond this hardware limit, we address the trade-off in pure Matrix Product State (MPS) emulators, where standard compression yields severe truncation errors and strict compression triggers intractable tensor rank explosions. We propose a novel partitioned emulation, namely the SV-MPS strategy: by routing non-interacting terms into an exact sparse SV core and delegating interacting terms to the MPS engine, this approach achieves emulation of 36 to 40 qubits with controlled approximations. This partitioning significantly reduces GPU resource requirements while maintaining robust accuracy across ADAPT-VQE iterations. Ultimately, Hyperion offers a high-fidelity platform dedicated to the development of new quantum algorithms for chemistry, enabling the modeling of realistic chemical systems at accuracies approaching the exact Full Configuration Interaction (FCI) / Complete Basis Set (CBS) limit.
Compiling classically optimized matrix product states (MPSs) into quantum circuits is a promising route to initial-state preparation for strongly correlated molecules, but the accuracy, gate cost, and classical scalability of existing MPS compilation methods have not been systematically assessed. Here, we benchmark representative analytical, variational, and hybrid MPS compilation methods for strongly correlated systems including hydrogen chains and iron-sulfur clusters. We compare state infidelity, CNOT gate count, classical runtime, and parallel scalability across different system sizes and bond dimensions. We also introduce a divide-and-conquer environment-aware compilation algorithm (DCE), which optimizes each local isometry approximation according to its contribution to the prepared-state fidelity. The results reveal complementary operating regimes: direct variational compilation methods are gate-efficient for some smaller molecular systems with O(10) qubits and O(10) bond dimensions or moderate accuracy targets with infidelity of order 10−1, whereas divide-and-conquer methods scale more favorably for larger systems and relatively higher bond dimensions of O(10-102), particularly when target infidelities below 10−1 are required. Within the latter family, environment-aware optimization improves accuracy over unitary-distance-based compilation while retaining task-level parallelism. For the FeMo-cofactor (FeMoco), we find the DCE algorithm together with the MPS obtained in the entanglement-minimized orbitals (EMOs) provides a resource-efficient route to initial-state preparation. Our results provide practical guidance for selecting and developing MPS compilation methods for strongly correlated molecular simulations.
Predicting the properties of correlated materials and molecules often requires a many-body description that goes beyond single-particle and mean-field approximations. Tensor networks address this challenge by exploiting the entanglement structure of quantum states to construct compact, systematically improvable representations. Although developed largely for idealized model Hamiltonians, these methods are increasingly being integrated into material-specific calculations. This Perspective introduces their underlying principles and examines how network geometry, bond-dimension truncation, and approximate contraction determine the accuracy and computational reach of these approaches. We survey applications across regimes of increasing complexity, ranging from ground-state properties of quantum magnets and itinerant-fermion systems to excitation spectra, nonequilibrium dynamics, finite-temperature and open systems, and molecular electronic structure. We then examine four routes connecting these methods to real materials, including experimentally constrained models, downfolded Hamiltonians, dynamical mean-field theory with tensor network impurity solvers, and quantum embedding. Throughout, we evaluate the maturity of existing capabilities and their principal limitations, synthesizing this assessment into a practical method-selection guide. We argue that reliable materials predictions require quantifying uncertainties introduced at each stage, from constructing material-specific Hamiltonians to extracting experimentally accessible observables. Finally, we identify the algorithmic advances and reproducible computational practices needed to establish tensor networks as a routine tool for predictive materials science and quantum chemistry.