Quantum simulators promise to solve problems in quantum chemistry and condensed matter physics, but they are limited by short qubit coherence times and errors from long gate sequences. Standard Trotterization requires circuit depths that grow quadratically with evolution time, quickly making computations infeasible. This work aligns with efforts to overcome these limitations: nearby in the archive are studies on quantum error correction, quantum memory, and noise suppression. This paper offers a hybrid path: compress the evolution into shallow variational circuits while preserving accuracy.
On the 9-qubit superconducting processor L9 with tunable couplers, we used the VTC protocol. The idea is to fit the parameters of a shallow parameterized circuit after each short Trotter step so that it approximates the exact evolved state. Optimization was performed using L-BFGS-B with a warm start from the previous step. To recover the survival amplitude ⟨ψ₀|ψ(t)⟩, we applied quantum state tomography (QST) followed by purification to a pure state and alignment of the global phase with numerical simulation. The time series was then analyzed by fitting multi-frequency sinusoids and Fourier transform.
For the H₂ molecule at five bond lengths (0.25–2.25 Å), the average state fidelity between experiment and simulation exceeded 99.6%. Extracted energies matched exact diagonalization within 2×10⁻³ atomic units, including nearly degenerate excited states at large distances. For the Fermi–Hubbard model in metallic, intermediate, and Mott phases, energy accuracies reached up to 7×10⁻⁴. In the Mott phase, we resolved three closely spaced levels with splitting on the order of 0.03, which is inaccessible to standard Trotterization due to rapid decoherence.
This work differs from neighboring studies by using dynamical evolution on real hardware, rather than classical post-processing, as in the previous work by the same group on the 3D Ising model. This is the first experimental demonstration of VTC for spectroscopy of two different classes of systems: molecular and lattice. The method bypasses coherence-time limitations by extending effective evolution without increasing circuit depth. This approach paves the way for studying metal–insulator transitions and molecular dissociation on NISQ devices.
Scaling to more qubits will face the problem of exponentially growing measurement counts for tomography. Informationally complete measurements, such as SIC-POVM or shadow tomography, could reduce the number of runs. Another challenge is balancing the expressivity of the ansatz with its trainability; warm starts, already built into the protocol, can help. In the future, the method could be applied to more complex molecules and lattices, including systems with topological phases.
The method is directly applicable in quantum chemistry for calculating electronic spectra of molecules and in condensed matter physics for simulating strongly correlated materials. It is also useful for quantum dynamics problems that require long evolution under limited coherence.
Immediate next steps include implementing shadow tomography to reduce measurement overhead and testing the protocol on systems with more qubits. We also plan to explore adapting VTC to noisy tasks and to using quantum error correction.
This work addresses the fundamental problem of accurately simulating quantum dynamics on noisy intermediate-scale devices. It offers a practical way to overcome coherence-time limitations without full error correction, which remains an open question for scaling quantum simulators.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
A dynamic spectroscopy protocol with variational trotterization compression (VTC) was implemented on a 9-qubit superconducting processor, L9. For the H2 molecule at five internuclear distances and for the Fermi-Hubbard model in three correlation regimes, eigenenergies were extracted from time evolution with an accuracy of 2×10⁻³ atomic units. The approach used L-BFGS-B optimization with a warm start, quantum state tomography with purification and phase alignment, and then fitting with multifrequency sinusoids and Fourier analysis.
Where its strength is
The method sidesteps the coherence-time limit by extending the effective evolution without increasing circuit depth, and it provides the first experimental demonstration of VTC for spectroscopy of molecular and lattice systems.
Where it could go next
Worth trying
Why this may matter
Extending VTC to more complex systems and integrating it with error-mitigation methods could turn quantum spectroscopy into a practical tool for quantum chemistry and condensed-matter physics on NISQ devices.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.54, against a usual 0.64. It looks like few have drilled nearby.
The energy accuracy of 2×10⁻³ atomic units is equivalent to an error of about 0.05 electronvolts, comparable to the thermal energy at room temperature (about 0.025 eV).
The idea of compressing quantum evolution into a compact circuit resembles the concept of 'folded dimensions' from science fiction, where complex processes are packed into simple representations to bypass the constraints of reality.