You can walk a long road, or you can fold it into a shorter route without losing the key landmarks. In quantum computing, that road is the time evolution of a state: it demands ever longer chains of operations, which quickly drown in noise on a real processor. Physicists have found a way to compress each step of the evolution into a compact, tunable circuit while keeping accuracy above 99%.
On the nine-qubit superconducting processor L9 with tunable couplers, they implemented the VTC protocol. After each short evolution step, the parameters of the shallow circuit were adjusted so that the state approached the exact one. To recover the survival amplitude, they used quantum state tomography followed by purification to a pure state and alignment of the global phase with numerical simulation. The time series was then analyzed by fitting multifrequency sinusoids and applying a Fourier transform.
For the hydrogen molecule H₂ at five bond distances (0.25–2.25 Å), the average state fidelity between experiment and simulation exceeded 99.6%. The 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 the metallic, intermediate, and Mott phases, the energy accuracy reached up to 7×10⁻⁴. In the Mott phase, they resolved three closely spaced levels with a splitting of about 0.03, which is inaccessible to standard Trotterization due to rapid decoherence.
It was unclear whether accurate energies of quantum systems could be extracted from real dynamics on a noisy processor without resorting to deep circuits with ancilla qubits. It turned out that variationally compressing each evolution step, followed by Fourier analysis of the time series, yields errors down to 2×10⁻³ atomic units, including nearly degenerate levels. The method can already be applied to compute electronic spectra of small molecules and models of strongly correlated materials on available quantum processors.
Compressed evolution brings us back to the image of a shorter route: instead of charting the entire path through noisy terrain, we traverse it in segments, each time checking the map and correcting the direction. This approach opens the way to studying metal–insulator transitions and molecular dissociation on NISQ devices.
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.