The depth advantage has a catch
A preprint presents a probabilistic quantum algorithm that could make a key part of imaginary-time evolution grow in circuit depth linearly with the number of iterations. Imaginary-time evolution here is used for ground-state preparation. Called PDBQITE, the method is presented as an alternative to the original recursive DB-QITE construction, whose depth is described as growing exponentially as more evolution steps are added.
The improvement comes with a built-in gamble. PDBQITE uses postselection, meaning it keeps only runs that produce the required measurement outcome. In the simulations, the chance of success at an individual step stays close to one, but the chance that all required steps succeed declines exponentially as the iteration count rises.
In first-order PDBQITE, each iteration uses one ancilla qubit, one controlled real-time evolution and one mid-circuit measurement. The paper gives an analytical lower bound for the per-step success probability that is favorable when the timestep is small: it is at least one divided by the square of one plus the square root of the timestep. That helps explain why individual updates can look reliable even while many updates create a cumulative probability problem.
To reduce the number of steps, the authors also test second-order PDBQITE. It permits larger imaginary-time steps but adds an ancilla qubit and an extra controlled real-time evolution, shifting some of the burden to a heavier iteration.
Tests on molecules and graphs
The molecular test used LiH and BeH2, with both PDBQITE orders starting from a Hartree-Fock initial state. The exercise was a ground-state simulation.
Both orders reached the study's chemical-accuracy target in those simulations. The second-order version did so in as few as two iterations and had roughly an order-of-magnitude higher cumulative success probability at that target, even though its per-step success was lower. Against PITE, the comparator used in the molecular tests, both PDBQITE variants were reported to perform better overall; PITE had success similar to first-order PDBQITE but worse energy per iteration and deeper circuits.
For a graph-optimization test, the main MaxCut benchmark used randomly weighted regular-graph instances: 20 instances at graph size n = 18, with vanilla QAOA tested at up to 17 layers.
Beyond the stated depth threshold, adding first-order PDBQITE was associated with a higher reported approximation ratio than vanilla QAOA, while the success probability remained greater than approximately 0.1. The result describes the tested regime and does not establish a universal advantage.
A trade-off, not a free shortcut
Another comparison used a 14-qubit antiferromagnetic Heisenberg model. First-order PDBQITE used fewer resources than PITE, reached similar energy and had significantly higher success probability. The paper also tests an amplitude-amplification variant designed to raise success probability. In the tested version, it reached the same approximation ratio with higher success probability, but each amplified iteration cost three times as much and state distortion required more iterations.
The main message is therefore a trade-off, not a free reduction in quantum cost. First-order PDBQITE addresses recursive depth with linear growth per iteration, while second-order PDBQITE can use larger steps at the price of extra controlled evolution and ancilla resources. The cumulative probability loss remains the central constraint.
The work is an arXiv preprint, version 1, and its evidence comes from analytical bounds and classical simulations of LiH, BeH2, graph benchmarks and a 14-qubit spin model. The comparisons are limited to the tested systems and settings, so the paper describes a resource-success trade-off rather than a universal replacement for existing methods.
Paper data and sources
Original title: A quantum double-bracket algorithm for imaginary-time evolution with exponentially shorter depth
Authors: Ioannis Kolotouros, Raul Garcia-Patron
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-09-29
DOI: Not available
Original paper · Full text