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The real- and imaginary-time evolution of quantum states are powerful toolsin physics, chemistry, and beyond, to investigate quantum dynamics, prepareground states or calculate thermodynamic observables. On near-term devices,variational quantum time evolution is a promising candidate for these tasks, asthe required circuit model can be tailored to trade off available devicecapabilities and approximation accuracy. However, even if the circuits can bereliably executed, variational quantum time evolution algorithms quickly becomeinfeasible for relevant system sizes due to the calculation of the QuantumGeometric Tensor (QGT). In this work, we propose a solution to this scalingproblem by leveraging a dual formulation that circumvents the explicitevaluation of the QGT. We demonstrate our algorithm for the time evolution ofthe Heisenberg Hamiltonian and show that it accurately reproduces the systemdynamics at a fraction of the cost of standard variational quantum timeevolution algorithms. As an application of quantum imaginary-time evolution, wecalculate a thermodynamic observable, the energy per site, of the Heisenbergmodel.

Variational Quantum Time Evolution without the Quantum Geometric Tensor