A hardware-efficient binary-tree ansatz has a closed-form diagonal Fubini–Study metric, enabling metric-aware VQE and time evolution without auxiliary circuits, with linear-in-k pruning for sparse sectors.
Equating quantum imaginary time evolution, Riemannian gradient flows, and stochastic implementations
2 Pith papers cite this work, alongside 1 external citations. Polarity classification is still indexing.
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abstract
We identify quantum imaginary time evolution as a Riemannian gradient flow on the unitary group. We develop an upper bound for the error between the two evolutions that can be controlled through the step size of the Riemannian gradient descent which minimizes the energy of the system. We discuss implementations through adaptive quantum algorithms and present a stochastic Riemannian gradient descent algorithm in which each step is efficiently implementable on a quantum computer. We prove that for a sufficiently small step size, the stochastic evolution concentrates around the imaginary time evolution, thereby providing performance guarantees for cooling the system through stochastic Riemannian gradient descent.
fields
quant-ph 2years
2026 2representative citing papers
A necessary and sufficient condition for the quantum imaginary-time Mpemba effect is that it depends only on the population ratios of excited states to the ground state.
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A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling
A hardware-efficient binary-tree ansatz has a closed-form diagonal Fubini–Study metric, enabling metric-aware VQE and time evolution without auxiliary circuits, with linear-in-k pruning for sparse sectors.
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Theory of Quantum Imaginary-Time Mpemba Effect
A necessary and sufficient condition for the quantum imaginary-time Mpemba effect is that it depends only on the population ratios of excited states to the ground state.