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Attested & literatureAlgorithmsVariational quantum eigensolver

Variational imaginary-time evolution

McLachlan-style projected imaginary-time dynamics update parameters toward low-energy states.

VQEvariational algorithmvariational imaginary-time evolution

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McLachlan-style projected imaginary-time dynamics update parameters toward low-energy states. This record separates the reusable method idea from any one molecule, Hamiltonian, optimizer, or device.

Circuit & simulation
What this takes and returns
TakesNothingWhat joins here

No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.

Nothing in the Atlas meets this end.

ReturnsNothingWhat joins here

No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.

Nothing in the Atlas meets this end.

This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →

Where this sits

This record is named by the layer graph at:

  • Variational imaginary-time evolution Method

    Takes A Hermitian HH reachable as a sum of terms, as sparse-access oracles or as a block-encoding; a way to prepare trial states, and — for the methods that need it — a trial state whose overlap with the ground state is not negligible; a target additive error ε\varepsilon and a confidence 1δ1-\delta. Returns A scalar estimate of the lowest eigenvalue with a stated additive-error guarantee, plus the run or query budget it consumed. Whether that estimate is also a rigorous upper bound is a property of the method and is not promised by the slot.

How it works

McLachlan-style projected imaginary-time dynamics update parameters toward low-energy states. In a complete experiment, the method must be paired with a defined qubit Hamiltonian, reference state, parameterized circuit, measurement grouping, classical optimizer, stopping rule, and error analysis. The catalog therefore treats it as a literature-backed algorithm record rather than pretending that one generic snippet is the paper's implementation. Use the cited source to recover assumptions and compare energy error, variance, circuit resources, measurement cost, optimizer evaluations, and robustness under the same instance and budget.

Implementation
Unsupported
vqe-imaginary-time.txt
METHOD: Variational imaginary-time evolution
SCOPE: McLachlan-style projected imaginary-time dynamics update parameters toward low-energy states.

This is a literature method record, not a fixed circuit.
Supply: Hamiltonian, reference state, ansatz, optimizer, measurement plan, and stopping rule.

A reference record, not runnable source. Leona cannot execute it, so it cannot be saved to your Library as a circuit.

Quantum vs classical

Classical baseline

Compare Variational quantum eigensolver with the strongest classical method for the same instance, input budget, and output metric.

Quantum claim

This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.

How to compare

Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.

Declared gaps

Nobody has reviewed this record for gaps yet.

Literature & references
Theory of variational quantum simulation2018 · Xiao Yuan, Suguru Endo, Qi Zhao, Ying Li, Simon Benjamin

Primary or survey context for Variational imaginary-time evolution; consult the paper for assumptions and implementation details.

arxiv.org/abs/1812.08767