Quantum Computation by Adiabatic Evolution2000 · Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Michael Sipser
Defines the adiabatic computation model and relates runtime to the spectral gap of the interpolation.
arxiv.org/abs/quant-ph/0001106 ↗Strong empiricalAlgorithmsOptimization · time-dependent Hamiltonian
Quantum adiabatic evolution
An optimization pattern that slowly deforms an easy ground state into the ground state of a problem Hamiltonian.
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Adiabatic evolution encodes a problem in the final Hamiltonian and relies on remaining near the instantaneous ground state during the interpolation. In a gate model, the continuous path is approximated by a sequence of short product-formula steps.
Circuit & simulation
q[0]
Prepare |++⟩H₀ RX stepHₚ RZZ step
q[1]
Prepare |++⟩H₀ RX stepHₚ RZZ step
Ground-state sector85%
Excited / diabatic leakage15%
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.
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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:
- Interpolate slowly to the problem Hamiltonian Method
Takes An Ising or QUBO operator, diagonal in the computational basis, whose extremal eigenvector encodes the problem's solution — given, for QAOA, as a sum of clause terms over bits and clauses; given, for adiabatic evolution, as the final Hamiltonian of an interpolation whose starting point has an easily-constructed ground state. Neither method is told how the operator was built, or by which encoding. Returns A bit string read off the computational basis — the assignment — together with the objective value it achieves, or, for the adiabatic route, the stated promise that this string is (with fidelity approaching 1, for a long enough evolution time) the true minimiser. Neither route returns an energy with an error bar; both return a string.
How it works
The adiabatic path uses H(s) = (1−s)H₀ + sHₚ. If the schedule is slow compared with the inverse square of the minimum gap, the state can track the ground state; near a small gap, the required runtime can grow sharply. A gate-model implementation approximates each short interval and must still measure final success, so a smooth schedule is only a construction check until the gap and diabatic error are evaluated.
Implementation
Native
adiabatic_interpolation.py
from qiskit import QuantumCircuit
qc = QuantumCircuit(2)
qc.h(0)
qc.h(1) # prepare the H0 ground state
for step in range(20):
s = (step + 1) / 20
dt = 0.05
qc.rx(-2 * (1 - s) * dt, 0)
qc.rx(-2 * (1 - s) * dt, 1)
qc.rzz(2 * s * dt, 0, 1)
FINAL_CIRCUIT = qcQuantum vs classical
Classical baseline
Classical annealing or local-search methods can inspect an objective directly, while adiabatic circuits pay for coherent evolution, gap-dependent runtime, and measurement.
Quantum claim
The quantum path may exploit tunneling and interference for some landscapes, but no generic speedup follows from using a smooth interpolation.
How to compare
Estimate or bound the minimum gap and compare final-state success probability with classical baselines at matched evaluation and runtime budgets.
Declared gaps
Nobody has reviewed this record for gaps yet.