Adiabatic Quantum Phase Estimation

• URL: http://arxiv.org/abs/2605.22770v1
• Date: Thu, 21 May 2026 17:31:36 GMT
• Title: Adiabatic Quantum Phase Estimation
• Abstract summary: Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $$ in Heisenberg-limited time $T= (1/)$.<n>Standard gate-based implementations of QPE require deep controlled time-evolution circuits and are not native to analog hardware.<n>We present a simple adiabatic protocol for QPE that achieves the optimal Heisenberg-limited scaling $T = Oleft( frac1 logleft(-1right)right)$ in both the precision $$
• Score: 47.3103723337301
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $ε$ in Heisenberg-limited time $T=Θ(1/ε)$. Standard gate-based implementations of QPE require deep controlled time-evolution circuits and are not native to analog hardware. Here, we present a simple adiabatic protocol for QPE that achieves (up to logarithmic factors) the optimal Heisenberg-limited scaling $T = O\left( \frac{1}ε \log\left(δ^{-1}\right)\right)$ in both the precision $ε$ and failure probability $δ$. By encoding eigenvalues in populations of computational basis states rather than complex phases, our approach is naturally robust against certain dephasing errors. The adiabatic protocol only requires the ability to couple a single ancilla qubit to the system Hamiltonian as well as pairwise couplings within the ancilla register.

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