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.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.

quant-pharXiv:2605.22770May 22, 20260 citations

Current production in ring condensates with a weak link

Axel Pérez-Obiol, Juan Polo, Taksu Cheon

We consider attractive and repulsive condensates in a ring trap stirred by a weak link, and analyze the spectrum of solitonic trains dragged by the link, by means of analytical expressions for the wave functions, energies, and currents. The precise evolution of current production and destruction in terms of defect formation in the ring and in terms of stirring is studied. We find that any excited state can be coupled to the ground state through two proposed methods: either by adiabatically tuning the link's strength and velocity through precise cycles which avoid the critical velocities and thus unstable regions or by keeping the link still while setting an auxiliary potential and imprinting a nonlinear phase as the potential is turned off. We also analyze hysteresis cycles through the spectrum of energies and currents.We consider attractive and repulsive condensates in a ring trap stirred by a weak link, and analyze the spectrum of solitonic trains dragged by the link, by means of analytical expressions for the wave functions, energies, and currents. The precise evolution of current production and destruction in terms of defect formation in the ring and in terms of stirring is studied. We find that any excited state can be coupled to the ground state through two proposed methods: either by adiabatically tuning the link's strength and velocity through precise cycles which avoid the critical velocities and thus unstable regions or by keeping the link still while setting an auxiliary potential and imprinting a nonlinear phase as the potential is turned off. We also analyze hysteresis cycles through the spectrum of energies and currents.

arXiv:2007.11243Physical Review ADec 3, 20208 citations

Nonlinear Adiabatic Evolution of Quantum Systems

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Springer eBooksJan 1, 20181 citation

Nonlinear Adiabatic Evolution of Quantum Systems

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Springer eBooksJan 1, 201811 citations

Quantum Adiabatic Evolution

Alain Joye, Charles‐Edouard Pfister

NATO ASI series. Series B : PhysicsJan 1, 199415 citations

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.