Quantum algorithm for spectral projection by measuring an ancilla iteratively

Abstract

We propose a quantum algorithm for projecting a quantum system to eigenstates of any Hermitian operator, provided one can access the associated control-unitary evolution for the ancilla and the system, as well as the measurement of the controlling ancillary qubit. Such a Hadamard-test like primitive is iterated so as to achieve the spectral projection, and the distribution of the projected eigenstates obeys the Born rule. This algorithm can be used as a subroutine in the quantum annealing procedure by measurement to drive the system to the ground state of a final Hamiltonian, and we simulate this for quantum many-body spin chains.

arXiv comment18 pages, 15 figures, 1 table; close to the published version

References in corpus (19)

• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Efficient simulation of one-dimensional quantum many-body systems
• Simulated Quantum Computation of Molecular Energies
• On the Power of One Bit of Quantum Information
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Quantum Metropolis Sampling
• Adiabatic quantum computation with Cooper pairs
• Witnessing eigenstates for quantum simulation of Hamiltonian spectra
• Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark
• Quantum Simulations of Classical Annealing Processes
• A Quantum-Quantum Metropolis Algorithm
• Preparing ground states of quantum many-body systems on a quantum computer
• Quantum Algorithm for Spectral Measurement with Lower Gate Count
• Higher Order Methods for Simulations on Quantum Computers
• The measurement postulates of quantum mechanics are operationally redundant
• Stability of the Trotter-Suzuki decomposition
• Geometric Entanglement and Quantum Phase Transition in Generalized Cluster-XY models

Cited by in corpus (7)

• Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm
• Practicality of quantum adiabatic algorithm for chemistry applications
• Quantum Zeno approach for molecular energies with maximum commuting initialHamiltonians
• Semicoherent Symmetric Quantum Processes: Theory and Applications
• Quantum eigenstate broadcasting assisted by a coherent link
• Preparing low-variance states using a distributed quantum algorithm
• Co-Designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation