On low-depth algorithms for quantum phase estimation

Abstract

Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant mismatch, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the overlap between the initial state and the target state approaches one. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. As a second contribution, we propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.

Accepted at Quantum

References in corpus (9)

• Simulating Hamiltonian dynamics with a truncated Taylor series
• Entanglement-free Heisenberg-limited phase estimation
• General optimality of the Heisenberg limit for quantum metrology
• Optimal Quantum Measurements of Expectation Values of Observables
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
• Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation
• Learning many-body Hamiltonians with Heisenberg-limited scaling
• Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers
• On adaptive low-depth quantum algorithms for robust multiple-phase estimation

Cited by in corpus (26)

• Rapid initial state preparation for the quantum simulation of strongly correlated molecules
• Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Multiscale Embedding for Quantum Computing
• Quantum algorithms for scientific computing
• Phase-Sensitive Quantum Measurement without Controlled Operations
• Modeling the Performance of Early Fault-Tolerant Quantum Algorithms
• High ground state overlap via quantum embedding methods
• On proving the robustness of algorithms for early fault-tolerant quantum computers
• Qu-Trefoil: Large-Scale Quantum Circuit Simulator Working on FPGA With SATA Storages
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers
• Quantum computing quantum Monte Carlo algorithm
• Learning interacting fermionic Hamiltonians at the Heisenberg limit
• Quantum Phase Estimation by Compressed Sensing
• Optimal Low-Depth Quantum Signal-Processing Phase Estimation
• Heisenberg-limited Bayesian phase estimation with low-depth digital quantum circuits
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• Optimal Coherent Quantum Phase Estimation via Tapering
• Phase estimation with partially randomized time evolution
• Phase Estimation with Compressed Controlled Time Evolution
• Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering
• Towards Practical Quantum Phase Estimation: A Modular, Scalable, and Adaptive Approach
• High-Entanglement Capabilities for Variational Quantum Algorithms: The Poisson Equation Case
• Numerical investigation of the quantum inverse algorithm on small molecules
• Benchmarking Quantum Simulation of Chemical Hamiltonians using the Sorted-List Encoding