Quantum phase estimation with noisy qubits

Osama M. Raisuddin, Suvranu De

Muhammad Abdullah Ijaz, Muhammad Faryad

The quantum singular value transformation (QSVT) algorithm is a general framework to implement most of the known algorithms and provides a way forward for designing new algorithms. In the present work, the impact of noise on the QSVT algorithm is examined for bit flip, phase flip, bit-phase flip, and depolarizing noise models for a small number of qubits. The small number of noisy qubits approximates the currently available noisy quantum computers. For simulation results, the QSVT implementation of the Grover search and quantum phase estimation (QPE) algorithms is considered. These algorithms are among the basic quantum algorithms and form the building blocks of various applications of quantum algorithms. The results showed that the QSVT implementation of the Grover search and QPE algorithms has a consistently worse dependence upon noise than the original implementation for all four noise models. The probability of success of the Grover algorithm and phase measured by the QPE algorithm were found to exponentially depend upon the error probability in the noisy channels but only linearly dependent on the number of qubits.

Hiu Yung Wong

Jinyoung Ha, Jun Heo

In the process of implementing a quantum algorithm as a quantum circuit, the error rate of an actual quantum computer should be considered. In this paper, we confirm through simulation that the one control qubit quantum phase estimation algorithm performs better than the many control qubit quantum phase estimation algorithm on the noisy quantum processor. We use QISKit to simulate a quantum phase estimation algorithm. We performed the simulation considering the error rate of the IBM Q quantum processor. The error rate of the one control qubit quantum phase estimation algorithm is compared with the many control qubit quantum phase estimation algorithm.

Junxu Li

Here we revisit the quantum-phase-estimation (QPE) algorithm and devise an iterative method to improve the precision of QPE with propagators over a variety of time spans. For a given propagator and a certain eigenstate as input, QPE with a propagator is introduced to estimate the phase corresponding to an eigenenergy. Due to the periodicity of the complex exponential, we can pinpoint the eigenenergy in a branch of comblike ranges by applying QPE with propagators over longer time spans. Thus, by picking up appropriate time spans, the iterative QPE with corresponding propagators can enable us to pinpoint the eigenenergy more precisely. Moreover, even if there are only a few qubits as ancilla qubits, high precision is still available by the proposed iterative method. Our work provides a feasible and promising means toward precise estimations of an eigenvalue on noisy intermediate-scale quantum devices.

Hiu Yung Wong