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Quantum simulation of Pauli channels and dynamical maps: Algorithm and implementation.

Tomás Basile^1,2, Carlos Pineda²

¹Facultad de Ciencias. Universidad Nacional Autónoma de México, Ciudad de México, Mexico.

|April 10, 2024

Summary

This summary is machine-generated.

This study introduces a quantum algorithm for simulating Pauli channels and dynamical maps, crucial for understanding noise in quantum computing. The algorithm was successfully implemented on IBM quantum hardware, demonstrating its practical viability.

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Area of Science:

Quantum Information Science
Quantum Computing Algorithms
Quantum Error Correction

Background:

Pauli channels are essential models for quantum noise in quantum computing devices.
Simulating these channels is critical for developing robust quantum algorithms and error correction strategies.
Existing simulation methods may face limitations in scalability or efficiency.

Purpose of the Study:

To propose a novel quantum algorithm for simulating Pauli channels.
To extend the simulation capabilities to parametrized Pauli channels, also known as Pauli dynamical maps.
To determine the conditions under which N-qubit transformations can be realized with specific parametrized quantum circuits.

Main Methods:

Development of a quantum algorithm tailored for Pauli channel simulation.
Utilization of a parametrized quantum circuit to represent Pauli dynamical maps.
Mathematical derivation of conditions for achieving N-qubit transformations with single-parameter-dependent circuits.
Experimental implementation on IBM quantum computers.

Main Results:

A quantum algorithm for simulating Pauli channels and Pauli dynamical maps is proposed.
Mathematical conditions for circuit realizability of N-qubit transformations were established.
The algorithm was successfully implemented for a single qubit on IBM's quantum hardware.
The fidelity of the experimental implementation was quantitatively assessed.

Conclusions:

The proposed quantum algorithm provides an effective method for simulating Pauli channels and dynamical maps.
The findings contribute to a better understanding of noise modeling in quantum computing.
The experimental validation confirms the practical applicability and fidelity of the proposed approach on current quantum hardware.