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

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.