Simulating the operation of a quantum computer in a dissipative environment.

Area of Science:

• Quantum Computing
• Quantum Information Science
• Computational Physics

Background:

• Quantum computer operations are susceptible to decoherence from environmental interactions.
• Dissipation negatively impacts entangled quantum states and algorithm efficacy.

Purpose of the Study:

• To simulate quantum computer operations under environmental dissipation using the non-perturbative hierarchical equations of motion (HEOM) method.
• To analyze the effects of dissipation on entangled states and quantum algorithms.
• To develop an efficient method for simulating large multi-qubit systems in dissipative environments.

Main Methods:

• Employed the non-perturbative hierarchical equations of motion (HEOM) method for quantum system simulation.
• Generated and propagated multi-qubit entangled states within Shor's factorizing algorithm.
• Proposed and utilized a two-dimensional tensor network scheme for efficient simulation of many-qubit systems.

Main Results:

• Demonstrated that dissipation leads to a loss of fidelity and mutual information in Shor's algorithm, causing factorization failure.
• Successfully simulated a 21-qubit one-dimensional random circuit model using the proposed tensor network scheme.
• Quantified the detrimental effects of environmental interactions on quantum computational processes.

Conclusions:

• Environmental dissipation poses a significant challenge to the reliable operation of quantum computers.
• The HEOM method, augmented by a two-dimensional tensor network, provides a viable approach for simulating complex quantum systems in noisy environments.
• Accurate simulation of decoherence is crucial for understanding and improving quantum algorithm performance.