Good dynamics versus bad kinematics: is entanglement needed for quantum computation?

Area of Science:

• Quantum Information Science
• Quantum Computation

Background:

• Quantum computing aims to solve complex problems using quantum phenomena.
• Noise, or decoherence, is a major challenge in building stable quantum computers.
• Pseudopure state implementations, often using Nuclear Magnetic Resonance (NMR), are a practical approach to quantum computing.

Purpose of the Study:

• To investigate the necessity of entanglement in quantum computational protocols.
• To determine if entanglement is sufficient for achieving quantum advantage in noisy systems.
• To analyze the impact of white noise on entanglement-dependent quantum algorithms.

Main Methods:

• Theoretical analysis of quantum computational protocols.
• Modeling quantum states contaminated by white noise.
• Evaluating resource requirements (polynomial vs. exponential) for different protocols.

Main Results:

• Entanglement is demonstrated to be a necessary resource for a wide range of quantum computational protocols, including Shor's factorization algorithm.
• The presence of entanglement does not guarantee quantum advantage if the quantum state is sufficiently contaminated by noise.
• Sufficiently noisy states necessitate exponential resources, irrespective of entanglement.

Conclusions:

• Entanglement plays a vital role in enabling quantum computers to outperform classical computers for specific tasks.
• Robustness against noise is as critical as entanglement for realizing the potential of quantum computation.
• Future quantum computing research must address both entanglement generation and noise mitigation strategies.