Most quantum States are too entangled to be useful as computational resources

Area of Science:

• Quantum Information Science
• Quantum Computation

Background:

• Entanglement is widely considered essential for quantum computational speedups.
• Measurement-based quantum computing particularly emphasizes the need for highly entangled initial states.

Purpose of the Study:

• To investigate the role of entanglement in quantum computational speedups.
• To determine if excessive entanglement can impede universal quantum computation.

Main Methods:

• Analysis of the geometric measure of entanglement.
• Proving the fraction of useful n-qubit pure states.

Main Results:

• High values of the geometric measure of entanglement preclude states from offering universal quantum computational speedups.
• The fraction of useful n-qubit pure states is less than exp(-n^2).

Conclusions:

• Quantum states can be too entangled to be useful for computation.
• Entanglement's role in quantum speedups is more nuanced than previously assumed.