Counterintuitive Yet Efficient Regimes for Measurement-Based Quantum Computation on Symmetry-Protected Spin Chains

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Computational Complexity

Background:

• Nontrivial symmetry-protected topological (SPT) phases host quantum states with inherent computational power.
• Measurement-based quantum computation (MBQC) utilizes these states, with power unlocked by symmetry-breaking measurements.
• Conventional MBQC schemes avoid dense measurements to prevent unwanted entanglement.

Purpose of the Study:

• To investigate the computational performance of MBQC using densely packed symmetry-breaking measurements within SPT phases.
• To determine if dense measurements offer advantages over sparse configurations.

Main Methods:

• Theoretical analysis of quantum computation within SPT phases.
• Exploration of dense measurement regimes in contrast to sparse configurations.
• Consideration of physical assumptions regarding entanglement and correlations.

Main Results:

• Quantum computation remains functional even with densely packed symmetry-breaking measurements.
• Dense measurement configurations are shown to be the most resource-efficient mode of computation.
• This efficiency holds under reasonable physical assumptions.

Conclusions:

• Dense symmetry-breaking measurements in SPT phases are a viable and highly efficient strategy for MBQC.
• The findings challenge conventional approaches and open new avenues for resource optimization in quantum computation.