Measuring central charge on a universal quantum processor

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• High Energy Physics

Background:

• Central charge is a fundamental quantity in conformal field theories (CFTs).
• It dictates universality classes of critical points in 2D systems.
• Experimental measurement of central charge has been challenging.

Purpose of the Study:

• To experimentally determine the central charge of quantum spin chains.
• To demonstrate the capability of universal quantum processors for fundamental physics measurements.
• To validate the use of quantum computation for studying critical phenomena.

Main Methods:

• Utilized a universal quantum processor with a classically optimized variational quantum circuit.
• Employed advanced error mitigation techniques to prepare ground states.
• Implemented periodic boundary conditions using IBM quantum processor's heavy-hex structure.
• Extracted central charge from scaling behavior of Rényi entropy generalizations.

Main Results:

• Successfully prepared ground states of 1+1D quantum spin chain models at their critical points.
• Experimental results for the transverse field Ising (TFI) chain (c=0.5) and XXZ chain (c=1) are consistent with theoretical values.
• Achieved relative errors as low as 5 percent in the determination of central charge.

Conclusions:

• The central charge of quantum spin chains can be experimentally determined using quantum processors.
• This work establishes a new experimental approach for probing fundamental properties of CFTs.
• Quantum computing offers a powerful tool for exploring critical phenomena and condensed matter systems.