Strong Zero Modes in Integrable Quantum Circuits

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Quantum Many-Body Systems

Background:

• Integrable spin chains are known to host robust edge modes called strong zero modes (SZMs).
• Extending these concepts to the discrete-time dynamics of local quantum circuits, particularly in the Floquet setting, remains an active area of research.

Purpose of the Study:

• To investigate the existence and construction of strong zero modes (SZMs) in integrable quantum circuits.
• To adapt the concept of SZMs from continuous-time spin chains to discrete-time Floquet quantum circuits.
• To explore the potential for implementing these phenomena on current quantum platforms.

Main Methods:

• Focus on a prototypical integrable Trotterization of the XXZ Heisenberg spin chain.
• Exploitation of algebraic structures inherent to integrability, specifically commuting transfer matrices.
• Construction of an exact SZM operator within specific parameter regimes of the quantum circuit.

Main Results:

• Demonstrated the existence of an exact strong zero mode (SZM) operator in integrable Floquet quantum circuits.
• The construction method recovers known results in the continuous-time limit.
• Properties such as normalizability of the SZM are readily proven using the developed framework.
• Numerical simulations of infinite-temperature autocorrelation functions corroborate the theoretical predictions.

Conclusions:

• The study successfully extends the concept of strong zero modes (SZMs) to the realm of integrable quantum circuits.
• The developed algebraic approach offers a novel perspective for constructing and analyzing SZMs, distinct from prior methods.
• The findings hold promise for practical implementations of XXZ quantum circuits on existing quantum computing hardware.