Auxiliary-Free Replica Shadows: Efficient Estimation of Multiple Nonlinear Quantum Properties

Area of Science:

• Quantum Information Processing
• Many-Body Physics
• Quantum Computing

Background:

• Estimating nonlinear properties in quantum systems is crucial but challenging.
• Existing methods face issues like high sample complexity or complex circuit requirements.
• Need for efficient and practical estimation techniques for near-term quantum devices.

Purpose of the Study:

• To introduce an efficient auxiliary-free replica shadow (AFRS) framework.
• To overcome limitations of current methods for estimating nonlinear properties.
• To enable practical quantum information processing and many-body physics research.

Main Methods:

• Proposed the auxiliary-free replica shadow (AFRS) framework.
• Utilized joint entangling operations on input replicas.
• Integrated principles of shadow estimation.
• Developed a local-AFRS variant for local observables.

Main Results:

• AFRS offers exponential improvements in estimation accuracy over conventional shadow methods.
• AFRS enables simultaneous estimation of various nonlinear properties.
• Local-AFRS variant simplifies experimental implementation with constant-depth circuits.

Conclusions:

• The AFRS framework provides an efficient and practical solution for estimating nonlinear properties.
• This approach significantly advances capabilities for near-term quantum devices.
• Paves the way for broader applications in quantum information and physics.