Linear and Logarithmic Time Compositions of Quantum Many-Body Operators

Area of Science:

• Quantum Computing
• Quantum Information Science
• Computational Physics

Background:

• Constructing complex quantum many-body interactions is crucial for advancing quantum simulation and computation.
• Current methods for implementing these interactions can be resource-intensive in terms of time and qubit overhead.
• Developing efficient and scalable protocols is essential for realizing the potential of quantum technologies.

Purpose of the Study:

• To introduce a generalized framework for constructing many-body-interaction operations.
• To provide protocols that operate in linear or logarithmic time with linear ancilla qubits.
• To offer exact gate decompositions for various complex quantum operations.

Main Methods:

• A linear time protocol utilizing superposition of operator strings and dynamical decoupling.
• A logarithmic time protocol employing ancilla registers and parallel chaining operations.
• Development of exact gate decompositions for Pauli strings, Toffoli gates, and other many-body operators.

Main Results:

• Demonstrated linear and logarithmic time protocols for constructing many-body interactions.
• Achieved substantial reductions in time and space complexity compared to existing strategies.
• Showcased applicability to diverse physical interaction mechanisms (e.g., CNOT, XX, XX+YY).

Conclusions:

• The developed framework offers significant improvements in efficiency and scalability for quantum computations.
• The protocols are versatile and applicable to a broad range of many-body operators and physical systems.
• This work paves the way for more complex and resource-efficient quantum simulations and algorithms.