Quantum Circuits with Classically Simulable Operator Scrambling

Area of Science:

• Quantum information science
• Quantum computation
• Quantum complexity theory

Background:

• Quantum scrambling describes how quantum information spreads and becomes locally inaccessible.
• Classical simulability of quantum systems is generally believed to be limited, especially for systems exhibiting scrambling.
• Understanding the boundary between classical and quantum computational power is a key challenge.

Purpose of the Study:

• To introduce a new class of quantum circuits, termed super-Clifford circuits.
• To demonstrate that certain aspects of quantum scrambling can be classically simulated.
• To challenge the conventional understanding that classical simulability implies the absence of quantum scrambling.

Main Methods:

• Developing a novel family of quantum circuits (super-Clifford circuits).
• Analyzing the Heisenberg time evolution of nonlocal operators within these circuits.
• Mapping operator evolution to Clifford evolution in an enlarged operator space.

Main Results:

• Super-Clifford circuits allow for classically simulating the scrambling of a specific subspace of nonlocal operators.
• The time evolution of single Pauli strings results in operators with linearly growing operator entanglement.
• This linear growth of entanglement is observable even in systems with a large number of qubits.

Conclusions:

• Super-Clifford circuits provide a new, efficient technique for studying quantum scrambling.
• These circuits serve as explicit counterexamples to the intuition linking classical simulability and the absence of scrambling.
• The findings open new avenues for exploring quantum complexity and the limits of classical simulation.