Disentangling Magic States with Classically Simulable Quantum Circuits

Area of Science:

• Quantum Information Science
• Quantum Computing Theory

Background:

• Random Clifford circuits are a fundamental model in quantum computation.
• Non-Clifford gates like T gates introduce computational complexity (nonstabilizerness).
• Understanding the properties of circuits with doped non-Clifford gates is crucial for quantum advantage.

Purpose of the Study:

• To investigate the disentanglability of states generated by random Clifford circuits doped with non-Clifford phase gates.
• To determine the conditions under which these complex quantum states can be simplified.
• To explore the implications for classical simulation and quantum circuit design.

Main Methods:

• Analytical proof using a quantum error correction formulation.
• Numerical demonstrations of the theoretical findings.
• Analysis of consequences for Hamiltonian dynamics and state design.

Main Results:

• States from circuits with a limited number of non-Clifford gates (≤ number of qubits) can be completely disentangled.
• Efficient classical simulation of Pauli expectation values is possible for these states.
• The study reveals a novel representation for approximate state designs and a circuit compression scheme.

Conclusions:

• The presence of a small number of non-Clifford gates does not inherently prevent disentanglement or efficient classical simulation.
• This finding has significant implications for understanding the boundary between quantum and classical computational power.
• The proposed methods offer practical advancements in quantum circuit generation and compression.