Shallow Quantum Circuit for Generating Extremely Low-Entangled Approximate State Designs

Area of Science:

• Quantum Information Science
• Quantum Computing

Background:

• Random quantum states are crucial for quantum information science.
• Existing methods for generating these states can be resource-intensive.

Purpose of the Study:

• To discover a new ensemble of quantum states that act as ε-approximate state t-designs.
• To achieve extremely low entanglement, magic, and coherence in these states.

Main Methods:

• The study proves that entanglement, magic, and coherence can reach their theoretical lower bounds, Ω(log(t/ε)).
• An ancilla-free shallow quantum circuit is constructed for generating these states efficiently.
• The circuit transforms k-qubit designs into n-qubit ones without increasing support size.

Main Results:

• Quantum state resources achieve theoretical lower bounds for entanglement, magic, and coherence, independent of system size (O(1)).
• An efficient ancilla-free shallow quantum circuit is developed with depth O(t[logt]^{3}log n log[1/ε]).
• Classical simulation of random quantum states is reduced in cost.

Conclusions:

• The discovered quantum states and circuit offer a more efficient way to generate and utilize random quantum states.
• This leads to potential advancements in quantum information processing, including efficient quantum state certification via classical shadow tomography.