An Efficient Quantum Circuit Construction Method for Mutually Unbiased Bases in $n$-Qubit Systems

Understand

Mutually unbiased bases (MUBs) play a crucial role in numerous applications within quantum information science, such as quantum state tomography, error correction, entanglement detection, and quantum cryptography.

• Utilizing \(2^n + 1\) MUB circuits provides a minimal and optimal measurement strategy for reconstructing all \(n\)-qubit unknown states.
• It significantly reduces the number of measurements compared to the traditional \(4^n\) Pauli observables, also enhancing the robustness of quantum key distribution (QKD) protocols.
• Previous circuit designs that rely on a single generator can result in exponential gate costs for some MUB circuits.