Approximating outcome probabilities of linear optical circuits

Understand

Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit.

• In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear optical circuit using $s$-parameterized quasiprobability distributions.
• Notably, we can reduce the negativity bound of a circuit from exponential to at most polynomial for specific cases by modulating the shapes of quasiprobability distributions thanks to the norm-preserving property of a linear optical transformation.
• Consequently, our scheme renders an efficient estimation of outcome probabilities with precision depending on the classicality of the circuit.