Motivated by recent proposals for quantum proof of work protocols, we
investigate approaches for simulating linear optical interferometers using
digital quantum circuits. We focus on a second quantisation approach, where the
quantum computer’s registers represent optical modes. We can then use standard
quantum optical techniques to decompose the unitary matrix describing an
interferometer into an array of $2\times 2$ unitaries, which are subsequently
synthesised into quantum circuits and stitched together to complete the
circuit. For an $m$ mode interferometer with $n$ identical photons, this method
requires approximately $\mathcal{Ô}(m \log(n))$ qubits and a circuit depth of
$\mathcal{Ô}(m n^4 \log_2(n) \: \textrm{polylog}(n^4 / \epsilon))$. We present
a software package Aquinas (A QUantum INterferometer ASsembler) that uses this
approach to generate such quantum circuits. For reference, an arbitrary five
mode interferometer with two identical photons is compiled to a 10 qubit
quantum circuit with a depth of 1972.

Cet article explore les excursions dans le temps et leurs implications.

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