ffsim.qiskit.FermionicFFTJW¶

class ffsim.qiskit.FermionicFFTJW(norb, *, label=None)[source]¶

Bases: Gate

Fermionic fast Fourier transform under the Jordan-Wigner transformation.

Performs the discrete Fourier transform (DFT) on creation operators:

\[a^\dagger_k \mapsto \frac{1}{\sqrt{N}} \sum_{n=0}^{N-1} e^{-i 2\pi k n / N} a^\dagger_n\]

Implemented using a Cooley-Tukey decomposition into DFTs of prime size. Most of the resulting rotations are at fixed angles: \(\pi/2\) for mode permutations, \(\pi/4\) for DFTs of size 2, and twiddle-factor phases that are multiples of \(2\pi/N\). This is especially true when \(N\) is a power of 2. Compared with decomposing the DFT matrix directly with OrbitalRotationJW, the circuit needs far fewer arbitrary-angle rotations, which matters when those are expensive, as on fault-tolerant hardware. It uses more two-qubit gates, though, so prefer OrbitalRotationJW when two-qubit gate count is what matters.

Assumes qubits are ordered with the first norb qubits for spin alpha and the next norb qubits for spin beta.

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