Schrödingerization

oracq.algorithms.qode.schrodingerization

Construct a quantum representation of linear non-unitary evolution via an auxiliary coordinate and the Fourier transform.

oracq.algorithms.qode.schrodingerization.fourier_momentum(width, period)[source]

Diagonal-in-frequency BE as a bit-wise sum of projections; avoids constructing a dense matrix.

Parameters:

  • width – Frequency register bit width; projections are scanned bit by bit.

  • period – Auxiliary grid period; must be a positive finite real number and determines the frequency spacing 2π/period.

Returns:

Block encoding of the momentum operator with diagonal frequencies 2πk/period.

Return type:

BlockEncoding

class oracq.algorithms.qode.schrodingerization.SchrodingerPlan(auxiliary_width=2, period=8.0, selected_index=1)[source]

Bases: object

Configuration plan for the Schrödingerization auxiliary grid and readout channel.

Variables:

  • auxiliary_width (int) – Bits of the auxiliary p register; valid range 1..63.

  • period (float) – Period of the auxiliary grid; must be a positive finite real number.

  • selected_index (int) – Channel index of the final physical-solution readout, in 0..2**auxiliary_width-1.

Raises:

ValidationError – Any field is out of range or not a finite value.

auxiliary_width = 2
period = 8.0
selected_index = 1
oracq.algorithms.qode.schrodingerization.schrodinger_qode(generator, initial, time, *, plan=None, hamiltonian_function=<function taylor_hamiltonian>)[source]

u’=Gu with G=H1+iH2; Fourier lift −P⊗H1-I⊗H2 (forward flow recovered under the positive QFT convention).

Parameters:

  • generator – Block encoding of the evolution generator G.

  • initial – Preparation handle of the physical initial state.

  • time – Evolution duration; a non-negative finite real number.

  • plan – Auxiliary grid and readout channel configuration; defaults to 2 auxiliary bits, period 8, channel 1.

  • hamiltonian_function – Hamiltonian simulation implementation of the form (BE, time) returning a BlockEncoding; defaults to truncated Taylor.

Returns:

The physical-solution readout state oracle on the selected auxiliary channel, with correctness marked pending.

Return type:

StateOracle