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)

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

参数:

• 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.

返回:

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

返回类型:

BlockEncoding

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

基类：object

Configuration plan for the Schrödingerization auxiliary grid and readout channel.

变量:

• 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.

抛出:

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>)

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

参数:

• 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.

返回:

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

返回类型:

StateOracle