PDE 模型与适配

oracq.algorithms.input_model.pde

Composable spatial and initial-state inputs for quantum PDE methods.

class oracq.algorithms.input_model.pde.PDEGrid(*args, **kwargs)

基类：SpatialGrid, Protocol

Spatial rows, quantum derivative encodings, and their memory snapshots.

property qrams

QRAM snapshots backing the grid's derivative encodings.

derivative_encoding(derivative)

Return a block encoding of the sparse derivative operator.

class oracq.algorithms.input_model.pde.UniformGrid1D(start, stop, points, boundary='periodic', axis='x')

基类：object

Uniform spatial samples with an explicit interval and boundary convention.

Periodic samples cover [start, stop) with spacing (stop-start)/points. Zero Dirichlet samples are interior points with spacing (stop-start)/(points+1). Power-of-two periodic grids use shift circuits; other grids use a bounded spatial Pauli expansion of at most five qubits. Only spatial derivatives are materialized, never multilinear PDE ports.

start

stop

points

boundary = 'periodic'

axis = 'x'

property axes

Spatial axis names.

property size

Number of physical samples, excluding register padding.

property spatial_width

Address register width, retaining padding for arbitrary point counts.

property spacing

Physical sample spacing.

property qrams

Uniform grids do not require a memory bank.

coordinate(index)

Physical coordinate of a sample.

derivative_row(derivative, row)

Finite-difference row, with padding outside the physical grid zero.

derivative_encoding(derivative)

Encode a derivative while preserving the physical grid size.

class oracq.algorithms.input_model.pde.UnstructuredGridConfig(size, derivative_offsets, value_scale=1.0, axes=('x',))

基类：object

Layout of real discrete derivative matrices in a QRAM angle bank.

Each derivative key maps to a base address. A matrix uses base + row * 2**spatial_width + column and has entries value_scale*cos(pi*word/2**word_length). Thus a zero entry is an angle word 2**(word_length-1), not a zero word. Boundary conditions and geometric discretization are already incorporated in these matrices.

size

derivative_offsets

value_scale = 1.0

axes = ('x',)

encode_matrices(matrices, word_length, *, max_words=1048576)

Encode physical derivative matrices in this layout, including zero padding.

The amplitude error per entry is at most value_scale*pi/2**word_length. The negative endpoint is saturated to the largest word instead of wrapping a full turn to zero.

class oracq.algorithms.input_model.pde.UnstructuredGrid(qram, config)

基类：object

A spatial discretization supplied as QRAM derivative matrices.

The quantum adapter uses uniform row/column projection and QRAM angle transduction. Its normalization is 2**spatial_width * value_scale; it supports nonsymmetric real matrices and makes no sparse-access speedup claim. A different storage model can implement PDEGrid directly.

qram

config

property axes

Spatial axis names.

property size

Number of physical nodes.

property spatial_width

Node address width.

property qrams

The registered operator memory.

derivative_row(derivative, row)

Decode a physical row for reference evaluation and known coefficients.

derivative_encoding(derivative)

Query the configured table coherently and project both padding spaces.

class oracq.algorithms.input_model.pde.InitialLayout(grid, fields, max_words=4096)

基类：object

Physical fields and grid nodes, with field-major register padding.

grid

fields

max_words = 4096

property width

Combined component and spatial register width.

property size

Number of physical samples across all fields.

encode(values)

Pad physical samples without treating padded addresses as grid nodes.

class oracq.algorithms.input_model.pde.PDEProblem(grid, initial=<factory>, type='burgers', final_time=1.0, viscosity=0.1, known=<factory>)

基类：object

A PDE recipe whose grid and physical initial input can be composed independently.

type accepts burgers, heat, or an existing PolynomialPDE. Presets use one field u and the grid's first axis. known holds physical coefficient/forcing samples. Solver approximations belong to the method configuration, not this problem object.

grid

initial

type = 'burgers'

final_time = 1.0

viscosity = 0.1

known

equation