---
title: PrepareSlaterDeterminant (latest version)
description: API reference for qiskit_fermions.circuit.library.PrepareSlaterDeterminant in the latest version of qiskit-fermions
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit-fermions/circuit-library-prepare-slater-determinant
---

# PrepareSlaterDeterminant

*class* `PrepareSlaterDeterminant(occupation, rotation_unitary)`

Bases: [`FermionicGate`](/docs/api/qiskit-fermions/circuit-fermionic-gate "qiskit_fermions.circuit.fermionic_gate.FermionicGate")

Prepares a Slater determinant from an occupation and an orbital rotation.

This gate is the composition of an [`InitializeModes`](/docs/api/qiskit-fermions/circuit-library-initialize-modes "qiskit_fermions.circuit.library.InitializeModes") reference occupation followed by an [`OrbitalRotation`](/docs/api/qiskit-fermions/circuit-library-orbital-rotation "qiskit_fermions.circuit.library.OrbitalRotation"): it declares that the modes it acts on start in the determinant defined by `occupation` and are then rotated by `rotation_unitary`. Because the initial occupation is known, transpiling this gate can use the rectangular [`givens_decomposition_slater()`](/docs/api/qiskit-fermions/linalg-givens-decomposition-slater "qiskit_fermions.linalg.givens_decomposition_slater") for a reduced-gate-count synthesis (see [`GivensDecompositionSlaterDeterminantSynthesis`](/docs/api/qiskit-fermions/transpiler-passes-synthesis-givens-decomposition-slater-determinant-synthesis "qiskit_fermions.transpiler.passes.synthesis.GivensDecompositionSlaterDeterminantSynthesis")) rather than the full square decomposition an [`OrbitalRotation`](/docs/api/qiskit-fermions/circuit-library-orbital-rotation "qiskit_fermions.circuit.library.OrbitalRotation") alone would require.

Following the [`OrbitalRotation`](/docs/api/qiskit-fermions/circuit-library-orbital-rotation "qiskit_fermions.circuit.library.OrbitalRotation") convention $a^\dagger_i \mapsto \sum_j U_{ji} a^\dagger_j$, rotating the occupied modes maps them onto the corresponding columns of `rotation_unitary`; those columns span the occupied space of the prepared Slater determinant.

**Simulation semantics**

Under simulation this gate is **validate-then-rotate**, not a state producer: given an incoming state vector it validates that the vector is confined to the subspace `occupation` defines (via [`InitializeModes`](/docs/api/qiskit-fermions/circuit-library-initialize-modes "qiskit_fermions.circuit.library.InitializeModes")) and then applies `rotation_unitary` (via [`OrbitalRotation`](/docs/api/qiskit-fermions/circuit-library-orbital-rotation "qiskit_fermions.circuit.library.OrbitalRotation")). It therefore requires a real reference state vector, prepared externally (e.g. via [`ffsim.slater_determinant()`](https://qiskit-community.github.io/ffsim/api/stubs/ffsim.slater_determinant.html#ffsim.slater_determinant "(in ffsim)")). The *producer* behavior – emitting the gates that set the reference occupation – lives in the synthesis plugin, not the simulation path.

Applying (rather than dropping) the rotation is what guarantees that merging an [`InitializeModes`](/docs/api/qiskit-fermions/circuit-library-initialize-modes "qiskit_fermions.circuit.library.InitializeModes") and an [`OrbitalRotation`](/docs/api/qiskit-fermions/circuit-library-orbital-rotation "qiskit_fermions.circuit.library.OrbitalRotation") into this single gate leaves the simulated final state unchanged.

> **Caution**
>
> This is an early development prototype. Beware of changes to its interface without warning during the pre-release development of this package.

> **See also**
>
> [`InitializeModes`](/docs/api/qiskit-fermions/circuit-library-initialize-modes "qiskit_fermions.circuit.library.InitializeModes"), [`OrbitalRotation`](/docs/api/qiskit-fermions/circuit-library-orbital-rotation "qiskit_fermions.circuit.library.OrbitalRotation"), and [`givens_decomposition_slater()`](/docs/api/qiskit-fermions/linalg-givens-decomposition-slater "qiskit_fermions.linalg.givens_decomposition_slater").

Initializing an instance of this gate can be done with the arguments listed below.

**Parameters**

- **occupation** (*Sequence\[*[*bool*](https://docs.python.org/3/library/functions.html#bool)*]*) – a sequence of booleans indicating the reference occupation for each mode this gate acts on.
- **rotation\_unitary** (*np.ndarray*) – the $n \times n$ unitary matrix $U$ defining the orbital rotation via $a^\dagger_i \mapsto \sum_j U_{ji} a^\dagger_j$, where $n$ is the number of modes (`len(occupation)`). It must be square and unitary; this is the caller’s responsibility and is not verified.

**Raises**

[**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError) – if `rotation_unitary` is not a square matrix whose dimension matches the length of `occupation`.

## Attributes

### occupation

The reference occupation (one boolean per mode) the rotation is applied to.

### rotation\_unitary

The unitary matrix representing the orbital rotation coefficients.

**Protocol Methods**

### \_apply\_unitary\_placed\_

`_apply_unitary_placed_(vec, norb, nelec, copy, freg_indices)`

Validates the reference occupation and applies the rotation, placing modes onto `vec`.

Delegates to the gate’s definition (`_build_definition()`): the leading [`InitializeModes`](/docs/api/qiskit-fermions/circuit-library-initialize-modes "qiskit_fermions.circuit.library.InitializeModes") validates that `vec` is confined to the subspace `occupation` defines and the following [`OrbitalRotation`](/docs/api/qiskit-fermions/circuit-library-orbital-rotation "qiskit_fermions.circuit.library.OrbitalRotation") rotates it. See those gates’ `_apply_unitary_placed_` for the full semantics (subspace confinement and the rejection of spin-mixing rotations).

**Parameters**

- **vec** ([*ndarray*](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray)) – the reference state vector to validate and rotate.
- **norb** ([*int*](https://docs.python.org/3/library/functions.html#int)) – the number of spatial orbitals of the *global* state vector.
- **nelec** ([*int*](https://docs.python.org/3/library/functions.html#int)  *|*[*tuple*](https://docs.python.org/3/library/stdtypes.html#tuple)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*,* [*int*](https://docs.python.org/3/library/functions.html#int)*]*) – either a single integer for a spinless system, or a pair of integers storing the numbers of spin alpha and spin beta fermions.
- **copy** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – whether to copy the vector before operating on it.
- **freg\_indices** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]*) – the absolute (global) mode indices that this gate’s local modes map onto.

**Returns**

The transformed vector.

**Return type**

[*ndarray*](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray)