openfermion.ops.BinaryCode

The BinaryCode class provides a representation of an encoding-decoding pair for binary vectors of different lengths, where the decoding is allowed to be non-linear.

openfermion.ops.BinaryCode(
    encoding, decoding
)

Used in the notebooks

Used in the tutorials

As the occupation number of fermionic mode is effectively binary, a length-N vector (v) of binary number can be utilized to describe a configuration of a many-body fermionic state on N modes. An n-qubit product state configuration |w0> |w1> |w2> ... |wn-1>, on the other hand is described by a length-n binary vector w=(w0, w1, ..., wn-1). To map a subset of N-Orbital Fermion states to n-qubit states we define a binary code, which consists of a (here: linear) encoding (e) and a (non-linear) decoding (d), such that for every v from that subset, w = e(v) is a length-n binary vector with d(w) = v. This can be used to save qubits given a Hamiltonian that dictates such a subset, otherwise n=N.

Two binary codes (e,d) and (e',d') can construct a third code (e",d") by two possible operations:

Concatenation: (e",d") = (e,d) * (e',d') which means e": v" -> e'( e(v") ) and d": w" -> d( d'(w") ) where n" = n' and N" = N, with n = N' as necessary condition.

Appendage: (e",d") = (e,d) + (e',d') which means e": (v + v') -> e(v) + e'(v') and d": (w + w') -> d(w) + d'( w') where the addition is to be understood as appending two vectors together, so N" = N' + N and n" = n + n'.

Appending codes is particularly useful when considering segment codes or segmented transforms.

A BinaryCode-instance is initialized by BinaryCode(A,d), given the encoding (e) as n x N array or matrix-like nested lists A, such that e(v) = (A v) mod 2. The decoding d is an array or a list input of length N, which has entries either of type BinaryPolynomial, or of valid type for an input of the BinaryPolynomial-constructor.

The signs + and *, += and *= are overloaded to implement concatenation and appendage on BinaryCode-objects.

encoding np.ndarray or list

nested lists or binary 2D-array

decoding array or list

list of BinaryPolynomial (list or str).

TypeError non-list, array like encoding or decoding, unsuitable BinaryPolynomial generators,
BinaryCodeError in case of decoder/encoder size mismatch or decoder size, qubits indexed mismatch

decoder list

list of BinaryPolynomial: Outputs the decoding functions as components.

encoder scipy.sparse.csc_matrix

Outputs A, the linear matrix that implements the encoding function.

n_modes int

Outputs the number of modes.

n_qubits int

Outputs the number of qubits.

Methods

__add__

View source

__add__(
    appendix
)

Appends two binary codes via addition +.

Args
appendix BinaryCode

The code to append to the present one.

Returns (BinaryCode): global binary code

__mul__

View source

__mul__(
    factor
)

Concatenation of two codes or appendage the same code factor times in case of integer factor.

Args
factor int or BinaryCode

the BinaryCode to concatenate. In case of int, it will append the code to itself factor times.

Returns (BinaryCode): segmented or concatenated code

__rmul__

View source

__rmul__(
    factor
)

Appending the same code factor times.

Args
factor int

integer defining number of appendages.

Returns (BinaryCode): Segmented code.

Raises
TypeError factor must be an integer