o
    8Va7                     @   s   d Z ddlmZmZmZmZmZmZmZ ddl	m
Z
 ddlmZ ddlmZmZ ddlmZ ddlmZ ddlmZmZmZmZmZmZmZmZ g d	ZG d
d deZeZG dd deZ G dd de Z!G dd de Z"dS )at  An implementation of qubits and gates acting on them.

Todo:

* Update docstrings.
* Update tests.
* Implement apply using decompose.
* Implement represent using decompose or something smarter. For this to
  work we first have to implement represent for SWAP.
* Decide if we want upper index to be inclusive in the constructor.
* Fix the printing of Rk gates in plotting.
    )ExprMatrixexpIpiIntegerSymbolsqrt)qapply)QuantumErrorQExpr)eye)matrix_tensor_product)GateHadamardGateSwapGateOneQubitGateCGate	PhaseGateTGateZGate)QFTIQFTRkGateRkc                   @   sZ   e Zd ZdZdZdZdd Zedd Ze	dd	 Z
e	d
d Ze	dd ZdddZdS )r   z This is the R_k gate of the QTF.r   Rc                 G   s   t |dkrtd| |d }|d }|dkrt|S |dkr$t|S |dkr,t|S | |}tj| g|R  }| ||_	|S )N   z)Rk gates only take two arguments, got: %rr         )
lenr   r   r   r   
_eval_argsr   __new__Z_eval_hilbert_spaceZhilbert_space)clsargstargetkinst r(   ;/usr/lib/python3/dist-packages/sympy/physics/quantum/qft.pyr"   +   s    
zRkGate.__new__c                 C   s
   t |S N)r   r!   )r#   r$   r(   r(   r)   r!   @   s   
zRkGate._eval_argsc                 C   
   | j d S Nr   labelselfr(   r(   r)   r&   F      
zRkGate.kc                 C   s   | j d d S r,   r-   r/   r(   r(   r)   targetsJ   s   zRkGate.targetsc                 C   s   d| j t| jf S )Nz$%s_%s$)gate_name_latexstrr&   r/   r(   r(   r)   gate_name_plotN   s   zRkGate.gate_name_plotsympyc                 C   sF   |dkrt ddgdttdt t td| j  ggS td| )Nr6   r   r   r   z#Invalid format for the R_k gate: %r)r   r   r   r   r   r&   NotImplementedError)r0   formatr(   r(   r)   get_target_matrixR   s
   2zRkGate.get_target_matrixN)r6   )__name__
__module____qualname____doc__	gate_namer3   r"   classmethodr!   propertyr&   r2   r5   r9   r(   r(   r(   r)   r   &   s    



r   c                   @   s\   e Zd ZdZedd Zdd Zdd Zedd	 Z	ed
d Z
edd Zedd ZdS )Fourierz@Superclass of Quantum Fourier and Inverse Quantum Fourier Gates.c                 C   s:   t |dkrtd| |d |d krtdt|S )Nr   z*QFT/IQFT only takes two arguments, got: %rr   r   z!Start must be smaller than finish)r    r   r   r!   )r0   r$   r(   r(   r)   r!   _   s   
zFourier._eval_argsc                 K   s   | j di |S )Nr*   )_represent_ZGate)r0   optionsr(   r(   r)   _represent_default_basisi      z Fourier._represent_default_basisc                    s   | dd}|dkrtd|| jk rtd| | j| j  fddtD }t|}| jd dkrBtt	d| jd  |}| j|k rSt|t	d|| j  }|S )z:
            Represents the (I)QFT In the Z Basis
        nqubitsr   z.The number of qubits must be given as nqubits.z2The number of qubits %r is too small for the gate.c                    s&   g | ]  fd dt D qS )c                    s$   g | ]}|    t  qS r(   r	   ).0i)jomegasizer(   r)   
<listcomp>|   s    
z7Fourier._represent_ZGate.<locals>.<listcomp>.<listcomp>)range)rG   rJ   rK   )rI   r)   rL   |   s
    
z,Fourier._represent_ZGate.<locals>.<listcomp>r   )
getr   
min_qubitsrK   rJ   rM   r   r.   r   r   )r0   ZbasisrC   rF   ZarrayFTZmatrixFTr(   rN   r)   rB   l   s,   

zFourier._represent_ZGatec                 C   s   t | jd | jd S )Nr   r   )rM   r.   r/   r(   r(   r)   r2         zFourier.targetsc                 C   r+   r,   r-   r/   r(   r(   r)   rP      r1   zFourier.min_qubitsc                 C   s   d| j d | j d   S )z"Size is the size of the QFT matrixr   r   r   r-   r/   r(   r(   r)   rK      s   zFourier.sizec                 C   s   t dS )NrJ   )r   r/   r(   r(   r)   rJ      s   zFourier.omegaN)r:   r;   r<   r=   r?   r!   rD   rB   r@   r2   rP   rK   rJ   r(   r(   r(   r)   rA   \   s    
	


rA   c                   @   s<   e Zd ZdZd Zd Zdd Zdd Zdd Ze	dd	 Z
d
S )r   z&The forward quantum Fourier transform.c                 C   s   | j d }| j d }d}tt||D ]!}t|| }t|| D ]}t|| d t||d | }q!qt|| d D ]}t|| || d | }q=|S )z%Decomposes QFT into elementary gates.r   r   r   )r.   reversedrM   r   r   r   r   )r0   startfinishcircuitlevelrH   r(   r(   r)   	decompose   s   

"zQFT.decomposec                 K   s   t |  | S r*   )r   rW   )r0   ZqubitsrC   r(   r(   r)   _apply_operator_Qubit   rE   zQFT._apply_operator_Qubitc                 C   
   t | j S r*   )r   r$   r/   r(   r(   r)   _eval_inverse      
zQFT._eval_inversec                 C      t dt t | j S )Nr   r   r   r   rK   r/   r(   r(   r)   rJ      rQ   z	QFT.omegaN)r:   r;   r<   r=   r>   r3   rW   rX   rZ   r@   rJ   r(   r(   r(   r)   r      s    r   c                   @   s4   e Zd ZdZd ZdZdd Zdd Zedd Z	d	S )
r   z&The inverse quantum Fourier transform.z
{QFT^{-1}}c                 C   s   | j d }| j d }d}t|| d D ]}t|| || d | }qt||D ]$}tt|| D ]}t|| d t|| d | }q3t|| }q)|S )z&Decomposes IQFT into elementary gates.r   r   r   )r$   rM   r   rR   r   r   r   )r0   rS   rT   rU   rH   rV   r(   r(   r)   rW      s   

$zIQFT.decomposec                 C   rY   r*   )r   r$   r/   r(   r(   r)   rZ      r[   zIQFT._eval_inversec                 C   r\   )Nr]   r/   r(   r(   r)   rJ      rQ   z
IQFT.omegaN)
r:   r;   r<   r=   r>   r3   rW   rZ   r@   rJ   r(   r(   r(   r)   r      s    r   N)#r=   r6   r   r   r   r   r   r   r   Zsympy.functionsr
   Zsympy.physics.quantum.qapplyr   Zsympy.physics.quantum.qexprr   r   Zsympy.matricesr   Z#sympy.physics.quantum.tensorproductr   Zsympy.physics.quantum.gater   r   r   r   r   r   r   r   __all__r   r   rA   r   r   r(   r(   r(   r)   <module>   s    $(3?