o
    *ήc                     @   s   d Z ddlmZ ddlmZmZmZ ddlmZ ddl	m
Z
 ddl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)IIntegerpiSymbol)exp)Matrix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$t|S |dkr,t|S | |}tj| g|R  }| ||_	|S )N   z)Rk gates only take two arguments, got: %rr         )
lenr   r   r   r   
_eval_argsr   __new___eval_hilbert_spacehilbert_space)clsargstargetkinst r+   @/tmp/pip-target-vg8gfxp4/lib/python/sympy/physics/quantum/qft.pyr#   /   s    
zRkGate.__new__c                 C   s
   t |S N)r   r"   )r&   r'   r+   r+   r,   r"   D   s   
zRkGate._eval_argsc                 C   
   | j d S Nr   labelselfr+   r+   r,   r)   J      
zRkGate.kc                 C   s   | j d d S r/   r0   r2   r+   r+   r,   targetsN   s   zRkGate.targetsc                 C   s   d| j t| jf S )Nz$%s_%s$)gate_name_latexstrr)   r2   r+   r+   r,   gate_name_plotR   s   zRkGate.gate_name_plotsympyc                 C   sF   |dkrt ddgdttdt t td| j  ggS td| )Nr9   r   r   r   z#Invalid format for the R_k gate: %r)r	   r   r   r   r   r)   NotImplementedError)r3   formatr+   r+   r,   get_target_matrixV   s
   2zRkGate.get_target_matrixN)r9   )__name__
__module____qualname____doc__	gate_namer6   r#   classmethodr"   propertyr)   r5   r8   r<   r+   r+   r+   r,   r   *   s    



r   c                   @   s\   e Zd ZdZedd Zdd Zdd Zedd	 Z	ed
d Z
edd Zedd ZdS )Fourierz@Superclass of Quantum Fourier and Inverse Quantum Fourier Gates.c                 C   s:   t |dkrtd| |d |d krtdt|S )Nr   z*QFT/IQFT only takes two arguments, got: %rr   r   z!Start must be smaller than finish)r!   r   r   r"   )r3   r'   r+   r+   r,   r"   c   s   
zFourier._eval_argsc                 K   s   | j di |S )Nr-   )_represent_ZGate)r3   optionsr+   r+   r,   _represent_default_basism      z Fourier._represent_default_basisc                    s   | dd}|dkrtd|| jk rtd| | j| j  fddtD }t|}| jd dkrBtt	d| jd  |}| j|k rSt|t	d|| j  }|S )z:
            Represents the (I)QFT In the Z Basis
        nqubitsr   z.The number of qubits must be given as nqubits.z2The number of qubits %r is too small for the gate.c                    s&   g | ]  fd dt D qS )c                    s$   g | ]}|    t  qS r+   r
   ).0i)jomegasizer+   r,   
<listcomp>   s    
z7Fourier._represent_ZGate.<locals>.<listcomp>.<listcomp>)range)rJ   rM   rN   )rL   r,   rO      s
    
z,Fourier._represent_ZGate.<locals>.<listcomp>r   )
getr   
min_qubitsrN   rM   rP   r	   r1   r   r   )r3   basisrF   rI   arrayFTmatrixFTr+   rQ   r,   rE   p   s,   

zFourier._represent_ZGatec                 C   s   t | jd | jd S )Nr   r   )rP   r1   r2   r+   r+   r,   r5         zFourier.targetsc                 C   r.   r/   r0   r2   r+   r+   r,   rS      r4   zFourier.min_qubitsc                 C   s   d| j d | j d   S )z"Size is the size of the QFT matrixr   r   r   r0   r2   r+   r+   r,   rN      s   zFourier.sizec                 C   s   t dS )NrM   r   r2   r+   r+   r,   rM      s   zFourier.omegaN)r=   r>   r?   r@   rB   r"   rG   rE   rC   r5   rS   rN   rM   r+   r+   r+   r,   rD   `   s    
	


rD   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   )r1   reversedrP   r   r   r   r   )r3   startfinishcircuitlevelrK   r+   r+   r,   	decompose   s   

"zQFT.decomposec                 K   s   t |  | S r-   )r   r]   )r3   qubitsrF   r+   r+   r,   _apply_operator_Qubit   rH   zQFT._apply_operator_Qubitc                 C   
   t | j S r-   )r   r'   r2   r+   r+   r,   _eval_inverse      
zQFT._eval_inversec                 C      t dt t | j S )Nr   r   r   r   rN   r2   r+   r+   r,   rM      rW   z	QFT.omegaN)r=   r>   r?   r@   rA   r6   r]   r_   ra   rC   rM   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 ]$}tt|| D ]}t|| d t|| d | }q3t|| }q)|S )z&Decomposes IQFT into elementary gates.r   r   r   )r'   rP   r   rX   r   r   r   )r3   rY   rZ   r[   rK   r\   r+   r+   r,   r]      s   

$zIQFT.decomposec                 C   r`   r-   )r   r'   r2   r+   r+   r,   ra      rb   zIQFT._eval_inversec                 C   rc   )Nrd   r2   r+   r+   r,   rM      rW   z
IQFT.omegaN)
r=   r>   r?   r@   rA   r6   r]   ra   rC   rM   r+   r+   r+   r,   r      s    r   N)'r@   sympy.core.exprr   sympy.core.numbersr   r   r   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   sympy.matrices.denser	   sympy.functionsr   sympy.physics.quantum.qapplyr   sympy.physics.quantum.qexprr   r   sympy.matricesr   #sympy.physics.quantum.tensorproductr   sympy.physics.quantum.gater   r   r   r   r   r   r   r   __all__r   r   rD   r   r   r+   r+   r+   r,   <module>   s$    (3?