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https://github.com/SimoneGasperini/qiskit-symb

Python package for symbolic quantum computation in Qiskit
https://github.com/SimoneGasperini/qiskit-symb

qiskit quantum-computing symbolic-computation sympy

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Python package for symbolic quantum computation in Qiskit

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README 

        
![](/img/logo.png)





    

    

    

        






    

    




# Table of contents

- [Introduction](#introduction)

- [Installation](#installation)

    - [User-mode](#user-mode)

    - [Dev-mode](#dev-mode)

- [Usage examples](#usage-examples)

    - [_Sympify_ a Qiskit circuit](#sympify-a-qiskit-circuit)

    - [_Lambdify_ a Qiskit circuit](#lambdify-a-qiskit-circuit)

- [Qiskit Medium](#qiskit-medium)

- [Contributors](#contributors)



# Introduction

The `qiskit-symb` package is meant to be a Python tool to enable the symbolic evaluation of parametric quantum states and operators defined in [Qiskit](https://github.com/Qiskit/qiskit) by parameterized quantum circuits.



A Parameterized Quantum Circuit (PQC) is a quantum circuit where we have at least one free parameter (e.g. a rotation angle $\theta$). PQCs are particularly relevant in Quantum Machine Learning (QML) models, where the values of these parameters can be learned during training to reach the desired output.



In particular, `qiskit-symb` can be used to create a symbolic representation of a parametric quantum state or operator directly from the Qiskit quantum circuit. This has been achieved through the re-implementation of some basic classes defined in the [`qiskit/quantum_info/`](https://github.com/Qiskit/qiskit/tree/main/qiskit/quantum_info) module by using [sympy](https://github.com/sympy/sympy) as a backend for symbolic expressions manipulation.



# Installation



## User-mode

```

pip install qiskit-symb

```



:warning: The package requires `qiskit>=1`. See the official [Migration guides](https://docs.quantum.ibm.com/api/migration-guides) if you are used to a prevoius Qiskit version.



## Dev-mode

```

git clone https://github.com/SimoneGasperini/qiskit-symb.git

cd qiskit-symb

pip install -e .

```



# Usage examples



### _Sympify_ a Qiskit circuit

Let's get started on how to use `qiskit-symb` to get the symbolic representation of a given Qiskit circuit. In particular, in this first basic example, we consider the following quantum circuit:

```python

from qiskit import QuantumCircuit

from qiskit.circuit import Parameter, ParameterVector



y = Parameter('y')

p = ParameterVector('p', length=2)



pqc = QuantumCircuit(2)

pqc.ry(y, 0)

pqc.cx(0, 1)

pqc.u(0, *p, 1)



pqc.draw('mpl')

```

![](/img/example_circuit.png)



To get the *sympy* representation of the unitary matrix corresponding to the parameterized circuit, we just have to create the symbolic `Operator` instance and call the `to_sympy()` method:

```python

from qiskit_symb.quantum_info import Operator



op = Operator(pqc)

op.to_sympy()

```

```math

\left[\begin{matrix}\cos{\left(\frac{y}{2} \right)} & - \sin{\left(\frac{y}{2} \right)} & 0 & 0\\0 & 0 & \sin{\left(\frac{y}{2} \right)} & \cos{\left(\frac{y}{2} \right)}\\0 & 0 & e^{i \left(p[0] + p[1]\right)} \cos{\left(\frac{y}{2} \right)} & - e^{i \left(p[0] + p[1]\right)} \sin{\left(\frac{y}{2} \right)}\\e^{i \left(p[0] + p[1]\right)} \sin{\left(\frac{y}{2} \right)} & e^{i \left(p[0] + p[1]\right)} \cos{\left(\frac{y}{2} \right)} & 0 & 0\end{matrix}\right]

```



If you want then to assign a value to some specific parameter, you can use the `subs()` method passing a dictionary that maps each parameter to the desired corresponding value:

```python

new_op = op.subs({p: [-1, 2]})

new_op.to_sympy()

```

```math

\left[\begin{matrix}\cos{\left(\frac{y}{2} \right)} & - \sin{\left(\frac{y}{2} \right)} & 0 & 0\\0 & 0 & \sin{\left(\frac{y}{2} \right)} & \cos{\left(\frac{y}{2} \right)}\\0 & 0 & e^{i} \cos{\left(\frac{y}{2} \right)} & - e^{i} \sin{\left(\frac{y}{2} \right)}\\e^{i} \sin{\left(\frac{y}{2} \right)} & e^{i} \cos{\left(\frac{y}{2} \right)} & 0 & 0\end{matrix}\right]

```



### _Lambdify_ a Qiskit circuit

Given a Qiskit circuit, `qiskit-symb` also allows to generate a Python lambda function with actual arguments matching the Qiskit unbound parameters.

Let's consider the following example starting from a `ZZFeatureMap` circuit, commonly used as a data embedding ansatz in QML applications:

```python

from qiskit.circuit.library import ZZFeatureMap



pqc = ZZFeatureMap(feature_dimension=3, reps=1)

pqc.draw('mpl')

```

![](/img/zzfeaturemap_circuit.png)



To get the Python function representing the final parameteric statevector, we just have to create the symbolic `Statevector` instance and call the `to_lambda()` method:

```python

from qiskit_symb.quantum_info import Statevector



pqc = pqc.decompose()

statevec = Statevector(pqc).to_lambda()

```



We can now call the lambda-generated function `statevec` passing the `x` values we want to assign to each parameter. The returned object will be a *numpy* 2D-array (with `shape=(8,1)` in this case) representing the final output statevector `psi`.

```python

x = [1.24, 2.27, 0.29]

psi = statevec(*x)

```



This feature can be useful when, given a Qiskit PQC, we want to run it multiple times with different parameters values. Indeed, we can perform a single symbolic evalutation and then call the lambda generated function as many times as needed, passing different values of the parameters at each iteration.



# Qiskit Medium

Read my [blog post](https://medium.com/p/b6b4407fa705) introducing to `qiskit-symb` published on the official Qiskit Medium blog.



![](/img/medium.png)



# Contributors



    
Simone Gasperini

    
Sebastian
Brandhofer