Table of contents

• Introduction
• Installation
  • User-mode
  • Dev-mode
• Usage examples
  • Sympify a Qiskit circuit
  • Lambdify a Qiskit circuit
• Qiskit Medium
• Contributors

Introduction

The qiskit-symb package is meant to be a Python tool to enable the symbolic evaluation of parametric quantum states defined by 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 directly from the Qiskit quantum circuit. This has been achieved through the re-implementation of some basic classes defined in the qiskit/quantum_info/ module by using sympy as a backend for symbolic expressions manipulation.

Installation

User-mode

pip install qiskit-symb

Dev-mode

git clone https://github.com/SimoneGasperini/qiskit-symb.git
cd qiskit-symb
pip install requirements-dev.txt
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:

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(p[0], 0, p[1], 1)

pqc.draw("mpl")

To get the sympy representation of the unit-norm complex vector prepared by the parameterized circuit, we just have to create the symbolic Statevector instance and call the to_sympy() method:

from qiskit_symb.quantum_info import Statevector

psi = Statevector(pqc)
psi.to_sympy()

$$\left[\begin{matrix}\cos{\left(\frac{p[0]}{2} \right)} \cos{\left(\frac{y}{2} \right)} & - e^{1.0 i p[1]} \sin{\left(\frac{p[0]}{2} \right)} \sin{\left(\frac{y}{2} \right)} & \sin{\left(\frac{p[0]}{2} \right)} \cos{\left(\frac{y}{2} \right)} & e^{1.0 i p[1]} \sin{\left(\frac{y}{2} \right)} \cos{\left(\frac{p[0]}{2} \right)}\end{matrix}\right]$$

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

new_psi = psi.subs({p: [-1, 2]})
new_psi.to_sympy()

$$\left[\begin{matrix}\cos{\left(\frac{1}{2} \right)} \cos{\left(\frac{y}{2} \right)} & e^{2.0 i} \sin{\left(\frac{1}{2} \right)} \sin{\left(\frac{y}{2} \right)} & - \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{y}{2} \right)} & e^{2.0 i} \sin{\left(\frac{y}{2} \right)} \cos{\left(\frac{1}{2} \right)}\end{matrix}\right]$$

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:

from qiskit.circuit.library import zz_feature_map

pqc = zz_feature_map(feature_dimension=3, reps=1)
pqc.draw("mpl")

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

from qiskit_symb.quantum_info import Statevector

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.

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 evaluation and then call the lambda generated function as many times as needed, passing different values of the parameters at each iteration.

Contributors

Simone Gasperini

Sebastian Brandhofer

Inho Choi