Quantum State Tomography is an important technique in Quantum Computing, allowing us to estimate the state of a quantum system. Quantum states cannot be measured directly, but through this technique, the state can be reconstructed statistically, given a number of measurements.
In the following sections, we'll introduce Quantum State Tomography and show you how to implement it using Qiskit, a Python language framework for quantum computing.
In Quantum Mechanics, the state of a quantum system is described by a state vector which encapsulates all the information about the system. However, when a quantum system is measured, the system collapses to one of the possible states, giving a probabilistic outcome.
To work around this, and find the most probable quantum state, Quantum State Tomography is employed. This experimental technique involves taking multiple measurements in numerous different bases to reconstruct the quantum state.
For our implementation, first, make sure that you have Qiskit installed. It can be installed with the pip package manager.
pip install qiskit
Now, a simple way to implement Quantum State Tomography in Qiskit is as follows:
from qiskit import QuantumCircuit from qiskit.ignis.verification.tomography import state_tomography_circuits, StateTomographyFitter from qiskit import execute from qiskit import Aer # A quantum circuit to prepare the quantum state qc = QuantumCircuit(2, 2) qc.h(0) qc.cx(0, 1) qst_qc = state_tomography_circuits(qc, [0, 1]) # Generating the state tomography circuits simulator = Aer.get_backend('qasm_simulator') # QASM simulator from Aer qst_qc_results = execute(qst_qc, simulator, shots=1000).result() # Execute the circuits on the simulator qst_fitter = StateTomographyFitter (qst_qc_results, qst_qc) # Fitting the results into the tomography fitter rho_fit = qst_fitter.fit() # Fit the results and get the density matrix print(rho_fit)
The code snippet above prepares a quantum state using a quantum circuit, constructs the state tomography circuits for the two qubits, executes the circuits and fits the results to derive the density matrix.
Quantum State Tomography is a handy tool for working with quantum systems. As quantum computing continues to progress, techniques like Quantum State Tomography will only become increasingly important.
In this post, we've shown you how Quantum State Tomography can be implemented using Qiskit. Although Qiskit facilitates many of the complex computations behind the scenes, understanding the principles behind these techniques can be invaluable in the field of Quantum Computing.