Error in probabilities

October 21, 2024 The Editorial Board - Teamware Solutions

It might be like a dream to work on quantum programming these days. So, let us take ourselves into a dream of being on a mission in deep space. Very much like Star Trek missions!

Imagine you’re at the helm of a spaceship navigating the uncharted cosmos, ensuring that every piece of your tech integrates seamlessly. Now, swap the spaceship for a quantum computer and the cosmos for entangled qubits, and you’ve got the task of quantum error correction nearly instantly. Just as you’d troubleshoot and fix glitches in a vast IT infrastructure, quantum error correction ensures our quantum systems stay on course, fault-free. Without those quantum computers onboard being error-free we would not be in any state to engage! Isn’t it? In this brave new quantum world, even the tiniest blip can cause cosmic chaos, and that’s where your integrator expertise comes in—keeping the quantum ship steady in the stormy seas of decoherence. Welcome aboard, space-tech pioneers! to the world of correcting errors in quantum measurements.

Quantum error correction isn’t just about solving problems; it’s about preventing them from derailing your quantum mission. Think of it as your onboard toolkit: you have error correction codes like the Shor code and the Steane code, each designed to tackle different types of quantum “bugs.” These codes detect and correct errors that arise due to qubit decoherence and other quantum noise. In a framework like Qiskit, you might leverage the QuantumCircuit and Aer simulators. These codes detect and correct errors that arise due to qubit decoherence and other quantum noise. Much like how you’d set up redundancies and fail-safes in a classic IT environment, quantum error correction uses redundancy in qubits to ensure the integrity of your data. By mapping out these error correction strategies, you’re essentially creating a safety net for your quantum computations, keeping your ship on course and your mission critical. Ready to dive into the code that will save your quantum ship from the void? Let’s get started!

Having mentioned Qiskit already let us take a quick look at a snippet that causes error in measuring the state of the qubit.

Let us see what we are doing here.

We are initialising a quantum circuit with a single bit. Notices we are using a single qubit to store information. A simple bit flip error would throw the quantum circuit away from reality. We are simulating this error in the line

Before we simulate the error we are using a Hadamard operator to put the bit in superposition in the circuit.

We do that so that we eventually measure the outcome. Had we not simulated the error, after the superposition a measurement must have yielded 1 with a bit value of ‘0’. Next, let us fix this issue.

Notice in this circuit we initialise with 3 qubits. It is key for us to grasp this. We must spread the information over many qubits to be able to correct it later. The thing with probability is that it has to be dealt with a larger sample. The sample is the qubits in this case. So, after introducing the error in the code above we measure the syndrome using 

By providing the expected value over the qubits using a controlled-NOT gate (cx).

Once the syndrome is detected we next apply the error correction on the bit flipped using a simple c_if operator before we collapse the circuit with a quantum measurement.

There are many algorithms that identify the error. We leave you with a task to identify them and build a correction code.