Understanding superposition in Quantum Computing

In understanding the phenomenon of 'superposition' let us try to understand the application of Quantum Theory to the world of computers


Navdeep Singh Mangat (with team PROMOT)

5/27/20242 min read

green and blue light showing photon superposition
green and blue light showing photon superposition
How Quantum theory could affect computing as we know it through Quantum Computing (No Cats were harmed in writing this blog)

How Superposition Allows Quantum Computers to Process Vast Amounts of Data Quickly.

Quantum computers harness the power of superposition to process data in ways that classical computers cannot. Think about how we used to learn flow charts in our schools. Either there was a way that led to the next step with a ‘Yes’ or there was a way that that stopped the process with a ‘No’. So it was an ‘either’, ‘or’ process. In quantum state, a particle, a qubit in this case, can be in both the positions, simultaneously, creating parallel flow charts.

Understanding Superposition in Quantum Computing

In classical computing, a bit can be either 0 or 1. For a system with \( n \) bits, there are \( 2^n \) possible combinations of these bits, but a classical computer can only operate on one combination at a time.

In quantum computing, a qubit can be in a superposition of both 0 and 1 simultaneously. For a system with \( n \) qubits, the quantum computer can operate on all \( 2^n \) combinations simultaneously. This massive parallelism is what gives quantum computers their potential for extraordinary speed and power.

Process Flow: Superposition in Quantum Computing

Let's visualise this with a process chart that outlines how quantum computers use superposition to process data:

1. Initialisation:

- Classical computers initialise bits to 0 or 1.

- Quantum computers initialise qubits to a superposition state where each qubit can be both 0 and 1.

2. Quantum Superposition:

- Qubits enter a superposition state, representing all possible combinations of 0 and 1 simultaneously.

- Example: For 2 qubits, the states would be \( |00\rangle, |01\rangle, |10\rangle, \) and \( |11\rangle \).

3. Quantum Operations:

- Quantum gates perform operations on qubits in superposition.

- These gates manipulate the probabilities of qubits being in certain states without collapsing the superposition.

4. Quantum Entanglement:

- Qubits may become entangled, meaning the state of one qubit is dependent on the state of another.

- Entanglement allows for complex correlations and faster data processing.

5. Interference and Measurement:

- Quantum algorithms use interference to amplify the probabilities of correct answers and diminish incorrect ones.

- Measurement collapses the superposition into a single state, giving the result of the computation.

Example: Grover's Search Algorithm

To give a practical example, consider Grover's Search Algorithm, a quantum algorithm used to search an unsorted database:

1. Initialisation:

- Qubits are initialised in a superposition of all possible states.

2. Superposition:

- If there are \( N \) items in the database, the superposition allows the quantum computer to examine all \( N \) states simultaneously.

3. Oracle and Amplitude Amplification:

- A quantum oracle marks the correct state by flipping its phase.

- Amplitude amplification increases the probability of measuring the correct state.

4. Measurement:

- When measured, the qubits collapse to the correct state with high probability, giving the desired result.

In summary, superposition allows quantum computers to explore multiple possibilities simultaneously, providing a massive speedup for certain types of problems. The combination of superposition, entanglement, and quantum operations enables quantum computers to process vast amounts of data quickly and efficiently.