| Circuits |
|---|
Deutsch's Algorithm |
Harrow-Hassidim-Lloyd Algorithm |
Quantum Phase Estimation |
Test circuit |
| Hardware |
|---|
NMR Qubit |
| Documentation |
|---|
Adding Quantum Circuits |
Adding Quantum Gates |
Quantum Gates and Operations |
Getting Started |
Interactive Quantum Circuits |
Project Structure |
JSON Schemas |
Glossary |
The Deutsch Algorithm offers arguably the simplest example of how quantum computers can utilise superposition to solve problems more efficiently than standard computers.
Given an arbitrary function,
With traditional computation, two queries would be required to solve this problem, simply evaluating
For simple functions, this is trivial, however consider an arbitrary function that offers some challenge in its computation, solving this problem with a single query would certainly be beneficial.
Begin with the initial state,
After the passing through the first set of Hadamard gates, the initial state is transformed into
Recall that
Next the phase oracle is applied, since the input is in a superposition, the matrix is distributed into each of the superposition states, leaving us with a state of
However, recalling that
The state can be further simplified to
Before applying the final Hadamard gate to the first qubit, consider each case individually, firstly that
Applying the final gate gives a final state of
The first qubit will always be measures as a 0.
In the other case, where
Applying the final gate gives a final state of
The first qubit will always be measures as a 1.
Hence, if
Whilst currently lacking commercial use cases, the Deutsch algorithm serves as a proof of concept, demonstrating the ability of quantum computing to solve problems in a more efficient way than traditional computation.
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