Technology, Data Science and Quantum Computing

How the simplest quantum binary classifier looks like? While searching in internet for the smallest quantum classifier I came across the article from Maria Schuld “Building the world’s smallest quantum classifier” (1) and, based on the circuit proposed there, I thought an even smaller classifier could be built. Here I show a simple variational circuit that can be applied to a 2-feature dataset for binary classification. Though the example is questionable for practical purposes, it gives interesting insights on how to apply quantum computing to machine learning. The circuit is composed of two parts: the embedding, which transforms the classical data into quantum states, and the ansatz, which is parametrized, and the parameters are optimized using a particle swarm optimization algorithm (2). The circuit and the findings follow. First, we need a dataset! Instead of searching for real datasets which must be cleaned, normalized, etc… I’ve created one. The dataset contains 60 samples, each s...

  Quantum algorithms such as Deutsch, Bernstein-Vazirani, Simon and Grove rely on Oracles. A particular class of Oracles, the phase Oracles, allows to selectively switch phases of the input state, thus helping these algorithms to distinguish states by their phases. In this blog I will explore a bit more this class of Oracles Firstly. lets revisit the superposition state for a single qubit $|0\rangle$ after applying the Hadamard gate:                     $ H\otimes|0\rangle = \frac {1} {\sqrt{2}} ( |0\rangle + |1\rangle ) = |+\rangle $ To recap, this is a state of maximum uncertainty when measured in the computational basis. In simple terms, it represents a state where, when measured, has equal probability of being 0 or 1. As mentioned before, the trick to make the information conveyed by a state more useful is to include a local phase to it. This can be achieved by adding a new qubit in the superposition state $|-\rangle =...

  The Deutsch Algorithm is an excellent example of the application of quantum parallelism using superposition of states. The problem which is solved by the algorithm is the following: Given an unknown function f(x): {0:1} -> {0,1}, by using the minimum amount of queries to this function, determine if the function is constant (it always returns 0 or always returns 1) or balanced (on half of the inputs it returns 0 and the other half, 1). In the classical case, we need to query the function twice, one for x=0 and a second for x=1. In case of the quantum algorithm, a single query can define if the function is balanced or constant. There are many articles explaining how the algorithm works. Here I've taken a different approach: After a brief recap of the algorithm, the analysis of the algorithm follows by opening each state and showing how the problem definition and the function we want to classify contributes to the algorithm output.  On its simplest form, the algorithm utiliz...

In Quantum Computing, by far the most popular example of controlled gate is the control-not gate. Most, if not all, the textbooks start with an example of control-not and afterwards, expands to the more generalized concept of controlled gates. It is indeed an effective way to gently introduce the topic, making a smooth connection between the existing classical gate - XOR - and the quantum control-not gate - CNOT. But simplicity is not always synonym of completeness. Controlled gates are a little spookier than initially presented by the textbooks. You will see here that there is more to the controlled gates than shown in the first chapters of quantum computing textbooks. Firstly, a quick recap on the control-not gate.  The control-not gate is a quantum gate with 2 input qubits: the first qubit is the 'control' qubit and the second one the 'target'. The control qubit controls the NOT operation to be applied in the target qubit - if the control qubit is in state |1>,...

Those programming using Quantum Computers will, eventually, come across this somewhat awkward observation when using the simulators or the real computers. The topic is often neglected by tutorials in quantum computing, and, to a certain extend, it is understandable that tutorials do not tackle it at first. In fact, if you are simply running operations on circuits in the machine, it will be hard to spot or bother about it. Nevertheless, it can cause a great deal of confusion and pain for those who are unaware or overlook it. The problem, firstly addressed in the classical computers and now resurfacing with the quantum computers, is related to the order that qubits are organized on a sequence of qubits. Note that, when considering a sequence of qubits, and considering their significance in relation to the sequence, there are two ways to order them: either the qubit on the leftmost position of the sequence is considered the least significant qubit of the sequence, or the one in the right...