### July 18, 2018

## The World of Photonic Quantum Computing

The past two weeks have been packed with knowledge, excitement, and confusion.

I’ve been interning at Xanadu, a quantum computing startup in Toronto. Not only have **I met some incredibly intelligent people, I’ve also hit a major learning curve. **At Xanadu, I’ve been coding quantum circuits and quantum machine learning models but before we dive into my first project, let’s learn about what Xanadu does.

**Xanadu: Building the world’s first practical quantum computer**

**Xanadu has taken an interesting approach to quantum computing.**

While companies like Rigetti and IBM use the qubit model , Xanadu is developing a continuous variable model.

And there are numerous benefits for adapting the Continuous Variable (CV)model. For example, the CV model requires less coupled systems to perform computations. Nevertheless, while the CV model has certain advantages over the qubit model, it also presents its own problems and limitations.

The first apparent difference between these two models deal with quantum bits, the information carrying units of a quantum computer. While the qubit model uses discrete-valued qubits, the CV model uses **qumodes that reside in an infinite dimensional space.**

h u h?

Yes, quantum operations in CV quantum computers operate in an infinite dimensional space called the Hilbert space. In other words, these operations are non-localized. Although this concept sounds abstract, we must remember that things work differently on a quantum level. And if you like the weirdness of Hilbert space, you’ll love what comes next.

Qumodes are collections of photons that have been operated on. We’ll see later that you can morph qumodes into new shapes using quantum logic gates. Similar to the qubit model, CV quantum computing also uses quantum logic gates to perform different operations on bits.

**Visualizing Quantum States**

My first project at Xanadu developed my intuition behind how CV quantum gates operate on qumodes.

**Vacuum State**

To start off, we’ll have a look at the vacuum state. This is the initial state of a qumode. When measuring the vacuum state we get |0 〉

The probability distribution of the vacuum state is represented on a wigner function. Here all the values are positive.

The vacuum state can be evolved into different states by applying quantum logic gates to qumodes.

**Squeezed State**

The gate applied here is called a squeezing gate. It is one of the most basic CV quantum gates. You can think of someone squeezing the vacuum state by a certain force until it becomes a certain shape. It shifts the vacuum states’s quadratures by x^−r x̂ ϕ on quadrature x̂ and e ^r ϕ on quadrature p̂.

**Cubic Phase Gate**

The squeezing gate, displacement gate, rotation gate and beamsplitter gates are all Gaussian gates. But the really weird quantum states can be created using Non-Gaussian states such as the Cubic Phase Gate.

This gate works by shifting the p̂ quadrature by γx̂ 2. But the interesting part are the darker purple areas. If you have a look at the colour bar, we can see that those areas represent a location where the qumode has a negative probability distribution.

This concept baffled me. Although it doesn’t make sense intuitively, the math computes and it has been proven theoretically.

The implications of using a qumode in a negative probability state are not known. CV quantum computing is in it’s early stages of development. But it brings the opportunity to use the quantum weirdness of photons to potentially solve some of the world’s biggest problems.

For the next couple of weeks, I’ll be working on developing quantum machine learning models at Xanadu.

If you want to learn more about continuous variable quantum states and their physical representations, I coded a couple of quantum circuits in the notebook below: