The Dutch Science Council (NWO) has awarded Veni grants of up to 320,000 euro per project to 20 promising UvA and Amsterdam UMC researchers. One of the recipients of the Veni is QuSoft researcher John van de Wetering, who won the grant on his project *A diagrammatic toolbox for quantum circuit simulation.*

Van de Wetering will use a language of diagrams, the ZX-calculus, to unify different approaches to simulating quantum computations, which will allow for larger simulations. To congratulate John we asked him what are the goals of his research and to tell us about the tools he is planning to use.

**John.**Quantum computers are now a reality and getting better every single day. But as they still have few quantum bits (qubits), it is important that we make the most of what we have by optimising the software we run on them as much as possible. This requires a robust chain of compilation tools which optimises the code and also verifies that the code is correct.

In this project I will use a diagrammatic language called the ZX-calculus to unify different approaches to simulating quantum computations. Classical simulation allows us to verify correctness of the computations. In addition, because this problem is closely related to the field of tensor networks, it also allows us to solve other problems. I will use the connection of quantum simulation to condensed-matter physics and logical-formula solving to find areas where these improved techniques can lead to more efficient computations in these fields.

**What is the ZX-calculus?**

**John.**A common tool for quantum computing researchers is to represent a computation using a quantum circuit, which is a graphical representation of a computation through time. While this does an adequate job of representing the computation, it is not an ideal tool for

**reasoning**about the computation. The ZX-calculus can be seen as an extension of quantum circuits that is less rigid and allows for representing a larger class of computations using

**ZX-diagrams**. More importantly, these diagrams can be rewritten graphically using the rules of the

**ZX-calculus**. This extra flexibility and the rewrite rules allows us to reason about a large class of interesting objects – like quantum computations, problems in condensed-matter physics, or logical formulas – without ever having to calculate the underlying matrices.

**Figure**: Left: The quantum teleportation in the circuit model. This protocol has Alice and Bob starting with an entangled state. Then after Alice does some measurements and sends these outcomes to Bob, Bob ends up with the state that Alice had: the quantum state of Alice has ‘teleported’ to Bob. Right: The same protocol as a ZX-diagram, with a diagrammatic proof that it indeed reduces to a channel (a wire) that transmits whatever Alice has to Bob.

**Software and resources**

**John.**This project will continue building on our open-source quantum compiler

**PyZX**(https://github.com/zxcalc/pyzx), which allows for large-scale rewriting of diagrams and quantum computations.

If you’d like to learn more about how we can use the ZX-calculus to reason about quantum computation and quantum compilation, you can check out my now freely available preprint of the textbook Picturing Quantum Software

**:**An Introduction to the ZX-Calculus and Quantum Compilation that I have written together with prof. Aleks Kissinger (University of Oxford): https://github.com/zxcalc/book.