Chris Heunen

Also about circuits: the physics Nobel prize just announced!

So much material for titles here, too! "If you liked it you shoulda put a rig on it", "The rig is up", "Taking back control". What's your favourite?

Theorem: these two ways to build a theory of controlled circuits are the same! Practically, this means the equations are complete, and we can use them to manipulate and optimise controlled circuits. Foundationally, this pins down what this not-quite-data-or-control-flow control really is about.

Another thing you can do is make a new theory where 'controlled gates' are, roughly, matrices of base gates. Technically, you freely adjoin sums to the base (tensor) prop, universally giving it rig structure.

The equations all have natural interpretations. For example, the complementarity equation (e) says that a gate on the target wire is the same as a positively controlled and then a negatively controlled version of it: the control bit is either on or off.

The equations governing controlled gates.

Start with any base circuit theory, in terms of tensors only; technically, as a prop. Build a new controlled circuit theory that has controlled versions of the base gates, subject to these equations.

The key is that circuits contain controlled gates. It's not quite data flow, nor control flow, in the usual computer science sense. But it is clearly important. Can we take back this control, and separate this control from a base theory of uncontrolled circuits? Yes we can!

Have you ever wondered why we describe circuits with matrices? I mean, circuits are about tensor products, while matrices are about direct sums. This new paper with Louis Lemonnier and @manchegobaby.bsky.social gives a practically useful explanation: arxiv.org/abs/2510.05032.

Quantum circuits are just a phase Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and even advanced quantum programming languages essentially function as circuit descrip...

A new quantum programming construct: more abstract than circuits, capturing important examples elegantly and in fact universal, yet simple and intuitive. With prototype compiler and clean categorical semantics to boot!

With Alex Rice, Chris McNally, and Louis Lemonnier:
arxiv.org/abs/2507.11676

I presented a taster poster on our upcoming work in distributed quantum compilation at the Uni of Edinburgh’s Informatics internal research showcase this Tuesday.

Focus: our upcoming model/hardware-agnostic intermediate representation for compilation of quantum programs (quite a mouthful I know!)

A discussion of the success of Bell Labs as a research organization and why we have nothing like it anymore.

Hadamard-$Π$: Equational Quantum Programming Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qubit basis-changing g...

A sound and complete finite system of equations to manipulate Toffoli+Hadamard quantum circuits you say, so you can automate circuit optimisation, you say? Why of course, here you go: arxiv.org/abs/2506.06835, with Wang Fang and @manchegobaby.bsky.social.

90% of doing science is being open to new ideas.

M*-categories: Where limits in analysis and category theory meet This article introduces M*-categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hilbert spaces and bounded linea...

🚨 New preprint alert 🚨

Always wanted to know the connection between analytic limits and categorical limits? Tired of having to establish directed colimits of contractions when directed colimits of isometries suffice? You're in luck!

Now on www.arxiv.org/abs/2505.17432. With Matt Di Meglio.

Edinburgh local curious about how physics is shaping computer science?
Come along to this light & fun Pint of science session, and hear me ramble about quantum computers. Perfect for the curious general public!

Register here: pintofscience.co.uk/event/subato...

Two more days to get your application in! Apply now at quantuminformatics-cdt.ac.uk.

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Applications are now open for September 2025 entry to the EPSRC Centre for Doctoral Training in Quantum Informatics. At least 16 fully-funded PhD studentships are available! Apply at quantuminformatics-cdt.ac.uk.

📢PhD Positions in Quantum Computing
Applications are now open for the new CDT in Quantum Informatics. We are recruiting 16 students to start Sept 2025. Positions are fully funded for 4 years. Apply now:
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