The XP stabiliser formalism

—by Mark Webster

As part of his PhD, Mark Webster has been investigating ways of efficiently representing general quantum states that cannot be simulated using classical computing.

Representing a general quantum state requires an amount of information that grows exponentially with system size.  One way to describe quantum states more compactly is using the Pauli stabiliser formalism.  States within this formalism demonstrate some aspects of quantum behaviour, such as superposition and entanglement; however, these behaviours can also be simulated using a classical computer.

I have been working on a generalisation of the Pauli stabiliser formalism called the XP stabiliser formalism, which allows us to represent a wider range of states.  These states cannot always be simulated classically, suggesting the formalism captures some of the advantages we expect from quantum computing.

The new formalism may have applications in producing robust quantum memories, creating resource states that help to realise universal quantum computers and in condensed matter physics.  There are still many interesting open questions.  Possible research directions include:

• Finding good error-correction protocols,
• Determining which topological phases may be represented in the new formalism, and
• Developing useful quantum codes (which could be applied, for instance, in quantum memories or magic state distillation).

A key challenge for me was that it took a long time to be able to read and understand papers in this field!  I had been away from university for a long time, and it was really helpful to talk with young researchers in my group. This informal mentoring—often over a few beers—really accelerated my development.

I also found that coding up examples in Python made things much more concrete and easier to understand.  This also helped me to quickly come up with hypotheses and test them ahead of proving them mathematically.  I’ve now released the code as a package for others to use and explore the new formalism.  It would also be great to talk with others in EQUS about possible applications and implications of the work. 

Read the full paper here: https://arxiv.org/abs/2203.00103.  Mark Webster is a PhD student in the Sydney Quantum Theory Laboratory at the University of Sydney, working with Chief Investigator Stephen Bartlett.  He is a member of EQUS’ Mentoring and Career Development committee and is leading the roll-out of the new EQUS mentoring program (https://hub.equs.org/mentoring-program; requires login).  If you haven’t already signed up to be a mentor or mentee, please do so!