A look inside the Xanadu algorithms team with Juan Miguel Arrazola

"The first thing to understand," Juan Miguel Arrazola told me, "is the difference between an algorithm and an application."

An algorithm, he explained, is a set of instructions designed to execute a computational procedure. This differs from an application, which is a very specific, useful task that is targeted by an algorithm. Think A* Search (the algorithm) in relation to Google Maps (the application).

Bridging the gap between these two areas is not a simple task. At Xanadu headquarters, where Juan Miguel serves as the Director of Quantum Algorithms, the team sits together in a block of desks often heavy with concentration. In these open-air quarters, members work each day to implement and advance algorithmic tools, identify potential application areas and find solutions to problems that define an industry.

When we sat down a few weeks ago, I knew it was a rare opportunity. An hour is precious when your days are stacked with overseeing one of the fastest growing teams at the company. Having this conversation, though, was important. The field of quantum computing has no lack of open questions, but the Xanadu algorithms team is bent on answering the most consequential: what will we use quantum computers for?

Xanadu has bet on Hamiltonian simulation as a leading contender, putting forward algorithms of this kind for applications such as vibronic dynamics, simulating photosensitizers for cancer treatments, and modelling extreme ultraviolet photolithography (EUV).

How are these focus areas decided, though? Does it typically start with the application or with the algorithm? To answer this, he pulled up a flywheel style diagram he has referenced in this context many times before.

Sometimes, he elaborated, a very important, well positioned application comes to light and the team works backward to develop strategies to solve it. Other times, useful algorithms emerge on their own. Xanadu's continued work on quantum simulation, for example, takes an application-first approach, while some strategies, like quantum machine learning's train classical, deploy quantum strategy, are algorithm-first.

How this plays out is highly dependent on the people doing the work.

When I asked Juan Miguel what sets the team apart, his answer was immediate: diverse experts working side by side. At Xanadu, domain experts gather from various fields and work with dedicated algorithm scientists to identify useful problems and figure out how to solve them. "Addressing applications can be a problem because each is its own universe," reflected Juan Miguel, "which is very hard to coordinate. You need to go deep enough to do meaningful work but not so deep that you slow down progress". This ethos is incorporated from the very beginning, with algorithm-focused candidates expected to be well-versed in applications and domain experts expected to have algorithmic know-how.

To Juan Miguel, the interplay between applications and algorithms is crucial and shockingly overlooked in the industry. He pointed to the example of the XPRIZE quantum applications challenge, which requires participants to "develop quantum algorithms ... designed to tackle complex problems", in which Xanadu is a finalist. He said many impressive algorithms were put forward but lacked a clear application, indicating a significant gap in how algorithms are being developed.

Building and maintaining a strong, coherent interdisciplinary team capable of addressing both is not easy. Juan Miguel describes himself as a bridge builder tasked with connecting people and subteams to balance breadth and depth. A battery chemist, for example, might care very deeply about achieving highly accurate X-ray absorption simulations, while a quantum algorithm scientist may be much more hung up on the cost of implementing the simulation algorithm itself.

Successfully balancing these worlds requires constant translation of domain-specific technical language, transfer of technical knowledge, and justification of often niche areas of interest. That effort is clearly paying off. Today, the Xanadu algorithms team is widely recognized for its leadership as an XPRIZE finalist and maintaining a steady drumbeat of vital technical outputs. These include halving the cost of QROM, advancing Trotter product formulas for quantum chemistry, and algorithms for simulating vibronic dynamics. As I combed through these outputs, though, I started to wonder where they all began.

"The process often starts with pure ideas," responded Juan Miguel when I asked him to elaborate on the life cycle of an algorithm, "with informal but promising ideas moving forward as either an application or algorithm". The Xanadu algorithms team has recently made efforts to formalize the development process, introducing a tiered approach to advancing and refining projects. "The goal is to create a filter," he said, that allows for team members to begin with free-form, creative inputs and selectively move forward with the most promising applications and algorithms. With each stage, projects are expected to meet more demanding metrics for performance, commercial value, and resource requirements. Having good ideas is one thing, but being able to rigorously advance and evaluate your outcomes is another.

In Juan Miguel's eyes, the capacity to carry out resource estimation is quintessential.

In his ideal world, everyone would integrate resource estimation into their algorithm development workflows and publication practices. This is something that Xanadu took an early bet on, with the time consuming nature of by-hand resource estimation becoming clear early in projects such as simulating battery materials using ionic pseudopotentials. Instead of running the risk of spending months repeatedly computing these figures, the Xanadu team developed resource estimation tools in PennyLane that target specific algorithmic components such as Trotter product formulas. This solidified resource estimation as an essential part of the algorithms workflow and has led to a continually growing expansion of PennyLane estimation tools.

Juan Miguel believes that the growing dossier of resource estimation aids is an indisputable sign that researchers should be adopting resource estimation as an integral part of algorithms development. "The tools exist," he emphasized, "it has never been easier to carry out resource estimations". He recalled instances of meeting with collaborators and being able to perform quick resource estimations to provide the receipts they needed to satisfy their questions. To him, this is the most obvious way to describe the performance of the state-of-the-art.

Historically, the quantum industry has been benchmarked by acronyms describing the scale and behaviour of quantum hardware (and associated algorithms). While the noisy intermediate-scale quantum (NISQ) era saw the development of devices with modest qubit counts and an acceptance of environmental sensitivity, the fault tolerant quantum computing (FTQC) era (where the bulk of serious research effort is now directed) will usher in larger scale, error resistant architectures.

"It doesn't matter what we call it," said Juan Miguel, "these acronyms are artificial walls".

His perspective is that upholding these pseudo-prescient titles introduces the risk of theory chasing hardware. Doing so forces us to set an upper bound on available resources for a given period of time. This introduces the risk that the so-called 'early FTQC' era will fall into the same habits of NISQ, which did well at delivering proof-of-concept devices but provided little in terms of commercial, useful devices.

To him, these labels are self-limiting. Rather than designing algorithms for different 'eras', it is more productive to figure out the requirements to solve valuable problems on quantum computers and use these as targets for hardware. This will avoid 'chasing hardware', which may stunt the development of theory as goals become narrowly focused on interfacing with specific devices. To put it bluntly, "algorithms are what point to the value of quantum computers".

It is best practice to forget the era, focus on the particular problem, and optimize as much as possible.

This pragmatic filter also dictates which problems Xanadu decides not to work on. I asked Juan Miguel his thoughts on the quantum approximate optimization (QAOA) algorithm, which Xanadu CEO Christian Weedbrook had recently discussed on LinkedIn. Juan Miguel agreed that it is not the most worthwhile pursuit for his team. "Optimization does not need to always be optimal," he pointed out, "it just needs to be good enough". This means that advantages in optimization algorithms often have to do with scale rather than complexity, which has yielded little evidence of the benefits of using quantum algorithms over classical.

As our conversation (and meeting room booking) rapidly approached its end, I used the final few minutes to ask Juan Miguel about his wishes for the field of algorithms research. "I wish more people did resource estimation by default to give me the cost of their algorithm." he began, "The stakes are too high and we need more people focusing on the resources that they are using". To emphasize these high stakes, he pointed to The Grand Challenge of Quantum Applications as a rallying cry for the field of quantum algorithms. In his eyes, the fact that we are gaining clarity on the prominent "pathways and critical obstacles" (as they are described in the paper) is a gift that emphasizes the importance of focused, quantifiable work toward solving some of the world's biggest problems.

In his ideal world, resource estimations would be front and center in every quantum algorithm published, making it easy for others to continue improving and comparing existing work.

"I also wish more people knew that we can simulate many properties of interest by reducing them to time-dynamics, not ground-state energies", he said. Simplifying systems to the ground state is a key in classical simulation. In quantum, Juan Miguel is confident we need not limit ourselves in the exact same way and should remain open to achieving desired outcomes in new, creative fashions.

The Xanadu algorithms team works at an intense intersection. Every day, the members of the algorithm team work to push ideas through a rigorous pipeline designed to allow only the most feasible, established, and useful ideas to make it through. In tandem with other teams such as architecture, software, and hardware, the idea of implementability and resource prioritization are always top of mind.

The challenges and goals that the field of quantum algorithms face are lofty. Maybe you can help! The Xanadu algorithms team uses PennyLane throughout their workflow and supports the creation and maintenance of public resources related to their work. For example, you can

• Explore applications that the algorithms team is currently prioritizing and actively developing,
• Check out the PennyLane demos that carry out resource estimation for Xanadu's XAS and vibronics algorithms,
• Keep your eyes on PennyLane Labs, which is constantly evolving to enable algorithmic research,

New quantum algorithms and applications are being proposed with increasing frequency. It just takes the right team to make them into something spectacular.

Think you have what it takes? See our open positions on the Xanadu algorithms team.