Author:Dr. Ossi Niemimäki

QUANTUM COMPUTING
-️ August 2, 2022

Quantum mechanics has been a hot topic for quite some time now. To be fair, how could it not with the bizarre physical principles and the immense possibilities it provides in computations.

Through the lens of one of our quantum mathematicians, Dr. Ossi Niemimäki, this article takes a standpoint on what it means to understand quantum mechanics and why we don’t need to do so — at least in the sense that you might think.

It was 120 years ago when the word quantum in its current meaning first started appearing in scientific publications. The crucial observation at the time was that physical properties such as energy were not mapping out a continuous space but, in fact, jumping around in discrete packets.

This and many other counterintuitive observations later becoming part of quantum mechanics puzzled scientists at the time. As such, the theories of “quanta” were met with a fair share of resistance in the community. Contradictions with the existing classical models were a topic for much debate.

Little by little, however, different approaches were developed to successfully account for these phenomena. Some of these, such as the foundational ideas of Heisenberg and Schrödinger, are still taught as part of the standard introduction to quantum mechanics.

In essence, these developments were driven by two goals. First, to make sense of the observations and to be able to construct reasonable predictions that could be further tested. Second, to better understand the overall structure of this new confounding physics.

Above all, these considerations were practical.

Aside from these, a third question began to emerge: what to make out of the conceptual challenge posed by the quantum perspective of Nature? We’ll get back to this head-scratcher in a moment.

There is one particular aspect in the arising new physics that would significantly impact the whole science: heavy reliance on abstract mathematics.

Old masters such as Newton, Huygens, and Maxwell had already made great use of mathematics in constructing physical theories. Still, it was quantum mechanics that really began connecting these two fields in an unprecedented way.

As the dynamics of quantum mechanics were being written, physicists needed to come to terms with concepts like Hilbert spaces, linear transformations, and noncommutative algebra: stuff that every aspiring quantum computer scientist needs to learn to this day.

Despite being an apparent dive into the abstract, this helped pull back the curtain of mysticism and made the quantum world more approachable.

Partly this was also an answer to that third question of the foundations. Through the abstraction, we may have a logical path but can still be confused with questions such as: What even is matter? What is information? How do we line these fine quantum states with the reality we see? (In our experience, books on a table are not entangled or in any fluctuating energy state, they just are.)

The problem here is one of perspective. The mathematics of the quanta gives us tools that work: they give concrete and precise answers to questions that can be tested. So why not put the question the other way around: why shouldn't Nature work this way? After all, the logic checks out, and we can verify it to a level of atom-splitting accuracy. It’s only us and our limited human perspective that brings in the confusion.

We have the mathematical structure and models that allow us to make predictions. As long as the rules we abide by are logical and coherent, we can disregard the discomfort of trying to wrap our human minds around the apparent unintuitiveness of our universe.

Even brilliant thinkers such as Einstein took issues with what he felt was unintuitive or incomplete in quantum mechanics, perhaps most concretely in the seemingly paradoxical concept of quantum entanglement. And yet, today, we exploit this entanglement directly with quantum computers. Incidentally, the famous entanglement paper (Einstein-Podolsky-Rosen, 1935) is now also the most cited of his works: confusion can be great fuel for new discoveries!

While philosophy - especially in the Socratic sense - is often good for you, let mathematics do its magic here. We can set our own intuition, or rather, the lack thereof aside, and rely on these well-tested theories to predict and guide our way through the mysterious way the universe presents itself.

By accepting the fact that, apparently, this is how physics works at the core level, we can stop pondering why and begin putting reality itself into use.

That is precisely what has been happening in the last few decades, with quantum computers being heavily researched and developed.

There are similarities between the story of quantum mechanics and quantum computing: how everything started from a simple idea of understanding some observations better and how new mathematical thinking was needed.

In quantum computing, we have moved from the desire to simulate purely quantum systems to concretely manipulating quantum states as an answer to a wide array of different problems.

What started as a conceptual dream of theoretical physicists has become an engineering and business venture. The arising mathematics here - perhaps - is that of applied category theory, in its promise of translating problems from vastly different areas of study into one another.

Or maybe it will be something completely different and new: while we can guess, we are too close to it, as were the budding quantum physicists back in the 1920s. What we can do is to make the best out of what’s available to us and try not to resist the change.

We are doing our fair share of this exploration here at Quanscient by developing quantum algorithms for electromagnetics, CFD, and mechanics simulations. We don’t see the books on the table becoming entangled, and yet - perhaps with some help from those books - we can very concretely see what effects quantum entanglement can have on our simulation algorithms.

While the macroscale world we are mapping may not reveal itself to be anything like quantum to our eyes, we can greatly benefit from being able to manipulate things deep down beneath the surface of our reality.