Extended answer

I have been thinking a bit more about this, and here are three somewhat loose thoughts, which I think are ultimately related.

**1. Nature as computation**

It seems to me that Nature might be inherently computational, rather than merely describable through computation. Our most fundamental understanding of quantum mechanics already lends itself to this interpretation: the path-integral formulation describes physical evolution through a sum over all possible histories, with interference determined by their phases. Perhaps this is not just a mathematical trick for describing something more fundamental, but a glimpse of what physical reality actually is: a continuous process of computation.

Of course, this does not imply that Nature literally enumerates all possible paths like a classical computer. Rather, the physical evolution itself is the computation, and the path integral is one of several mathematical languages we have invented to describe it.

What I find particularly interesting is that we may never be able to “break this spell.” Every deeper physical law we discover could itself be understood as another description of an underlying computational process. Even an analytical solution would simply be a compact human representation of that process, not necessarily something more fundamental than the computation itself.

Too often, it feels like we regard computation as an approximation of Nature’s more fundamental analytical laws. But perhaps we have this hierarchy backwards. Perhaps the analytical laws are our approximations, abstractions, or compressions of an inherently computational reality. Classical mechanics, for example, emerges in suitable limits of quantum mechanics, and many of its elegant analytical solutions may be understood as special cases in which an otherwise enormously complex physical evolution admits a remarkably simple description.

In this perspective, the limitations of computational physics are not necessarily limitations of computation as such, but of the particular finite representations and architectures we use. Nature does not need to store a wavefunction in memory, discretize space, truncate a basis set, or numerically evaluate a path integral. It simply carries out the computation using what seems to be infinite resources (this is untenable to many, I can agree). Perhaps what we call the laws of physics are ultimately our attempts to discover the computational structure of that evolution.

**2. Theory as a language of concepts**

Our own brains and social constructs have created certain segregations of concepts, which causes us to invent “theory” as an additional carrier of information.

It is quite plausible that an alien species would have a very different conceptual basis for describing exactly the same physical reality. They might, for instance, treat chirality, topological invariants, or certain structures on a lattice as much more fundamental concepts than we do. They might start from symmetries, information, or relationships between objects, rather than from particles, forces, and trajectories.

Pushing things up or down on the high-level versus low-level concept spectrum creates a new theoretical language. A concept we consider emergent might be treated as fundamental in another formulation, while something we regard as fundamental might become a derived property.

Feynman has an interesting observation along these lines: the same physical laws can often be formulated in radically different mathematical languages. Newtonian mechanics, Lagrangian mechanics, and the principle of least action are examples of different routes to the same physical predictions.

So in a way, theory is partly a social construct. Not because physical reality is subjective, or because every theory is equally valid, but because the concepts, abstractions, and hierarchies we choose to describe it are ours. Nature does not necessarily privilege one of these representations.

This also makes the distinction between theoretical and computational physics rather interesting. If a theoretical framework is a compact, human-chosen representation of physical relationships, and a simulation explores the consequences of those relationships, then the two are not fundamentally separate intellectual activities. They are different ways of extracting and organizing information about Nature.

**3. Quantum computing and ab initio materials science**

Lastly, I want to stop and think about the importance of quantum computing in materials design and computational quantum chemistry.

Currently, methods such as Density Functional Theory (DFT) start from quantum mechanics but introduce a computationally manageable representation of a many-electron system. DFT is exact in principle for ground-state properties, but in practical calculations we have to approximate the exchange-correlation functional, and usually introduce further approximations through basis sets, numerical discretization, and other modeling choices.

We do this largely because representing the full quantum many-body wavefunction becomes prohibitively expensive on classical computers as the system grows.

Quantum algorithms are interesting here, although I think the more fascinating idea is the possibility of using *Nature itself* to perform the calculations.

Rather than representing a quantum system through an exponentially large collection of classical numbers, we might construct another physical quantum system whose states and interactions encode the system we want to study.

This is particularly clear in analog quantum simulation, where a controllable quantum system is engineered to reproduce a target Hamiltonian. Digital quantum computers offer another route, using algorithms such as quantum phase estimation to extract energies and other properties of a simulated quantum system.

In either case, we are exploiting physical quantum evolution itself rather than explicitly calculating every amplitude on a classical machine. We are effectively allowing one piece of Nature to reproduce the behavior of another.

Of course, this does not mean that we can simply perform an infinite path integral without approximation. We still need to encode the appropriate Hamiltonian, prepare the relevant quantum states, control errors, and extract information through measurements. Nor does quantum computing automatically eliminate the approximations made in DFT; in many cases, it would instead allow us to solve the underlying many-body problem using a different representation, potentially avoiding the need for an approximate exchange-correlation functional.

But the conceptual shift is remarkable. Instead of asking how accurately a finite classical calculation can reproduce quantum behavior, we ask whether a controllable quantum system can directly embody the physics we wish to investigate.

If this becomes practical at scale, it could radically change which materials problems are computationally accessible, particularly strongly correlated electron systems and quantum chemistry problems where classical approximations become unreliable.

**Bringing these thoughts together**

This brings me back to the original statement: “Quantum-based materials calculations are a simulation activity, not a theoretical activity.”

I think there is a good argument for calling them simulation activities insofar as we start from an existing theoretical framework and computationally investigate its consequences for a particular material. We are not necessarily developing new physical laws; we are exploring what those laws imply for systems too complicated to solve analytically.

But I am reluctant to draw a strict boundary. An *ab initio* calculation is an application of theory, a simulation of a physical system, and potentially a source of new theoretical understanding, all at once.

Perhaps the distinction is less about what Nature is doing and more about how we choose to organize our attempts to understand it.