Quantum simulation is the original reason quantum computing was imagined, that is, using a controllable quantum system to understand natural quantum systems, molecules, materials and nuclei, which classical computers can only approximate.
It is also the application with the soundest theoretical advantage and the most concrete industrial use cases, from pharmaceuticals to new materials or new batteries. This guide covers the whole territory, from the difficulty that motivates it to the difference from quantum emulation, from the two families of simulators to the workflow with which a molecule is simulated, through to the competing classical methods and how everything is validated before spending on hardware, the terrain on which HumanQ already develops its emulation projects today.
What is quantum simulation?
Quantum simulation is the use of a well-controlled quantum system to reproduce the behaviour of another quantum system that we do not know how to calculate, such as the properties of a molecule, the dynamics of electrons in a solid or the phases of a magnetic material. The idea exploits an affinity of nature, because the simulator obeys the same laws as the simulated system, and therefore natively represents what a classical machine must encode at exponential cost. There are two embodiments, dedicated analogue simulators and algorithmic simulation on a universal quantum computer, both discussed below. The Wikipedia entry offers the historical background.
Why are quantum systems hard for classical computers?
The difficulty arises from the exponential growth of the state space, since describing exactly n interacting quantum particles requires a number of coefficients that doubles with every particle added.
Fifty spins exceed the memory of any supercomputer, while a pharmaceutical-sized molecule is out of the question.
Classical methods get around the obstacle with approximations, often excellent ones, but there are regimes, such as strong electron correlation and out-of-equilibrium dynamics, in which approximations fail systematically. This is exactly the boundary where quantum simulation promises its value, because it does not aim to replace computational chemistry where it works, but to unlock the problems where it today has to give up.
A quantitative estimate helps, since adding particles to an exact description multiplies the classical resources exponentially, whereas on a quantum simulator the cost grows linearly as the system size increases.
What is the difference between quantum simulation and quantum emulation?
The pair of terms generates constant confusion, and the distinction is the foundation of this site’s glossary. Quantum simulation reproduces nature, because its target is a physical system, a molecule or a lattice of spins. Quantum emulation, by contrast, reproduces the machine, since the target is the quantum processor itself, reconstructed on classical infrastructure to develop and test circuits.
The two activities fit together in a precise workflow, in which the circuit that will simulate the molecule is designed, verified and calibrated in emulation, where every quantity is inspectable, and only afterwards, if the problem requires it, run on real hardware. Simulating is the end, while emulating is the means by which one arrives prepared, and it is precisely on this means that HumanQ concentrates its projects, to keep the focus on what can be developed already today.
What are analogue and digital simulators?
The analogue simulator is a custom-built physical system, such as ultracold atoms in optical lattices, trapped ions or arrays of Rydberg atoms, whose parameters are tuned so that its Hamiltonian coincides with that of the system to be studied, after which it is prepared, left to evolve and measured. It is powerful and already operational on hundreds of particles, but rigid, since each platform simulates the family of models for which it was built. Digital simulation instead uses a universal processor, in which the evolution is broken down into gates, with full programmability and, in prospect, error correction, at the price of circuit depths that are very demanding today. The distinction mirrors that between analogue and digital computers in the twentieth century, and history suggests how things will settle.
How do you simulate a molecule?
The standard workflow has four steps.
- Hamiltonian. From the molecule, the electronic Hamiltonian is constructed in an orbital basis, an object of classical quantum chemistry.
- Mapping. Fermionic operators are translated into qubit operators with transformations such as Jordan-Wigner or Bravyi-Kitaev.
- Preparation and estimation. A parametric quantum circuit (called an ansatz) prepares a trial quantum state on the coprocessor. The machine then performs the measurements to estimate the expectation value of the energy, computing the individual terms of the mapped Hamiltonian.
- Optimisation. The measurement results are sent to a classical optimiser, which updates the circuit parameters to lower the energy. The process iterates in a feedback loop until it converges towards the ground state, following the VQE (Variational Quantum Eigensolver) algorithm described among the quantum algorithms.
On future machines, phase estimation will replace the variational loop with a direct and exact reading of the energy.
Which applications in pharmaceuticals and materials?
The most frequently cited applications, in order of concreteness, are three.
- Bonding chemistry and catalysis. Understanding active sites and reaction energies, with the emblematic case of nitrogenase and nitrogen fixation, today an industrial process with a very high energy cost.
- Pharmaceuticals. Binding affinities and conformations where electron correlation matters, in addition to, not in place of, existing computational pipelines.
- Materials. Batteries, cathodes and electrolytes, superconductors, quantum magnetism, etc.
The seriousness of the research imposes the timescale, since the systems that can be treated today are still immature, and the current value lies in building method and skills on reduced problems, so as to scale when the hardware does. The European programmes of the Quantum Flagship fund exactly this trajectory. A concrete indicator to follow is the size of the systems treated in leading publications, whose growth is steady, and the overtaking of classical methods will happen by degrees, problem by problem, not in a single event.
What did Feynman say and why is it still relevant?
In 1982, closing the conference that marked the birth of quantum computing, Richard Feynman observed that nature is not classical and that, to simulate it faithfully, a quantum machine is needed. It was not a provocation but a scientific manifesto: the aim is not simply to speed up existing algorithms, but to map reality onto an architecture that respects its intrinsic laws, avoiding the forced approximations of traditional computers.
Decades later this diagnosis remains unassailable. Quantum simulation is the application with the soundest theoretical justification in the whole sector: in this domain, the advantage does not depend on algorithmic conjectures or software shortcuts, but on the perfect structural correspondence between the physico-chemical problem and the emulation model.
Which classical methods compete?
Classical methods are formidable, highly evolved competitors, and every new architecture must measure itself against them before promising revolutions. The frontier of quantum emulation is in fact measured against baselines of excellence, and not against brute-force diagonalisation:
| Classical method | Strengths | Intrinsic limits |
|---|---|---|
| DFT (Density Functional Theory) | Excellent cost-to-accuracy ratio; dominates industrial computational chemistry. | Fails in regimes of strong electron correlation. |
| Tensor networks (e.g. DMRG) | Pinpoint precision on specific systems. | Limited to low-dimensional systems or those with low entanglement. |
| Quantum Monte Carlo | Covers broad families of complex models. | Stumbles on the ‘sign problem’ in frustrated fermionic systems. |
Every serious claim of superiority in simulation must declare which of these classical baselines it has surpassed and by what margin. This is a synergistic competition: the quantum challenge is pushing the classical algorithms themselves to extraordinary progress, to the benefit of computational research as a whole.
How is a simulation validated in emulation?
Validation in emulation is the acceptance test that separates a credible project from a demo, because the chain of approximations is checked link by link. The evolved state is compared with the exact solution on small instances, the discretisation error is measured as the step varies, the effect of noise is estimated by activating calibrated models, and the number of measurements and the circuit depth are sized. When the circuit reaches the hardware, every discrepancy thus already has an expected explanation. It is exactly the workflow for which HumanQ exists, where these validation projects are developed already today, without waiting for tomorrow’s hardware.
The Trotter-Suzuki decomposition
The time evolution e−iHt is approximated by breaking the Hamiltonian into simple terms and alternating them in short steps, the Trotter-Suzuki decomposition, with an error that can be controlled through the step length. In emulation the Trotter error is measured directly, by comparing the evolved state with the exact solution as the step varies, something impossible on real hardware where the state cannot be inspected.
When does it pay to invest in quantum simulation?
It pays to invest when three conditions meet.
- A documented limit. In the organisation’s problem portfolio there is chemistry or materials science where classical methods show documented, not generic, limits.
- A value that justifies it. The economic value of unlocking that limit justifies a multi-year programme, because that is what this is.
- The will to build in-house skills. Competitive advantage will lie in knowing how to pose the problems, not in access to hardware, which will be a commodity.
The recommended path starts small, with a reduced instance of the real problem, prototyped in emulation with a classical baseline alongside, within a quantum readiness project with clear exit metrics. And if the three conditions are not yet in place, the honest answer is to wait and monitor, because in quantum simulation arriving second with judgement costs less than arriving first without method.
Bring your molecule to the HumanQ platform in emulation
HumanQ develops quantum emulation projects applied to simulation, from the Hamiltonian to the circuit, from validation in emulation to comparison with the classical baseline, to build today what tomorrow’s hardware will run. Discover quantum emulation or contact the HumanQ team to assess your use case.