The reason we can't accurately simulate molecules on classical computers is that they perform quantum calculations. What changes when we use quantum hardware?
📖 Read more: Quantum Security for Banks: The Race Before Q-Day
🧪 Why Classical Computers Can’t “See” Molecules
Chemistry, at its core, is quantum physics. Every molecule consists of nuclei and electrons that obey the Schrödinger equation. But solving it exactly is only feasible for the simplest system — the isolated hydrogen atom. As soon as a second electron is added, the complexity explodes.
The reason is Hilbert space: the mathematical “space” where a quantum system's wave function lives grows exponentially with the number of particles. According to estimates, a system of just 30 particles requires so many memory resources that even the most powerful supercomputers cannot handle them. For a pharmaceutical molecule with hundreds of electrons, the situation is a dead end.
Classical computational chemistry addresses this problem through approximations. The Hartree-Fock method, developed at MIT in the 1950s, treats each electron as if it moves in an average field — ignoring the detailed interaction between electrons. Density Functional Theory (DFT), which won the 1998 Nobel Prize in Chemistry for Walter Kohn and John Pople, typically scales as O(N³). But the most accurate method, CCSD(T), scales as O(M⁷), limiting its use to molecules with fewer than 25 atoms.
We don’t lack theory — we lack the computational power to apply it to complex molecules.
💡 Feynman’s Idea: “Use Quantum Systems”
The idea that nature “runs” quantum calculations is not new. Yuri Manin first formulated it in 1980 in his book Computable and Noncomputable, and Richard Feynman independently in 1982 in his landmark paper “Simulating Physics with Computers” in the International Journal of Theoretical Physics. Their logic was simple: if nature operates quantum-mechanically, then only a quantum system can simulate it efficiently.
Seth Lloyd proved theoretically in 1996 in Science that a “universal quantum simulator” can reproduce the evolution of any quantum system using a number of qubits proportional to the number of particles — instead of the exponential number of bits required by a classical computer. This was theoretically revolutionary, but practical implementation took decades.
⚙️ How Quantum Chemical Simulation Works
The basic idea is remarkably elegant. Instead of representing a molecule's electrons as numbers in classical memory (bits), we “map” them onto qubits — quantum bits that can exist in superposition and become entangled with each other. The mathematical Jordan-Wigner or Bravyi-Kitaev transformations convert a molecule's Hamiltonian into tensor products of Pauli matrices, expressions that a quantum circuit can “run.”
The most popular algorithm today is the Variational Quantum Eigensolver (VQE), proposed in 2014 by Alberto Peruzzo, Alán Aspuru-Guzik, and Jeremy O'Brien. The VQE is hybrid: a quantum processor prepares a trial wave function (ansatz) and measures its energy, while a classical computer optimizes parameters via gradient descent. The process repeats until the ground state is found — the state of minimum energy of the molecule.
• 2014: First simulation of HeH⁺ (helium hydride) on a photonic quantum processor
• 2017: Kandala's team (IBM) simulates BeH₂ (beryllium hydride) with hardware-efficient VQE
• 2020: Google uses Sycamore (12 qubits) for Hartree-Fock simulation of the H₁₂ chain
💊 From Small Molecules to Drugs
The promise is enormous. Today, developing a new drug costs an average of $2.6 billion and takes 10-15 years. A large portion of that cost is devoted to experimentally testing candidate molecules that ultimately fail. If we could accurately simulate how a molecule interacts with a target protein, we would eliminate countless dead ends.
Computational chemistry is already used extensively in the pharmaceutical industry. Databases like ChEMBL and DrugBank store millions of experimental data points, while DFT methods are used daily to calculate HOMO/LUMO energies and molecular orbitals of drug candidates. But the accuracy of these methods remains limited — the “chemical accuracy” (1 kcal/mol or 4 kJ/mol) needed for realistic predictions often isn't achieved for large molecules.
A “holy grail” here is FeMoco — the iron-molybdenum cofactor of the nitrogenase enzyme, which catalyzes the fixation of atmospheric nitrogen into ammonia. Industrial ammonia synthesis (the Haber-Bosch process) consumes 1-2% of global energy. If we understand how nitrogenase achieves this at room temperature, we could design catalysts that save enormous amounts of energy. But FeMoco contains a transition metal complex — exactly the kind of system where classical methods fail.
⚖️ The Great Debate: Are We Close Enough?
This is where the real tension in the field lies. Today's quantum computers belong to the NISQ (Noisy Intermediate-Scale Quantum) era — they have tens or hundreds of qubits, but with significant noise and errors. The VQE, while theoretically promising, faces serious practical obstacles.
A central problem is "barren plateaus": as the number of qubits increases, the gradient of the cost function tends toward zero, making optimization extremely difficult. The algorithm can get stuck in suboptimal solutions without being able to “see” where the real ground state is.
On the other hand, proponents emphasize that progress is exponential. In 2014, the best demonstration was a two-atom molecule (HeH⁺). In just six years, Google simulated a 12-atom hydrogen chain. The development of error mitigation techniques, combined with noise reduction in qubits, promises chemically relevant simulations within the next decade.
Quantum chemistry won’t replace laboratories tomorrow. But it may radically change how we discover drugs — if we overcome the technological barriers.
The 2013 Nobel Prize in Chemistry (Martin Karplus, Michael Levitt, Arieh Warshel) recognized multiscale models combining quantum mechanics with classical mechanics (QM/MM) for large biomolecular systems. Quantum computational chemistry represents the next step: exclusively quantum methods without classical approximations in the chemical part.
The clash of views remains open. Some academics believe the pharmaceutical application is decades away — quantum computers must first demonstrate “quantum advantage” on chemical problems that the best classical algorithm cannot solve. Others believe that even today's NISQ technology can provide useful results on targeted problems, paving the way for pharmaceutical discoveries that currently seem impossible.