Questions: Quantum Chemistry Simulation

Question 1

Why is quantum chemistry a promising application for near-term quantum computers despite NISQ-era hardware limitations?

Model answer: Quantum chemistry requires exponential classical resources but maps naturally to quantum computers: electrons are quantum particles, and molecular Hamiltonians can be directly encoded. The advantage is fundamental (exponential), not algorithmic luck. Second, chemical accuracy (< 1 kcal/mol) is achievable with moderate precision; small errors in quantum simulation still yield useful results. Third, VQE uses shallow circuits (variational ansatze) compatible with noisy hardware. Finally, there are clear near-term applications (drug discovery, materials science) with significant economic value, motivating investment in error correction and scaling.

Quantum chemistry benefits from a fundamental exponential advantage and is relatively forgiving of errors compared to other quantum algorithms. This makes it the highest-priority near-term quantum application.

Question 2

The Jordan-Wigner transformation maps fermionic operators to Pauli strings. How many qubits are needed to simulate an N-electron system?

• A. O(log N) qubits
• B. O(N) qubits
• C. O(N^2) qubits
• D. N qubits (one per electron, infeasible for large N)

Answer: (B)

The Jordan-Wigner transformation requires O(N) qubits to represent N spin-orbitals (electrons + constraints). Each spin-orbital maps to one qubit. For a molecule with 2N electrons in N spin-orbitals, you need N qubits. This is efficient compared to the classical Hilbert space (2^N), but still challenging for large molecules: simulating a 100-qubit molecule requires 100 logical qubits (or more with error correction). This is a major bottleneck for practical quantum chemistry.