Self-Assessment Quiz: Quantum Simulation

Twenty questions on Hamiltonian simulation, Trotterization, encodings, and why simulation is the most defensible quantum application. Aim for 16+.

Question 1

Feynman's original motivation for quantum computers was:

A) Breaking cryptography B) Simulating quantum systems, which costs classical resources exponential in particle count C) Faster arithmetic D) Random number generation

Question 2

Simulating $n$ interacting spin-½ particles classically requires storing:

A) $n$ numbers B) $n^2$ C) $2^n$ complex amplitudes D) $n!$

Question 3

Quantum simulation is considered the most defensible application because:

A) It is easiest to implement B) The classical baseline is genuinely exponential, with no structure to exploit C) It needs fewest qubits D) It requires no error correction

Question 4

Time evolution under a Hamiltonian $H$ is:

A) $e^{-iHt}$ B) $Ht$ C) $H^t$ D) $e^{Ht}$

Question 5

Trotterization approximates $e^{-i(A+B)t}$ by:

A) $e^{-iAt}e^{-iBt}$ repeated in small steps B) $e^{-iABt}$ C) $A + B$ D) $e^{-iAt} + e^{-iBt}$

Question 6

The first-order Trotter error per step scales as:

A) $O(t)$ B) $O(t^2[A,B])$ C) $O(1)$ D) Zero

Question 7

Trotter error vanishes when:

A) $A$ and $B$ commute B) $t$ is large C) Never D) The system is classical

Question 8

Second-order (symmetric) Trotter formulas improve error to:

A) $O(t^2)$ B) $O(t^3)$ per step C) $O(t)$ D) No improvement

Question 9

The Jordan–Wigner transformation maps:

A) Fermionic operators to qubit operators B) Qubits to bits C) Bosons to fermions D) Hamiltonians to circuits

Question 10

A drawback of Jordan–Wigner is:

A) It is not exact B) It introduces long strings of $Z$ operators, raising gate cost C) It requires more qubits than orbitals D) It only works for 1D systems

Question 11

The Bravyi–Kitaev encoding improves on Jordan–Wigner by:

A) Reducing operator weight to $O(\log n)$ B) Using fewer qubits C) Eliminating the need for simulation D) Being classical

Question 12

Qubitization and LCU methods offer:

A) Better asymptotic scaling than Trotterization for many Hamiltonians B) Fewer qubits always C) Classical speedup D) Exact simulation with one gate

Question 13

A quantum simulation's output is typically:

A) The full wavefunction B) Expectation values of observables, or an energy via QPE C) All amplitudes D) A classical trajectory

Question 14

Analog quantum simulation differs from digital in that it:

A) Engineers a physical system to mimic the target Hamiltonian directly, without gates B) Uses analog electronics C) Is always less accurate D) Requires error correction

Question 15

The most cited near-term target for quantum simulation is:

A) Weather forecasting B) Molecular electronic structure and correlated materials C) Financial modelling D) Video rendering

Question 16

True or false: Quantum simulation gives exponential speedup for all physical systems.

Question 17

True or false: Classical methods like DMRG and quantum Monte Carlo are already exact for many systems.

Question 18

True or false: A quantum simulator gives you the full wavefunction to inspect.

Question 19

Short answer. Explain why simulation avoids the data-loading bottleneck that defeats many other proposed quantum speedups.

Question 20

Short answer. Why is the fermionic sign problem the specific reason quantum Monte Carlo fails where quantum simulation might succeed?

Answer Key