IBM A1000-099: Assessment: Foundations of Quantum Computing Advanced Practice Exam: Hard Questions 2025

A quantum algorithm requires maintaining coherence across 50 qubits for 100 microseconds to complete its computation. The available quantum processor has a T2 coherence time of 75 microseconds and average gate time of 50 nanoseconds. Error mitigation shows a 0.1% error rate per two-qubit gate. When implementing a circuit with 200 two-qubit gates and 150 single-qubit gates, what is the PRIMARY limiting factor for successful execution?

During the implementation of a variational quantum eigensolver (VQE) for a molecular Hamiltonian, you observe that the optimization landscape has numerous local minima causing convergence issues. The circuit depth is 40 gates with 12 qubits. Which combination of strategies would MOST effectively address this challenge while maintaining quantum advantage?

You are designing a quantum circuit that applies a controlled-U³(θ, φ, λ) gate where U³ represents an arbitrary single-qubit rotation. The target quantum processor only natively supports CNOT, RZ, and SX (√X) gates. What is the MINIMUM number of CNOT gates required to decompose this controlled-U³ operation?

A quantum error correction implementation using the [[7,1,3]] Steane code encounters a scenario where syndrome measurement indicates errors on qubits 2, 4, and 6. Given that the code can correct any single-qubit error and detect certain two-qubit errors, what should be the CORRECT interpretation and recovery action?

When implementing Grover's algorithm to search an unstructured database of N=2^20 elements on IBM Quantum hardware with realistic noise levels (gate fidelity ~99.5% for single-qubit, ~99% for two-qubit), you observe decreasing success probability after the theoretical optimal number of iterations. What phenomenon explains this behavior and what is the BEST mitigation strategy?

You are optimizing a quantum circuit for execution on IBM Quantum's heavy-hex topology. The circuit requires implementing a 5-qubit chain of CNOT gates (q0→q1→q2→q3→q4) where qubits 0 and 4 are not directly connected on the coupling map. The transpiler produces a circuit with 15 additional SWAP gates. Using manual optimization, what approach would yield the LOWEST gate count while maintaining circuit functionality?

In a quantum phase estimation (QPE) algorithm implementation for finding eigenvalues of a 4×4 unitary matrix with 8-bit precision, you observe that the inverse quantum Fourier transform (QFT) is consuming 60% of the total circuit depth. Which optimization technique would provide the MOST significant depth reduction while maintaining algorithmic accuracy?

A quantum chemistry simulation using the Jordan-Wigner transformation maps a fermionic Hamiltonian with 20 spin-orbitals to a qubit Hamiltonian. When implementing time evolution using Trotterization, you need to choose between first-order Trotter with 100 steps or second-order Trotter with 40 steps for the same target accuracy. Considering both algorithmic error and hardware noise with two-qubit gate error rate of 0.5%, which approach is PREFERABLE and why?

You are using Qiskit Runtime to execute a variational algorithm with 500 iterations on IBM Quantum hardware. The classical optimizer requires access to expectation values after each circuit execution. Network latency between your classical system and the quantum backend is 150ms per round-trip. What architectural pattern would MINIMIZE total execution time?

When implementing a quantum circuit that prepares an equal superposition of all computational basis states except |000⟩ and |111⟩ on a 3-qubit system, you need to determine the optimal gate sequence. Which approach requires the FEWEST two-qubit gates while achieving exact preparation?