IBM A1000-088 - Assessment: Foundations of Quantum Computing Advanced Practice Exam: Hard Questions 2025

A quantum algorithm requires implementing a controlled-U³ gate where U is a single-qubit rotation. Due to hardware limitations, your quantum processor only supports native gates: CNOT, single-qubit rotations (Rx, Ry, Rz), and measurements. The circuit depth must be minimized to reduce decoherence effects. What is the most efficient decomposition strategy?

You are implementing Grover's algorithm on IBM Quantum hardware to search an unstructured database of N=256 elements. After running the circuit, you observe that the success probability is only 65% instead of the theoretical 95%+. Your circuit uses approximately 100 two-qubit gates. Which combination of factors is MOST likely causing this degradation?

A research team is designing a variational quantum eigensolver (VQE) to find the ground state energy of a 12-qubit molecular Hamiltonian with 1,847 Pauli terms. The team observes that convergence is extremely slow and the optimizer frequently gets stuck in local minima. They are using 15 layers of hardware-efficient ansatz with 180 parameters. What architectural modification would provide the MOST significant improvement?

When using Qiskit Runtime on IBM Quantum Platform, you need to execute a parameterized circuit 50,000 times with different parameter values as part of an optimization loop. The circuit has 10 parameters that change each iteration based on classical optimizer feedback. Which approach minimizes both total execution time and cost?

You are analyzing the T1 and T2 coherence times of qubits on an IBM Quantum processor before running a critical quantum simulation. Qubit 5 shows T1=120μs and T2=85μs, while Qubit 12 shows T1=95μs and T2=110μs. Your circuit requires these qubits to maintain coherence for approximately 80μs. How should you interpret these measurements and adjust your circuit design?

A quantum circuit implements the Quantum Fourier Transform (QFT) on 8 qubits as part of Shor's algorithm. The circuit topology of the target IBM Quantum processor has limited connectivity with coupling map forming a linear chain. The QFT requires controlled phase rotations between all qubit pairs. What is the theoretical minimum number of SWAP gates required to execute this circuit on the linear topology while maintaining algorithmic correctness?

During quantum phase estimation (QPE) to estimate eigenvalues of a 5-qubit unitary operator U, you allocate 8 counting qubits for precision. After running the circuit, you observe that certain eigenvalue estimates appear at wrong bit positions (e.g., eigenvalue φ=0.375 appears as 0.750). The oracle implementation is verified correct. What is the MOST likely root cause and solution?

Your organization is evaluating whether to use quantum annealing versus gate-based quantum computing for a portfolio optimization problem with 200 assets and quadratic constraints. The problem can be formulated as a QUBO with approximately 20,000 interactions. Which technical consideration should MOST heavily influence this architectural decision?

You are implementing error mitigation for a 15-qubit quantum circuit using probabilistic error cancellation (PEC). After characterizing the noise, you find that implementing PEC requires sampling from a quasi-probability distribution with negativity ν=45. Your circuit originally required 10,000 shots for acceptable statistics. How does PEC fundamentally impact your execution requirements?

A team is using Qiskit to simulate a 20-qubit quantum circuit on classical hardware for validation before running on real quantum hardware. The circuit has depth 150 with approximately 300 two-qubit gates. Using the default statevector simulator with full state vector storage, the simulation fails with out-of-memory errors on a system with 64 GB RAM. Which combination of approaches would enable successful simulation while maintaining reasonable accuracy?