IBM A1000-113 Advanced Practice Exam: Hard Questions 2025

You are implementing a variational quantum eigensolver (VQE) to find the ground state energy of a molecular Hamiltonian. After multiple iterations, you observe that the energy converges to a value significantly higher than the theoretical ground state, and the optimization landscape shows multiple local minima. Which combination of strategies would MOST effectively address this issue?

When designing a quantum circuit for execution on IBM Quantum hardware with limited qubit connectivity, you need to implement a circuit requiring connectivity between qubits q0 and q4, but the coupling map only allows direct connections through intermediate qubits. The transpiler inserts multiple SWAP gates, significantly increasing circuit depth from 10 to 45 gates. What is the MOST effective approach to minimize the impact on circuit fidelity?

You observe that a quantum circuit executing Grover's algorithm on a 5-qubit system returns the correct answer with probability 0.45 instead of the theoretical 0.95. Analysis shows T1 and T2 times of 100μs and 80μs respectively, and the circuit has a total execution time of 25μs with 120 gates. Which error source is MOST likely the dominant factor, and what mitigation strategy would be most effective?

A quantum phase estimation (QPE) algorithm requires 8 ancilla qubits to achieve the desired precision for eigenvalue estimation. However, the available quantum processor has only 27 qubits with an average two-qubit gate error of 0.8%. You need to balance precision requirements against hardware constraints. What architectural decision provides the BEST trade-off?

When implementing a quantum circuit in Qiskit, you discover that the QuantumCircuit.decompose() method applied to a complex custom gate results in a decomposition with significantly different unitary behavior compared to the original gate definition. The original gate was defined using a custom matrix with small numerical errors (order 10^-15). What is the MOST likely root cause and solution?

You are analyzing the performance of a Quantum Approximate Optimization Algorithm (QAOA) for a Max-Cut problem on a graph with 12 nodes. After 200 iterations with p=3 layers, the approximation ratio plateaus at 0.72 despite theoretical predictions suggesting 0.85+ for this problem size. Circuit analysis shows good gate fidelities and proper parameter initialization. What is the MOST likely explanation for the performance gap?

A quantum state tomography experiment on a 3-qubit system requires measuring the expectation values of 4^3 = 64 Pauli operators. Due to quantum processor scheduling constraints, you have limited shot budget and execution time. The target state has known structure with only 8 significant density matrix elements. How should you optimize the measurement strategy?

When executing a circuit with mid-circuit measurements and conditional operations on IBM Quantum hardware, you observe that jobs fail with errors related to dynamic circuit constraints. The circuit measures 3 qubits at depth 50, applies classical conditionals based on measurement outcomes, and continues with 30 more quantum gates. What is the MOST likely constraint violation?

You are implementing a quantum error mitigation strategy that combines zero-noise extrapolation (ZNE) with probabilistic error cancellation (PEC). After applying both techniques, the computational overhead increases by 50x and the final results show higher variance than using ZNE alone. What is the BEST explanation and corrective action?

A research team implements a quantum Fourier transform (QFT) circuit on 10 qubits and observes that the output distribution has high overlap with the expected result for the first 6 frequency components, but significant deviations in the higher-frequency components. The circuit uses 45 controlled-phase gates with average fidelity 98.5%. What phenomenon BEST explains this pattern?