IBM A1000-128 Advanced Practice Exam: Hard Questions 2025

A quantum algorithm requires implementing a controlled-rotation gate with an angle θ that depends on the measurement outcome of an ancilla qubit in a mid-circuit measurement. The circuit must maintain coherence for subsequent operations. Which approach best addresses the hardware constraints of current IBM Quantum systems while preserving the algorithmic requirements?

An organization is designing a variational quantum eigensolver (VQE) to find the ground state energy of a molecular Hamiltonian with 12 qubits. After initial runs, they observe that the optimization converges to different local minima despite using identical initial parameters. The cost function exhibits barren plateaus in certain regions. What is the most effective strategy to mitigate this issue?

A quantum circuit designed for a 127-qubit IBM Quantum processor needs to implement a global entangling operation across all qubits, but the native connectivity graph is a heavy-hexagon lattice with limited qubit connections. The circuit must minimize SWAP gate overhead while maintaining circuit depth below the coherence limit. What is the optimal compilation strategy?

During execution of a quantum phase estimation (QPE) algorithm on IBM Quantum hardware, you observe that the measured phase has systematic bias errors that scale with the number of controlled-unitary operations. Readout error mitigation and gate error mitigation have been applied, but accuracy remains insufficient. Analysis shows that two-qubit gate fidelities vary significantly across different qubit pairs. What advanced mitigation strategy would most effectively address this issue?

A research team is implementing Grover's algorithm to search an unstructured database of 2^20 entries using amplitude amplification. They plan to use multiple IBM Quantum processors in parallel, each handling a subset of the search space. However, they must account for the fact that real quantum hardware introduces noise that degrades the amplitude amplification effect. What is the critical consideration for determining the optimal number of Grover iterations?

An enterprise application requires simulating a quantum circuit classically using Qiskit before deploying to hardware. The circuit has 35 qubits with a depth of 150 gates, including multi-qubit entangling operations. The simulation repeatedly fails due to memory constraints on available classical infrastructure. What is the most effective approach to obtain meaningful simulation results?

A quantum machine learning application uses a parameterized quantum circuit (PQC) as a feature map for classification. During training, the researchers notice that the quantum kernel matrix becomes nearly identity-like, resulting in poor classification performance. The circuit uses a hardware-efficient ansatz with depth 10 and includes RY and RZ rotation gates parameterized by classical data. What is the most likely root cause and solution?

A financial institution is evaluating quantum computing for portfolio optimization using QAOA (Quantum Approximate Optimization Algorithm). The problem involves 100 assets with various constraints, requiring approximately 150 qubits when encoded. Current IBM Quantum systems have up to 127 qubits available. The deadline for demonstrating quantum advantage is 18 months. What is the most realistic and technically sound strategy?

While debugging a complex quantum circuit on IBM Quantum hardware, you observe that certain measurement outcomes appear with higher probability than expected from simulation, specifically for states where multiple qubits are in the |1⟩ state. The effect is more pronounced for qubits with higher indices in the processor topology. After checking basic errors, you suspect crosstalk. What diagnostic approach would best confirm and characterize this hypothesis?

A quantum chemistry application requires computing the expectation value of a molecular Hamiltonian that consists of 500 Pauli terms. Executing each term as a separate circuit would require 500 circuit executions. The research team needs to optimize this to work within a limited allocation of quantum computing time. What strategy would provide the most significant reduction in required circuit executions while maintaining accuracy?