IBM A1000-136 Advanced Practice Exam: Hard Questions 2025

A team claims their 2-qubit circuit creates a Bell state, but the histogram from Z-basis measurements shows ~50% |00⟩ and ~50% |11⟩, identical to what a classical correlated mixture could produce. They must demonstrate genuine entanglement using only local measurement basis changes and repeated shots (no full tomography requirement). Which approach is the most appropriate to verify entanglement on IBM Quantum hardware?

You have a 3-qubit circuit where the algorithm critically depends on a phase kickback. The team suspects that an added measurement in the middle of the circuit “shouldn’t matter” because they are not using the measured qubit later as a control. On hardware, results change drastically compared to simulation without mid-circuit measurement. What is the best explanation for the discrepancy?

A developer implements Grover’s algorithm for a small search space and uses a diffusion operator. They observe that increasing the number of Grover iterations beyond a certain point reduces the probability of measuring the marked item, even on an ideal simulator. They suspect a bug, but the oracle is correct. What is the most accurate explanation?

You are optimizing a circuit for execution on a real IBM backend. Two candidate implementations of a 2-qubit entangling step are available: (1) a single native entangling gate (as supported by the backend) with surrounding single-qubit rotations, or (2) a decomposition into multiple CNOTs because it matches a textbook circuit. Which choice is generally the best practice for reducing error, and why?

A Qiskit user submits a circuit to hardware and notices unexpectedly low success probability. They suspect the transpiler mapped their logical qubits to a poor physical layout. They want to reduce SWAP insertion and two-qubit depth without manually rewriting the circuit. Which action is most appropriate?

A team runs a variational algorithm (VQE-like) and gets unstable energy estimates across repeated executions on hardware. They already fixed the random seed in their classical optimizer and use the same circuit. They want a mitigation strategy that targets readout bias without changing the ansatz. What is the best next step?

A user compares two simulators: an ideal statevector simulator and a noisy simulator that models gate and readout errors. Their circuit’s success probability is high on the ideal simulator, moderate on the noisy simulator, and very low on hardware. Which is the most defensible conclusion and next diagnostic step?

You need to estimate ⟨P⟩ for many Pauli strings P in a chemistry Hamiltonian. Running each Pauli term with separate circuits is too costly on hardware. You are allowed to insert only single-qubit basis-change gates before measurement. Which strategy provides the best reduction in circuit executions while remaining correct?

A circuit uses a controlled operation where the control qubit is in superposition. A developer replaces the controlled-U with: measure the control, classically apply U if the measurement is 1, then continue. They argue this is equivalent because it applies U conditionally. In which case is this replacement valid without changing the computation’s outcome distribution?

A developer uses Qiskit’s transpilation and notices the compiled circuit has more two-qubit gates than the original. The circuit includes several single-qubit rotations interleaved with CNOTs. They want to reduce two-qubit count while keeping functionality. Which refactoring most often enables the transpiler to cancel or commute gates to reduce entangling operations?