IBM A1000-128 Intermediate Practice Exam: Medium Difficulty 2025

A quantum developer is designing a circuit to prepare a Bell state |Φ+⟩ = (|00⟩ + |11⟩)/√2. After applying a Hadamard gate to qubit 0, which gate should be applied next to complete the entanglement?

Your organization is evaluating quantum computing for drug discovery simulations. The molecular system you need to simulate has 40 spin orbitals. Approximately how many qubits would be required using a direct mapping approach, and what is the primary challenge?

When using IBM Qiskit Runtime, a developer notices their variational quantum eigensolver (VQE) algorithm is taking longer than expected. Which optimization strategy would most directly reduce the total execution time?

A quantum circuit experiences significant decoherence after gate operations. If the T1 time (amplitude damping) is 100 μs and T2 time (dephasing) is 80 μs, and your circuit has a total gate execution time of 50 μs, what is the most appropriate strategy to improve circuit fidelity?

You are implementing Grover's algorithm to search an unstructured database of N=256 items. How many iterations of the Grover operator should be applied to maximize the probability of finding the target item?

An enterprise is developing a quantum application using IBM Quantum services. They need to test their algorithm on different backend configurations before deploying to real hardware. Which sequence of actions best represents the recommended development workflow?

A quantum system is described by a Hamiltonian with eigenvalues λ₁ = 2 and λ₂ = 5. Using the Quantum Phase Estimation algorithm with 3 precision qubits, what phase values would be detected for these eigenvalues after the quantum Fourier transform?

In the context of quantum error correction, why is a minimum of 5 physical qubits required for the smallest error-correcting code (the [[5,1,3]] code)?

A financial services company wants to use quantum computing for portfolio optimization with 50 assets and multiple constraints. Their problem requires finding the minimum of a quadratic function. Which quantum approach is most suitable for this near-term NISQ application?

When transpiling a quantum circuit for IBM quantum hardware, the transpiler converts your circuit to use only the native gate set. If a backend supports CX, ID, RZ, SX, and X as native gates, what happens when your circuit contains a CNOT and a Hadamard gate?