Questions: Quantum Circuits

Question 1

In a quantum circuit diagram, what does a vertical line connecting two qubits with a dot on one and a circle-plus on the other represent?

• A. A SWAP gate exchanging the two qubit states
• B. A CNOT gate with the dot as control and the circle-plus as target
• C. A measurement of both qubits in the Bell basis
• D. A classical conditional operation

Answer: (B)

The standard circuit notation uses a filled dot for the control qubit and a circle-plus (oplus symbol) for the target qubit of a CNOT gate. The vertical line shows that the gate couples the two qubits. If the control qubit is |1>, the target qubit gets flipped. A SWAP gate is typically drawn with two X symbols connected by a line.

Question 2

Quantum circuits must apply all gates sequentially — two gates on different qubits in the same time step would violate unitarity.

• T. True
• F. False

Answer: False

Gates on disjoint sets of qubits can be applied simultaneously — they act on independent subsystems and their combined effect is the tensor product of the individual gates, which is still unitary. This parallelism is why circuit depth (time steps) is a separate measure from total gate count. Minimizing depth is important because qubits decohere over time, so shallower circuits are more practical.

Question 3

Why is measurement typically placed at the end of a quantum circuit rather than interspersed throughout?

Model answer: Measurement collapses the qubit to a definite classical state, destroying the superposition and any entanglement involving that qubit. Once measured, a qubit can no longer participate in quantum interference. Deferring measurement to the end preserves quantum coherence throughout the computation. By the principle of deferred measurement, any mid-circuit measurement followed by classical control can be replaced by a quantum-controlled operation with measurement deferred to the end.

The principle of deferred measurement shows that mid-circuit measurement is never necessary for the final outcome distribution — it can always be postponed. This simplifies circuit analysis because you can reason entirely in terms of unitary evolution until the final measurement. In practice, some error correction schemes do use mid-circuit measurement, but the computational power is the same.