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A1: Generate State −∣0⟩- \ket{0}

Time Limit: 3 seconds

Memory Limit: 512 MiB

Score: 100 points

Writer:ST12

Editorial

Quantum computers use the concept of "quantum gates" to manipulate the state of qubits.

In this problem, you can transition from the zero state ∣0⟩\ket{0} to the state −∣0⟩ - \ket{0} using the XX and ZZ gates.

First, apply the XX gate to the quantum state ∣0⟩\ket{0} to transition it to the quantum state ∣1⟩\ket{1}.

∣0⟩→X(0)∣1⟩\begin{equation} \ket{0} \xrightarrow{X(0)} \ket{1} \end{equation}

Next, apply the ZZ gate to the quantum state ∣1⟩\ket{1} to transition it to the quantum state −∣1⟩ - \ket{1}.

∣1⟩→Z(0)−∣1⟩\begin{equation} \ket{1} \xrightarrow{Z(0)} - \ket{1} \end{equation}

Finally, apply the XX gate to the quantum state −∣1⟩ - \ket{1} to transition it to the quantum state −∣0⟩-\ket{0}.

−∣1⟩→X(0)−∣0⟩\begin{equation} - \ket{1} \xrightarrow{X(0)} - \ket{0} \end{equation}

Although the global phase of ∣0⟩\ket{0} changes from 00 to π\pi, when measuring this qubit, the original state ∣0⟩\ket{0} is observed with a probability of 11.

These bit flips and phase flips are fundamental quantum operations.

Sample Code

Below is a sample program:

from qiskit import QuantumCircuit
 
 
def solve() -> QuantumCircuit:
    qc = QuantumCircuit(1)
 
    # 1 番目の量子ビット（インデックス 0）に X ゲートと Z ゲートを作用させます。
    qc.x(0)
    qc.z(0)
    qc.x(0)
 
    return qc

Supplementary Information