B4. Distinguish four 2-qubit states - 2

Codeforces

IDCF1002B4

Time1000ms

Memory256MB

Difficulty—

English · Original

Chinese · Translation

Formal · Original

You are given 2 qubits which are guaranteed to be in one of the four orthogonal states: Your task is to perform necessary operations and measurements to figure out which state it was and to return the index of that state (0 for , 1 for etc.). The state of the qubits after the operations does not matter. You have to implement an operation which takes an array of 2 qubits as an input and returns an integer. Your code should have the following signature: namespace Solution { open Microsoft.Quantum.Primitive; open Microsoft.Quantum.Canon; operation Solve (qs : Qubit\[\]) : Int { body { // your code here } } } [samples]

给定两个量子比特，它们保证处于以下四个正交态之一：你的任务是执行必要的操作和测量，以确定其处于哪个态，并返回该态的索引（0 对应，1 对应，依此类推）。操作后量子比特的状态无关紧要。你需要实现一个操作，该操作以包含 2 个量子比特的数组作为输入，并返回一个整数。你的代码应具有以下签名： [samples]

**Definitions** Let $\mathcal{H} = \mathbb{C}^2 \otimes \mathbb{C}^2$ be the Hilbert space of two qubits. Let $\{|\psi_0\rangle, |\psi_1\rangle, |\psi_2\rangle, |\psi_3\rangle\} \subset \mathcal{H}$ be a fixed set of four mutually orthogonal quantum states. **Given** An input state $|\psi\rangle \in \{|\psi_0\rangle, |\psi_1\rangle, |\psi_2\rangle, |\psi_3\rangle\}$, prepared in a 2-qubit register. **Objective** Design a quantum circuit (unitary operations and measurement) that, given $|\psi\rangle$, outputs the index $i \in \{0,1,2,3\}$ such that $|\psi\rangle = |\psi_i\rangle$, with certainty. The operation must return $i$ as an integer, based on measurement outcomes of the 2-qubit system. **Constraints** - Only unitary operations and projective measurements in the computational basis are permitted. - The final state of the qubits after measurement is irrelevant. - The distinguishing protocol must succeed with probability 1 for all four possible input states.

API Response (JSON)

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