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Is it possible to measure only one qubit of a two qubit quantum state?
It is also possible to measure just one qubit of a two-qubit quantum state. In cases where you measure only one of the qubits, the impact of measurement is subtly different because the entire state is not collapsed to a computational basis state, rather it is collapsed to only one sub-system.
How to represent the state of a qubit?
Either the qubit definitely outputs a 0, or it definitely outputs a 1. There is no overlap. One way to represent this with mathematics is to use two orthogonal vectors. |0⟩ = [1 0] |1⟩= [0 1]. | 0 ⟩ = [ 1 0] | 1 ⟩ = [ 0 1]. This is a lot of notation to take in all at once.
How are qubits measured in the middle of a circuit?
First, they can be thought of as Boolean tests for a property of a quantum state before the final measurement takes place. For example, one can ask, mid-circuit, whether a register of qubits is in the plus or minus eigenstate of an operator formed by a tensor product of Pauli operators.
How are qubits stored in a Qiskit circuit?
In Qiskit, we use the QuantumCircuit object to store our circuits, this is essentially a list of the quantum operations on our circuit and the qubits they are applied to. In our quantum circuits, our qubits always start out in the state | 0⟩|0⟩. We can use the initialize () method to transform this into any state.
What is the probability of both outcomes of swapping one qubit?
Both outcomes have 50% probability of occurring. The outcome being 50% probability for both can be intuited from the fact that the initial quantum state vector is invariant under swapping 0 0 with 1 1 on the first qubit. The mathematical rule for measuring the first or second qubit is simple.
What is the computational basis for two qubits?
The computational basis for two-qubit states is formed by the tensor products of one-qubit states. For example, we have
What is the quantum state vector of multiple qubits?
Just as with single qubits, the quantum state vector of multiple qubits holds all the information needed to describe the system’s behavior. For more information about vectors and tensor products, see Vectors and Matrices in Quantum Computing.