Daniel D. Stancil - Principles of Superconducting Quantum Computers

1.6 Consider the following three-qubit quantum state:Is qubit q2 entangled with the other two qubits? Explain why or why not.

1.7 Suppose we have a way of measuring a qubit in the |+⟩ and |−⟩ basis. As a reminder:Given a qubit in the |0⟩ state, what is the probability of measuring |+⟩? (Hint: Use the Born Rule.)Given a qubit in the |1⟩ state, what is the probability of measuring |+⟩?Given a qubit |R⟩=12|0⟩+i2|1⟩, what is the probability of measuring |−⟩?

1.8 Given a qubitWhat is the probability of measuring |0⟩?What is the probability of measuring |+⟩?What is the probability of measuring |−⟩?

1 1To be more precise, |0⟩ and |1⟩ are known as the “computational basis” or “standard basis” states. For this chapter, we will restrict our discussion to the standard basis and will simply refer to basis states.

2 2Note: There are classical multi-input logic gates that are reversible, called “conservative logic” gates. To date these have not been widely used, but they have the advantage of making it possible in principle to compute without dissipating power [1].

3 3Entanglement can be used to increase the capacity of a communication channel, however, using a protocol known as super-dense coding.

4 4The transpose of a matrix or vector is formed by interchanging the rows and columns. The transpose of a column vector gives a row vector. The transpose complex conjugate is formed by taking the transpose of the vector or matrix and then taking the complex conjugate of each element.

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