3.(25¹) 1). A quantum logic circuit is shown in Figure 1. It applies a Hadamard gate to the first qubit followed by a CNOT gate to both qubits. If inputs y(A)=0>, y(B)=0>, use matrix calculation to find out the output state of the quantum circuit (i.e. y(Out)=? in matrix form). Also find the output states of two qubits separately (i.e. y(A')=? Y(B')=?) in both vector form and matrix form. 1 Hint: Matrixes of Hadamard gate and CNOT gate are (1000) H 1 (1 √√2 (-)). 0100 CNOT 0001 (0010) For one qubit, ¥ = a[0) + A|1)=(a), the former one is vector form, and the later one is matrix form. A=10) H A'=? Out=? B=10) B'=? Figure 1. A Quantum logic circuit taking two Q-bits as input
3.(25¹) 1). A quantum logic circuit is shown in Figure 1. It applies a Hadamard gate to the first qubit followed by a CNOT gate to both qubits. If inputs y(A)=0>, y(B)=0>, use matrix calculation to find out the output state of the quantum circuit (i.e. y(Out)=? in matrix form). Also find the output states of two qubits separately (i.e. y(A')=? Y(B')=?) in both vector form and matrix form. 1 Hint: Matrixes of Hadamard gate and CNOT gate are (1000) H 1 (1 √√2 (-)). 0100 CNOT 0001 (0010) For one qubit, ¥ = a[0) + A|1)=(a), the former one is vector form, and the later one is matrix form. A=10) H A'=? Out=? B=10) B'=? Figure 1. A Quantum logic circuit taking two Q-bits as input
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Transcribed Image Text:3.(25') 1). A quantum logic circuit is shown in Figure 1. It applies a Hadamard gate to the
first qubit followed by a CNOT gate to both qubits. If inputs y(A)=|0>, y(B)=|0>, use
matrix calculation to find out the output state of the quantum circuit (i.e. y(Out)=? in
matrix form). Also find the output states of two qubits separately (i.e. y(A')=? Y(B')=?)
in both vector form and matrix form.
1
Hint: Matrixes of Hadamard gate and CNOT gate are
1 (1 1
(1000)
H =
(1)
0100
CNOT =
0001
(0010)
For one qubit,
¥ = a0) + B|1) = (a).
the former one is vector form, and the later one is matrix form.
A=10)
H
A'=?
Out=?
B=10)
B'=?
Figure 1. A Quantum logic circuit taking two Q-bits as input
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