Table 1 Quantum gates in the quantum computer of IBM Q.

From: Quantifying Quantum-Mechanical Processes

Methods

Single-qubit gate

Two-qubit gate

U 1

I

X

Y

Z

H

T

U 2

CNOT

α

1

0.884

0.941

0.871

0.863

0.836

0.799

1

0.782

S

0

0.276

0.158

0.304

0.318

0.358

0.438

0

1.302

F expt

1

0.959

0.980

0.960

0.953

0.947

0.934

1

0.757

  1. We implement seven essential quantum gates with IBM Q. U 1 and U 2 represent the ideal (target) single-qubit and two-qubit gates, respectively. The process fidelities of all experimental cases considered here:4 the identity gate (I), the Pauli operators (X, Y, Z), the Hadamard gate (H), the π/8 gate (T), and the CNOT gate, are all greater than the process fidelity thresholds \({F}_{C}=\mathrm{(1}+\sqrt{3}\mathrm{)/4}\sim 0.683\) and 0.467 (implying the average state-fidelity thresholds \({\bar{F}}_{s,C}\sim 0.789\) and 0.574, respectively), for single-qubit and two-qubit gate operations, respectively. Using (A4), conditioned on logarithms to base 2, their entropies are all less than the ultimate entropies of classical process S C = N, where N denotes the number of qubits being processed.
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