I am currently using the Cirq pakage and when drawing the circuit structure, I constantly encountered the PhISwap gate, like in here. What does this gate mean?
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1 Answer
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In Cirq, the PhasedISwapPowGate (i.e. PhISwap) is a fractional ISWAP conjugated by Z rotations. With phase exponent $p$ and exponent $t$, it is equivalent to the composition
$$(\text{Z}^{-p} \otimes \text{Z}^p) \text{ISWAP}^t (\text{Z}^p \otimes \text{Z}^{-p})$$
and is given by the matrix:
$$
\left(\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & c & i\cdot s\cdot f & 0 \\
0 & i\cdot s \cdot f^* & c & 0 \\
0 & 0 & 0 & 1
\end{array}\right)
$$
where:
$$c = \cos(\pi \cdot t/2)$$
$$s = \sin(\pi \cdot t/2)$$
$$f = \exp(2\pi i \cdot p)$$
and star indicates complex conjugate.
The PhasedISwapPowGate is initialized with the following parameters:
phase_exponent: Union[float, sympy.Symbol] = 0.25
exponent: Union[float, sympy.Symbol] = 1.0
In the circuit diagram, these parameters relate to the string gate representation as:
0: ───PhISwap(phase_exponent)────────────
│
1: ───PhISwap(phase_exponent)^exponent───
These parameters relate to the matrix representation as:
c = np.cos(np.pi * exponent / 2)
s = np.sin(np.pi * exponent / 2)
f = np.exp(2j * np.pi * phase_exponent)
Source: phase_iswap_gate.py
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$\begingroup$ Thanks for the reply. I find that the ciruict contains
PhISwap(0.25)^-0.645. I suppose in this case p=0.25 and t=1. However, what does the^-0.645mean? $\endgroup$ Mar 10, 2022 at 6:00 -