pyquil.simulation.matrices module¶
Standard gate set, as detailed in Quil whitepaper (arXiV:1608:03355v2)
- Currently includes:
I - identity \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)
X - Pauli-X \(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\)
Y - Pauli-Y \(\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}\)
Z - Pauli-Z \(\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\)
H - Hadamard \(\frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}\)
S - PHASE(pi/2) \(\begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix}\)
T - PHASE(pi/4) \(\begin{pmatrix} 1 & 0 \\ 0 & e^{i \pi / 4} \end{pmatrix}\)
PHASE(\(\phi\)) - PHASE \(\begin{pmatrix} 1 & 0 \\ 0 & e^{i \phi} \end{pmatrix}\)
RX(\(\phi\)) - RX \(\begin{pmatrix} \cos(\phi / 2) & -i \sin(\phi/2) \\ -i \sin(\phi/2) & \cos(\phi/2) \end{pmatrix}\)
RY(\(\phi\)) - RY \(\begin{pmatrix} \cos(\phi / 2) & -\sin(\phi / 2) \\ \sin(\phi/2) & \cos(\phi/2) \end{pmatrix}\)
RZ(\(\phi\)) - RZ \(\begin{pmatrix} \cos(\phi/2) - i \sin(\phi/2) & 0 \\ 0 & \cos(\phi/2) + i \sin(\phi/2) \end{pmatrix}\)
U(\(\theta, \phi, \lambda\)) - U3 \(\begin{pmatrix} \cos(\theta/2) & - \exp{i\lambda} \sin(\theta/2) \\ \exp{i\phi} \sin(\theta/2) & \exp{i\phi + \lambda} \cos(\theta/2) \end{pmatrix}\)
CZ - controlled-Z \(P_0 \otimes I + P_1 \otimes Z = \begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&1&0 \\ 0&0&0&-1 \end{pmatrix}\)
CNOT - controlled-X / controlled-NOT \(P_0 \otimes I + P_1 \otimes X = \begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&0&1 \\ 0&0&1&0 \end{pmatrix}\)
CCNOT - double-controlled-X \(P_0 \otimes P_0 \otimes I + P_0 \otimes P_1 \otimes I + P_1 \otimes P_0 \otimes I + P_1 \otimes P_1 \otimes X\)
CPHASE00(\(\phi\)) - controlled-phase-on-|00> \(\text{diag}(e^{i \phi}, 1, 1, 1,)\)
CPHASE01(\(\phi\)) - controlled-phase-on-|01> \(\text{diag}(1, e^{i \phi}, 1, 1,)\)
CPHASE10(\(\phi\)) - controlled-phase-on-|10> \(\text{diag}(1, 1, e^{i \phi}, 1)\)
CPHASE(\(\phi\)) - controlled-phase-on-|11> \(\text{diag}(1, 1, 1, e^{i \phi})\)
SWAP - swap \(\begin{pmatrix} 1&0&0&0 \\ 0&0&1&0 \\ 0&1&0&0 \\ 0&0&0&1 \end{pmatrix}\)
CSWAP - controlled-swap \(P_0 \otimes I_2 + P_1 \otimes \text{SWAP}\)
ISWAP - i-phase-swap \(\begin{pmatrix} 1&0&0&0 \\ 0&0&i&0 \\ 0&i&0&0 \\ 0&0&0&1 \end{pmatrix}\)
PSWAP(\(\phi\)) - phi-phase-swap \(\begin{pmatrix} 1&0&0&0 \\ 0&0&e^{i\phi}&0 \\ 0&e^{i\phi}&0&0 \\ 0&0&0&1 \end{pmatrix}\)
XY(\(\phi\)) - XY-interaction \(\begin{pmatrix} 1&0&0&0 \\ 0&\cos(\phi/2)&i\sin(\phi/2)&0 \\ 0&i\sin(\phi/2)&\cos(\phi/2)&0 \\ 0&0&0&1 \end{pmatrix}\)
SQISW - XY(:math: pi/2)-interaction \(\begin{pmatrix} 1&0&0&0 \\ 0&\frac{1}{\sqrt{2}}&\frac{i}{\sqrt{2}}&0 \\ \frac{i}{\sqrt{2}}&\frac{1}{\sqrt{2}} \\ 0&0&0&1 \end{pmatrix}\)
FSIM(\(\theta, \phi\)) - XX+YY interaction with conditonal phase on |11> \(\begin{pmatrix} 1&0&0&0 \\ 0&\cos(\frac{\theta}{2})&i\sin(\frac{\theta}{2})&0 \\ 0&i\sin(\frac{\theta}{2})&\cos(\frac{\theta}{2})&0 \\ 0&0&0&e^{i \phi} \end{pmatrix}\)
PHASEDFSIM(\(\theta, \zeta, \chi, \gamma, \phi\)) - XX+YY interaction with conditonal phase on |11> \(\begin{pmatrix} 1&0&0&0 \\ 0&\ e^{-i(\gamma+\zeta)}\cos(\frac{\theta}{2})&ie^{-i(\gamma-\chi)}\sin(\frac{\theta}{2})&0 \\ 0&ie^{-i(\gamma+\chi)}\sin(\frac{\theta}{2})&e^{-i(\gamma-\zeta)}\cos(\frac{\theta}{2})&0 \\ 0&0&0&e^{ i\phi - 2i\gamma} \end{pmatrix}\)
RXX(\(\phi\)) - XX-interaction \(\begin{pmatrix} \cos(\phi/2)&0&0&-i\sin(\phi/2) \\ 0&\cos(\phi/2)&-i\sin(\phi/2)&0 \\ 0&-i\sin(\phi/2)&\cos(\phi/2)&0 \\ -i\sin(\phi/2)&0&0&cos(\phi/2) \end{pmatrix}\)
RYY(\(\phi\)) - YY-interaction \(\begin{pmatrix} \cos(\phi/2)&0&0&i\sin(\phi/2) \\ 0&\cos(\phi/2)&-i\sin(\phi/2)&0 \\ 0&-i\sin(\phi/2)&\cos(\phi/2)&0 \\ i\sin(\phi/2)&0&0&cos(\phi/2) \end{pmatrix}\)
RZZ(\(\phi\)) - ZZ-interaction \(\begin{pmatrix} 1&0&0&0 \\ 0&\cos(\phi/2)&-i\sin(\phi/2)&0 \\ 0&-i\sin(\phi/2)&\cos(\phi/2)&0 \\ 0&0&0&1 \end{pmatrix}\)
- Specialized gates / internal utility gates:
BARENCO(\(\alpha, \phi, \theta\)) - Barenco gate \(\begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&e^{i\phi} \cos\theta & -i e^{i(\alpha-\phi)} \sin\theta \\ 0&0&-i e^{i(\alpha+\phi)} \sin\theta & e^{i\alpha} \cos\theta \end{pmatrix}\)
P0 - project-onto-zero \(\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}\)
P1 - project-onto-one \(\begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}\)
- pyquil.simulation.matrices.PHASEDFSIM(theta: float, zeta: float, chi: float, gamma: float, phi: float) ndarray[source]¶
- pyquil.simulation.matrices.SIC3 = array([ 0.57735027+0.j , -0.40824829+0.70710678j])¶
The symmetric informationally complete POVMs for a qubit.
These can reduce the number of experiments to perform quantum process tomography. For more information, please see http://info.phys.unm.edu/~caves/reports/infopovm.pdf
- pyquil.simulation.matrices.bit_flip_operators(p: float) Tuple[ndarray, ndarray][source]¶
Return the phase flip kraus operators
- pyquil.simulation.matrices.bitphase_flip_operators(p: float) Tuple[ndarray, ndarray][source]¶
Return the bitphase flip kraus operators
- pyquil.simulation.matrices.dephasing_operators(p: float) Tuple[ndarray, ndarray][source]¶
Return the phase damping Kraus operators
- pyquil.simulation.matrices.depolarizing_operators(p: float) Tuple[ndarray, ndarray, ndarray, ndarray][source]¶
Return the phase damping Kraus operators