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mindquantum.core.gates

Gate module that provides different quantum gate.

Base Class

mindquantum.core.gates.BasicGate	BasicGate is the base class of all gates.
mindquantum.core.gates.NoneParameterGate	Base class for non-parametric gates.
mindquantum.core.gates.ParameterGate	Gate that is parameterized.
mindquantum.core.gates.QuantumGate	Base class for quantum gates.
mindquantum.core.gates.NoiseGate	Noise gate class.

Quantum Gate

API Name	Description	Math
mindquantum.core.gates.CNOTGate	Control-X gate.	No formula yet.
mindquantum.core.gates.FSim	FSim gate represent fermionic simulation gate.	$\mathrm{F}\mathrm{S}\mathrm{i}\mathrm{m}(\theta ,\varphi )=\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos (\theta )& -i\sin (\theta )& 0\\ 0& -i\sin (\theta )& \cos (\theta )& 0\\ 0& 0& 0& e^{-i\varphi }\end{array}\right)$
mindquantum.core.gates.GlobalPhase	Global phase gate.	$\mathrm{G}\mathrm{l}\mathrm{o}\mathrm{b}\mathrm{a}\mathrm{l}\mathrm{P}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}=\left(\begin{array}{cc}\exp (-i\theta )& 0\\ 0& \exp (-i\theta )\end{array}\right)$
mindquantum.core.gates.HGate	Hadamard gate.	$\mathrm{H}=\frac{1}{\sqrt{2}}\left(\begin{array}{cc}1& 1\\ 1& -1\end{array}\right)$
mindquantum.core.gates.IGate	Identity gate.	$\mathrm{I}=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$
mindquantum.core.gates.ISWAPGate	ISWAP gate.	No formula yet.
mindquantum.core.gates.Measure	Measurement gate that measure quantum qubits.	No formula yet.
mindquantum.core.gates.PhaseShift	Phase shift gate.	$\mathrm{P}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{S}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}=\left(\begin{array}{cc}1& 0\\ 0& \exp (i\theta )\end{array}\right)$
mindquantum.core.gates.Rn	Pauli rotate about a arbitrary axis in bloch sphere.	$\begin{array}{rl}\mathrm{R}\mathrm{n}(\alpha ,\beta ,\gamma )& =e^{-i(\alpha {\sigma }_x+\beta {\sigma }_y+\gamma {\sigma }_z)/2}\\ & =\cos (f/2)I-i\sin (f/2)(\alpha {\sigma }_x+\beta {\sigma }_y+\gamma {\sigma }_z)/f\\ & \text{where }f=\sqrt{{\alpha }^2+{\beta }^2+{\gamma }^2}\end{array}$
mindquantum.core.gates.RX	Rotation gate around x-axis.	$\mathrm{R}\mathrm{X}=\left(\begin{array}{cc}\cos (\theta /2)& -i\sin (\theta /2)\\ -i\sin (\theta /2)& \cos (\theta /2)\end{array}\right)$
mindquantum.core.gates.Rxx	Rxx gate.	$Rxx(\theta )=\exp (-i\frac{\theta }{2}X\otimes X)=\left(\begin{array}{cccc}\cos \frac{\theta }{2}& 0& 0& -i\sin \frac{\theta }{2}\\ 0& \cos \frac{\theta }{2}& -i\sin \frac{\theta }{2}& 0\\ 0& -i\sin \frac{\theta }{2}& \cos \frac{\theta }{2}& 0\\ -i\sin \frac{\theta }{2}& 0& 0& \cos \frac{\theta }{2}\end{array}\right)$
mindquantum.core.gates.Rxy	Rxy gate.	$Rxy(\theta )=\exp (-i\frac{\theta }{2}Y\otimes X)=\left(\begin{array}{cccc}\cos \frac{\theta }{2}& 0& 0& -\sin \frac{\theta }{2}\\ 0& \cos \frac{\theta }{2}& -\sin \frac{\theta }{2}& 0\\ 0& \sin \frac{\theta }{2}& \cos \frac{\theta }{2}& 0\\ \sin \frac{\theta }{2}& 0& 0& \cos \frac{\theta }{2}\end{array}\right)$
mindquantum.core.gates.Rxz	Rxz gate.	$Rxz(\theta )=\exp (-i\frac{\theta }{2}Z\otimes X)=\left(\begin{array}{cccc}\cos \frac{\theta }{2}& -i\sin \frac{\theta }{2}& 0& 0\\ -i\sin \frac{\theta }{2}& \cos \frac{\theta }{2}& 0& 0\\ 0& 0& \cos \frac{\theta }{2}& i\sin \frac{\theta }{2}\\ 0& 0& i\sin \frac{\theta }{2}& \cos \frac{\theta }{2}\end{array}\right)$
mindquantum.core.gates.RY	Rotation gate around y-axis.	$\mathrm{R}\mathrm{Y}=\left(\begin{array}{cc}\cos (\theta /2)& -\sin (\theta /2)\\ \sin (\theta /2)& \cos (\theta /2)\end{array}\right)$
mindquantum.core.gates.Ryy	Ryy gate.	$Ryy(\theta )=\exp (-i\frac{\theta }{2}Y\otimes Y)=\left(\begin{array}{cccc}\cos \frac{\theta }{2}& 0& 0& i\sin \frac{\theta }{2}\\ 0& \cos \frac{\theta }{2}& -i\sin \frac{\theta }{2}& 0\\ 0& -i\sin \frac{\theta }{2}& \cos \frac{\theta }{2}& 0\\ i\sin \frac{\theta }{2}& 0& 0& \cos \frac{\theta }{2}\end{array}\right)$
mindquantum.core.gates.Ryz	Ryz gate.	$Ryz(\theta )=\exp (-i\frac{\theta }{2}Z\otimes Y)=\left(\begin{array}{cccc}\cos \frac{\theta }{2}& -\sin \frac{\theta }{2}& 0& 0\\ \sin \frac{\theta }{2}& \cos \frac{\theta }{2}& 0& 0\\ 0& 0& \cos \frac{\theta }{2}& \sin \frac{\theta }{2}\\ 0& 0& -\sin \frac{\theta }{2}& \cos \frac{\theta }{2}\end{array}\right)$
mindquantum.core.gates.RZ	Rotation gate around z-axis.	$\mathrm{R}\mathrm{Z}=\left(\begin{array}{cc}\exp (-i\theta /2)& 0\\ 0& \exp (i\theta /2)\end{array}\right)$
mindquantum.core.gates.Rzz	Rzz gate.	$Rzz(\theta )=\exp (-i\frac{\theta }{2}Z\otimes Z)=\left(\begin{array}{cccc}{e}^{-i\frac{\theta }{2}}& 0& 0& 0\\ 0& e^{i\frac{\theta }{2}}& 0& 0\\ 0& 0& e^{i\frac{\theta }{2}}& 0\\ 0& 0& 0& e^{-i\frac{\theta }{2}}\end{array}\right)$
mindquantum.core.gates.RotPauliString	Arbitrary pauli string rotation.	$U(\theta )=e^{-i\theta P/2},P={\otimes }_i{\sigma }_i,\text{where }\sigma \in \{X,Y,Z\}$
mindquantum.core.gates.SGate	S gate.	$\mathrm{S}=\left(\begin{array}{cc}1& 0\\ 0& i\end{array}\right)$
mindquantum.core.gates.SWAPGate	SWAP gate that swap two different qubits.	No formula yet.
mindquantum.core.gates.SWAPalpha	SWAP alpha gate.	$\text{SWAP}(\alpha )=\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& \frac{1}{2}(1+e^{i\pi \alpha })& \frac{1}{2}(1-e^{i\pi \alpha })& 0\\ 0& \frac{1}{2}(1-e^{i\pi \alpha })& \frac{1}{2}(1+e^{i\pi \alpha })& 0\\ 0& 0& 0& 1\end{array}\right)$
mindquantum.core.gates.SXGate	Sqrt X (SX) gate.	$\mathrm{S}\mathrm{X}=\frac{1}{2}\left(\begin{array}{cc}1+i& 1-i\\ 1-i& 1+i\end{array}\right)$
mindquantum.core.gates.TGate	T gate.	$\mathrm{T}=\left(\begin{array}{cc}1& 0\\ 0& (1+i)/\sqrt{(}2)\end{array}\right)$
mindquantum.core.gates.U3	U3 gate represent arbitrary single qubit gate.	$\mathrm{U}3(\theta ,\varphi ,\lambda )=\left(\begin{array}{cc}\cos (\theta /2)& -e^{i\lambda }\sin (\theta /2)\\ e^{i\varphi }\sin (\theta /2)& e^{i(\varphi +\lambda )}\cos (\theta /2)\end{array}\right)$
mindquantum.core.gates.XGate	Pauli-X gate.	$\mathrm{X}=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$
mindquantum.core.gates.YGate	Pauli Y gate.	$\mathrm{Y}=\left(\begin{array}{cc}0& -i\\ i& 0\end{array}\right)$
mindquantum.core.gates.ZGate	Pauli-Z gate.	$\mathrm{Z}=\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)$
mindquantum.core.gates.GroupedPauli	Multi qubit pauli string gate.	$U={\otimes }_i{\sigma }_i,\text{where }\sigma \in \{I,X,Y,Z\}$
mindquantum.core.gates.Givens	Givens rotation gate.	$\mathrm{G}(\theta )=\exp (-i\frac{\theta }{2}(Y\otimes X-X\otimes Y))=\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \theta & -\sin \theta & 0\\ 0& \sin \theta & \cos \theta & 0\\ 0& 0& 0& 1\end{array}\right)$

Functional Gate

mindquantum.core.gates.UnivMathGate	Universal math gate.
mindquantum.core.gates.gene_univ_parameterized_gate	Generate a customer parameterized gate based on the single parameter defined unitary matrix.
mindquantum.core.gates.BarrierGate	Barrier gate will separate two gate in two different layer.

pre-instantiated gate

The gates blow are the pre-instantiated quantum gates, which can be used directly as an instance of quantum gate.

pre-instantiated gate	gate
mindquantum.core.gates.CNOT	mindquantum.core.gates.CNOTGate
mindquantum.core.gates.I	mindquantum.core.gates.IGate
mindquantum.core.gates.ISWAP	mindquantum.core.gates.ISWAPGate
mindquantum.core.gates.H	mindquantum.core.gates.HGate
mindquantum.core.gates.S	mindquantum.core.gates.PhaseShift (numpy.pi/2)
mindquantum.core.gates.SWAP	mindquantum.core.gates.SWAPGate
mindquantum.core.gates.SX	mindquantum.core.gates.SXGate
mindquantum.core.gates.T	mindquantum.core.gates.PhaseShift (numpy.pi/4)
mindquantum.core.gates.X	mindquantum.core.gates.XGate
mindquantum.core.gates.Y	mindquantum.core.gates.YGate
mindquantum.core.gates.Z	mindquantum.core.gates.ZGate

Quantum Channel

API Name	Description	Math
mindquantum.core.gates.AmplitudeDampingChannel	Amplitude damping channel express error that qubit is affected by the energy dissipation.	$\begin{array}{c}ϵ(\rho )=E_0\rho E_0^{†}+E_1\rho E_1^{†}\\ \text{where}{E}_0=\left[\begin{array}{cc}1& 0\\ 0& \sqrt{1-\gamma }\end{array}\right],E_1=\left[\begin{array}{cc}0& \sqrt{\gamma }\\ 0& 0\end{array}\right]\end{array}$
mindquantum.core.gates.BitFlipChannel	A bit flip channel.	$ϵ(\rho )=(1-P)\rho +PX\rho X$
mindquantum.core.gates.BitPhaseFlipChannel	A bit&phase flip channel.	$ϵ(\rho )=(1-P)\rho +PY\rho Y$
mindquantum.core.gates.DepolarizingChannel	A depolarizing channel.	$ϵ(\rho )=(1-P)\rho +P/4(I\rho I+X\rho X+Y\rho Y+Z\rho Z)$
mindquantum.core.gates.KrausChannel	A kraus channel.	$ϵ(\rho )=\sum _{k=0}^{m-1}{E}_k\rho E_k^{†}$
mindquantum.core.gates.PauliChannel	A pauli channel.	$ϵ(\rho )=(1-P_x-P_y-P_z)\rho +P_{x}X\rho X+P_{y}Y\rho Y+P_{z}Z\rho Z$
mindquantum.core.gates.GroupedPauliChannel	A group of pauli channels.	$ϵ(\rho )={\otimes }_i{ϵ}_{\text{pauli}}^i(\rho )$
mindquantum.core.gates.PhaseDampingChannel	A phase damping channel.	$\begin{array}{c}ϵ(\rho )=E_0\rho E_0^{†}+E_1\rho E_1^{†}\\ \text{where}{E}_0=\left[\begin{array}{cc}1& 0\\ 0& \sqrt{1-\gamma }\end{array}\right],E_1=\left[\begin{array}{cc}0& 0\\ 0& \sqrt{\gamma }\end{array}\right]\end{array}$
mindquantum.core.gates.PhaseFlipChannel	A phase flip channel.	$ϵ(\rho )=(1-P)\rho +PZ\rho Z$
mindquantum.core.gates.ThermalRelaxationChannel	Thermal relaxation channel.	$\begin{array}{c}ϵ(\rho )={\text{tr}}_1\left[\mathrm{\Lambda }({\rho }^T\otimes I)\right],\mathrm{\Lambda }=\left(\begin{array}{cccc}{ϵ}_{T_1}& 0& 0& {ϵ}_{T_2}\\ 0& 1-{ϵ}_{T_1}& 0& 0\\ 0& 0& 0& 0\\ {ϵ}_{T_2}& 0& 0& 1\end{array}\right)\\ \text{where}{ϵ}_{T_1}=e^{-T_g/T_1},{ϵ}_{T_2}=e^{-T_g/T_2}\end{array}$

Functional Class

mindquantum.core.gates.MeasureResult	Measurement result container.
mindquantum.core.gates.Power	Power operator on a non parameterized gate.