Custom gates

MultiRz(angle)

Multi-qubit Z-rotation gate. The 2-qubit version is equivalent to the ZZ gate, and the single-qubit version is equivalent to the Rz gate.

DoubleExcitation(ϕ)

Generate the matrix representation of the DoubleExcitation gate.

This gate performs an SO(2) rotation in the subspace ${|1100\rangle, |0011\rangle}$, transforming the states as follows:

\[|0011\rangle & \rightarrow \cos\left(\frac{\phi}{2}\right)|0011\rangle + \sin\left(\frac{\phi}{2}\right)|1100\rangle \ |1100\rangle & \rightarrow \cos\left(\frac{\phi}{2}\right)|1100\rangle - \sin\left(\frac{\phi}{2}\right)|0011\rangle\]

Examples

julia> using BraketSimulator

julia> ϕ = 3.56;

julia> gate_matrix =  BraketSimulator.DoubleExcitation(ϕ);

julia> m  = BraketSimulator.matrix_rep(gate_matrix);

julia> eq1 = m * [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

julia> eq2 = m * [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0];

julia> eq1 ==  [0, 0, 0, cos(ϕ/2), 0, 0, 0, 0, 0, 0, 0, 0, sin(ϕ/2), 0, 0, 0] == true;

julia> eq2 ==  [0, 0, 0, -sin(ϕ/2), 0, 0, 0, 0, 0, 0, 0, 0, cos(ϕ/2), 0, 0, 0] == true;

DoubleExcitationMinus(ϕ)

Generate the matrix representation of the DoubleExcitationMinus gate.

This gate performs an SO(2) rotation in the subspace ${|1100\rangle, |0011\rangle}$ with a phase-shift on other states:

\[|0011\rangle & \rightarrow \cos\left(\frac{\phi}{2}\right)|0011\rangle - \sin\left(\frac{\phi}{2}\right)|1100\rangle \ |1100\rangle & \rightarrow \cos\left(\frac{\phi}{2}\right)|1100\rangle + \sin\left(\frac{\phi}{2}\right)|0011\rangle \ |x\rangle & \rightarrow e^{-\frac{i\phi}{2}}|x\rangle \quad \text{for all other basis states } |x\rangle\]

Examples

julia> using BraketSimulator

julia> ϕ = 3.56;

julia> gate_matrix = BraketSimulator.DoubleExcitationMinus(ϕ);

julia> m  = BraketSimulator.matrix_rep(gate_matrix);

julia> eq1 = m * [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1];

julia> eq2 = m * [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1];

julia> eq1 ==  [exp(-im*ϕ/2), 0, 0, cos(ϕ/2), 0, 0, 0, 0, 0, 0, 0, 0, sin(ϕ/2), 0, 0, exp(-im*ϕ/2)] == true;

julia> eq2 ==  [exp(-im*ϕ/2), 0, 0, -sin(ϕ/2), 0, 0, 0, 0, 0, 0, 0, 0, cos(ϕ/2), 0, 0, exp(-im*ϕ/2)] == true;

DoubleExcitationPlus(ϕ)

Generate the matrix representation of the DoubleExcitationPlus gate.

This gate performs an SO(2) rotation in the subspace ${|1100\rangle, |0011\rangle}$ with a phase-shift on other states:

\[|0011\rangle & \rightarrow \cos\left(\frac{\phi}{2}\right)|0011\rangle - \sin\left(\frac{\phi}{2}\right)|1100\rangle \ |1100\rangle & \rightarrow \cos\left(\frac{\phi}{2}\right)|1100\rangle + \sin\left(\frac{\phi}{2}\right)|0011\rangle \ |x\rangle & \rightarrow e^{\frac{i\phi}{2}}|x\rangle \quad \text{for all other basis states } |x\rangle\]

Examples

julia> using BraketSimulator

julia> ϕ = 3.56;

julia> gate_matrix = BraketSimulator.DoubleExcitationPlus(ϕ);

julia> m  = BraketSimulator.matrix_rep(gate_matrix);

julia> eq1 = m * [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1];

julia> eq2 = m * [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1];

julia> eq1 ==  [exp(im*ϕ/2), 0, 0, cos(ϕ/2), 0, 0, 0, 0, 0, 0, 0, 0, sin(ϕ/2), 0, 0, exp(im*ϕ/2)] == true;

julia> eq2 ==  [exp(im*ϕ/2), 0, 0, -sin(ϕ/2), 0, 0, 0, 0, 0, 0, 0, 0, cos(ϕ/2), 0, 0, exp(im*ϕ/2)] == true;

SingleExcitation(ϕ)

Generate the matrix representation of the SingleExcitation gate.

This gate performs a rotation in the subspace ${|01\rangle, |10\rangle}$.

Examples

julia> using BraketSimulator

julia> ϕ = 3.56;

julia> gate_matrix = BraketSimulator.SingleExcitation(ϕ);

julia> m  = BraketSimulator.matrix_rep(gate_matrix);

julia> eq1 = m * [0, 1, 0, 0];

julia> eq2 = m * [0, 0, 1, 0];

julia> eq1 == [0, cos(ϕ/2), - sin(ϕ/2), 0] == true;
 
julia> eq2 == [0, sin(ϕ/2), cos(ϕ/2), 0] == true;

SingleExcitationMinus(ϕ)

Generate the matrix representation of the SingleExcitationMinus gate.

This gate performs a rotation in the subspace ${|01\rangle, |10\rangle}$ with a phase-shift.

Examples

julia> using BraketSimulator

julia> ϕ = 3.56;

julia> gate_matrix = BraketSimulator.SingleExcitationMinus(ϕ);

julia> m  = BraketSimulator.matrix_rep(gate_matrix);

julia> eq1 = m * [1, 1, 0, 0];

julia> eq2 = m * [1, 0, 1, 0];

julia> eq1 == [exp(-im*ϕ/2), cos(ϕ/2), - sin(ϕ/2), 0] == true;

julia> eq2 == [exp(-im*ϕ/2), sin(ϕ/2), cos(ϕ/2), 0] == true;

SingleExcitationPlus(ϕ)

Generate the matrix representation of the SingleExcitationPlus gate.

This gate performs a rotation in the subspace ${|01\rangle, |10\rangle}$ with a phase-shift.

Examples

julia> using BraketSimulator

julia> ϕ = 3.56;

julia> gate_matrix = BraketSimulator.SingleExcitationPlus(ϕ);

julia> m  = BraketSimulator.matrix_rep(gate_matrix);

julia> eq1 = m * [1, 1, 0, 0];

julia> eq2 = m * [1, 0, 1, 0];

julia> eq1 == [exp(im*ϕ/2), cos(ϕ/2), - sin(ϕ/2), 0] == true; 

julia> eq2 == [exp(im*ϕ/2), sin(ϕ/2), cos(ϕ/2), 0] == true;

FermionicSWAP(ϕ)

Generate the matrix representation of the FermionicSWAP gate.

This gate performs a rotation in adjacent fermionic modes under the Jordan-Wigner mapping, transforming states as follows:

\[|00\rangle & \rightarrow |00\rangle \ |01\rangle & \rightarrow e^{\frac{i\phi}{2}}\cos\left(\frac{\phi}{2}\right)|01\rangle - ie^{\frac{i\phi}{2}}\sin\left(\frac{\phi}{2}\right)|10\rangle \ |10\rangle & \rightarrow -ie^{\frac{i\phi}{2}}\sin\left(\frac{\phi}{2}\right)|01\rangle + e^{\frac{i\phi}{2}}\cos\left(\frac{\phi}{2}\right)|10\rangle \ |11\rangle & \rightarrow e^{i\phi}|11\rangle\]

Examples

julia> using BraketSimulator

julia> ϕ = 3.56;

julia> gate_matrix = BraketSimulator.FermionicSWAP(ϕ);

julia> m  = BraketSimulator.matrix_rep(gate_matrix);

julia> eq1 = m * [0, 0, 0, 0];

julia> eq2 = m * [0, 1, 0, 0];

julia> eq3 = m * [0, 0, 1, 0];

julia> eq4 = m * [0, 0, 0, 1];

julia> eq1 == [0, 0, 0, 0] == true;
 
julia> eq2 == [0, exp(im*ϕ/2.0)*cos(ϕ / 2.0), - im*exp(im*ϕ/2.0)*sin(ϕ/2.0), 0] == true;

julia> eq3 == [0, - im*exp(im*ϕ/2.0)*sin(ϕ/2.0), exp(im*ϕ/2.0)*cos(ϕ/2.0), 0] == true;

julia> eq4 == [0, 0, 0, exp(im * ϕ)] == true;