Bell States

Description

The function builds one of the four Bell states, according to the input qubits

Usage

Bell(qubit1, qubit2)

Arguments

Value

One of the Bell states as a vector depending on the input qubits.

References

https://en.wikipedia.org/wiki/Bell_state
https://books.google.co.in/books?id=66TgFp2YqrAC&pg=PA25&redir_esc=y

Examples

init()
Bell(Q$Q0, Q$Q0)
Bell(Q$Q0, Q$Q1)
Bell(Q$Q1, Q$Q0)
Bell(Q$Q1, Q$Q1)

CNOT gate

Description

This function operates the CNOT gate on a conformable input matrix/vector

Usage

CNOT(n)

Arguments

Value

A matrix or a vector after performing the CNOT gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
CNOT(Q$I4)
CNOT(Q$Q11)

Fredkin Gate

Description

This function operates the Fredkin gate on a conformable input matrix/vector

Usage

Fredkin(n)

Arguments

Value

A matrix or a vector after performing the Fredkin gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
Fredkin(Q$I8)
Fredkin(Q$Q110)

Hadamard Gate

Description

This function operates the Hadamard gate on a conformable input matrix/vector

Usage

Hadamard(n)

Arguments

Value

A matrix or a vector after performing the Hadamard operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
Hadamard(Q$Q0)
Hadamard(Q$I2)
Hadamard(Hadamard(Q$Q1))

Iterated Deletion of Strictly Dominated Strategies algorithm

Description

This function applies the IDSDS algorithm to result in the equilibrium strategies based on the rationaility of the players. The input parameters are equal dimensional payoff matrices for the first and the second players.

Usage

IDSDS(P1, P2)

Arguments

Value

A list consisting of the equilibrium strategies based on the rationality of the players by application of the IDSDS algorithm on P1 and P2.

References

https://arxiv.org/abs/1512.06808
https://en.wikipedia.org/wiki/Strategic_dominance

Examples

init()
Alice <- matrix(c(8, 0, 3, 3, 2, 4, 2, 1, 3), ncol=3, byrow=TRUE)
Bob <- matrix(c(6, 9, 8, 2, 1, 3, 8, 5, 1), ncol=3, byrow=TRUE)
IDSDS(Alice, Bob)

Nash Equilibrium

Description

This function finds out the Nash equilibria of the 2-D payoff matrix for the players. The input parameters are equal dimensional payoff matrices for the first and the second players.

Usage

NASH(P1, P2)

Arguments

Value

The cell positons of the Nash equilibrium/equilibria as a dataframe from the payoff matrices of the players.

References

https://arxiv.org/abs/1512.06808
https://en.wikipedia.org/wiki/Nash_equilibrium

Examples

init()
Alice <- matrix(c(4, 3, 2, 4, 4, 2, 1, 0, 3, 5, 3, 5, 2, 3, 1, 3), ncol=4, byrow=TRUE)
Bob <- matrix(c(0, 2, 3, 8, 2, 1, 2, 2, 6, 5, 1, 0, 3, 2, 2, 3), ncol=4, byrow=TRUE)
NASH(Alice, Bob)

Quantum Battle of the Sexes game: Payoff Matrix

Description

This function generates the payoff matrix for the Quantum Battle of Sexes game for all the four combinations of p and q. moves is a list of two possible strategies for each of the players and alpha, beta, gamma are the payoffs for the players corresponding to the choices available to them with the chain of inequalities, alpha>beta>gamma.

Usage

PayoffMatrix_QBOS(moves, alpha, beta, gamma)

Arguments

Value

The payoff matrices for the two players as two elements of a list.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/abs/quant-ph/0110096

Examples

init()
moves <- list(Q$I2, sigmaX(Q$I2))
PayoffMatrix_QBOS(moves, 5, 3, 1)

Quantum Hawk and Dove game: Payoff Matrix

Description

This function generates the payoff matrix for the Quantum Hawk and Dove game for all the four combinations of p and q. moves is a list of two possible strategies for each of the players and v, j, D are the value of resource, cost of injury and cost of displaying respectively.

Usage

PayoffMatrix_QHawkDove(moves, v, j, D)

Arguments

Value

The payoff matrices for the two players as two elements of a list.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0108075.pdf

Examples

init()
moves <- list(Q$I2, sigmaX(Q$I2))
PayoffMatrix_QHawkDove(moves, 50, -100, -10)

Quantum Prisoner's Dilemma game: Payoff Matrix

Description

This function generates the payoff matrix for the Quantum Prisoner's Dilemma game . moves is a list of the possible strategies for each of the players and w, x, y, z are the payoffs for the players corresponding to the choices available to them with the chain of inequalities, z>w>x>y. This function also plots the probability distribution plots of the qubits for all the possible combinations of the strategies of the players.

Usage

PayoffMatrix_QPD(moves, w, x, y, z)

Arguments

Value

The payoff matrices for the two players as two elements of a list.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0004076.pdf

Examples

init()
moves <- list(Q$I2, sigmaX(Q$I2), Hadamard(Q$I2), sigmaZ(Q$I2))
PayoffMatrix_QPD(moves, 3, 1, 0, 5)

Phase Gate

Description

This function operates the Phase gate on a conformable input matrix/vector

Usage

Phase(n)

Arguments

Value

A matrix or a vector after performing the Phase gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
Phase(Q$I2)
Phase(Q$Q_plus)

Hermitian Transpose of the Phase Gate

Description

This function operates the hermitian transpose of the Phase gate on a conformable input matrix/vector

Usage

PhaseDagger(n)

Arguments

Value

A matrix or a vector after performing the operation of the hermitian transpose of the Phase gate on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
Conj(t(Phase(Q$I2)))==PhaseDagger(Q$I2)
PhaseDagger(Q$Q_plus)

Quantum Battle of the Sexes game

Description

This function returns the expected payoffs to Alice and Bob with respect to the probabilities p and q. p+q should equal 1 and moves is a list of two possible strategies for each of the players and alpha, beta, gamma are the payoffs for the players corresponding to the choices available to them with the chain of inequalities, alpha>beta>gamma.

Usage

QBOS(p, q, moves, alpha, beta, gamma)

Arguments

Value

A vector consisting of the Payoffs to Alice and Bob as its two elements depending on the inputs.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/abs/quant-ph/0110096

Examples

init()
moves <- list(Q$I2, sigmaX(Q$I2))
QBOS(0, 1, moves, 5, 3, 1)
QBOS(1, 1, moves, 5, 3, 1)
QBOS(0.5, 0.5, moves, 5, 3, 1)

Quantum Two Person Duel game

Description

This function helps us to plot Alice's and Bob's expected payoffs as functions of alpha1 and alpha2. Psi is the initial state of the quantum game, n is the number of rounds, a is the probability of Alice missing the target, b is the probability of Bob missing the target, and alpha1, alpha2, beta1, beta2 are arbitrary phase factors that lie in -pi to pi that control the outcome of a poorly performing player.

Usage

QDuelsPlot1(Psi, n, a, b, beta1, beta2)

Arguments

Value

No return value, plots Alice's and Bob's expected payoffs as functions of alpha1 and alpha2.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0305058.pdf

Examples

init()
QDuelsPlot1(Q$Q10, 2, 0.66666, 0.5, 0.2, 0.8)

Quantum Two Person Duel game

Description

This function helps us to plot Alice's and Bob's expected payoffs as functions of the number of rounds n played in a repeated quantum duel. Psi is the initial state of the quantum game, n is the number of rounds, a is the probability of Alice missing the target, b is the probability of Bob missing the target, and alpha1, alpha2, beta1, beta2 are arbitrary phase factors that lie in -pi to pi that control the outcome of a poorly performing player.

Usage

QDuelsPlot2(Psi, n, a, b, alpha1, alpha2, beta1, beta2)

Arguments

Value

No return value, plots Alice's and Bob's expected payoffs as functions of the number of rounds n played in a repeated quantum duel.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0305058.pdf

Examples

init()
QDuelsPlot2(Q$Q01, 10, 0.66666, 0.5, -pi/2, pi/4, 0.6, 0.4)

Quantum Two Person Duel game

Description

This function helps us to plot the improvement in Alice's expected payoff as a function of a and b, if Alice chooses to fire at the air in her second shot, in a two round game. Psi is the initial state of the quantum game, n is the number of rounds, a is the probability of Alice missing the target, b is the probability of Bob missing the target, and alpha1, alpha2, beta1, beta2 are arbitrary phase factors that lie in -pi to pi that control the outcome of a poorly performing player.

Usage

QDuelsPlot3(Psi, alpha1, alpha2)

Arguments

Value

No return value, plots the improvement in Alice's expected payoff as a function of a and b, if Alice chooses to fire at the air in her second shot, in a two round game.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0305058.pdf

Examples

init()
Qs <- (Q$Q0+Q$Q1)/sqrt(2)
Psi <- kronecker(Q$Q1, Qs)
QDuelsPlot3(Psi, pi/3, pi/6)

Quantum Two Person Duel game

Description

This function helps us to plot the improvement in Bob's expected payoff as a function of a and b, if Bob chooses to fire at the air in her second shot, in a two round game. Psi is the initial state of the quantum game, n is the number of rounds, a is the probability of Alice missing the target, b is the probability of Bob missing the target, and alpha1, alpha2, beta1, beta2 are arbitrary phase factors that lie in -pi to pi that control the outcome of a poorly performing player.

Usage

QDuelsPlot4(Psi, alpha1, alpha2)

Arguments

Value

No return value, plots the improvement in Bob's expected payoff as a function of a and b, if Bob chooses to fire at the air in her second shot, in a two round game.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0305058.pdf

Examples

init()
Qs <- (Q$Q0+Q$Q1)/sqrt(2)
Psi <- kronecker(Q$Q1, Qs)
QDuelsPlot4(Psi, pi/3, pi/6)

Quantum Two Person Duel game

Description

This function returns the expected payoff to Alice for three possible cases for the Quantum Duel game:

1. The game is continued for n rounds and none of the players shoots at the air.

2. The game is continued for 2 rounds and Alice shoots at the air in her second round.

3. The game is continued for 2 rounds and Bob shoots at the air in her second round.

Psi is the initial state of the quantum game, n is the number of rounds, a is the probability of Alice missing the target, b is the probability of Bob missing the target, and alpha1, alpha2, beta1, beta2 are arbitrary phase factors that lie in -pi to pi that control the outcome of a poorly performing player.

Usage

QDuels_Alice_payoffs(Psi, n, a, b, alpha1, alpha2, beta1, beta2)

Arguments

Value

A list consisting of the payoff value to Alice depending on three situations of the quantum duel game: 1) The game is continued for n rounds and none of the players shoots at the air, 2) The game is continued for 2 rounds and Alice shoots at the air in her second round and 3) The game is continued for 2 rounds and Bob shoots at the air in her second round.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0305058.pdf

Examples

init()
QDuels_Alice_payoffs(Q$Q11, 5, 0.666666, 0.5, 0, 0, 0.2, 0.7)
Qs <- (Q$Q0+Q$Q1)/sqrt(2)
Psi <- kronecker(Qs, Qs)
QDuels_Alice_payoffs(Psi, 5, 0.666666, 0.5, 0, 0, 0.2, 0.7)

Quantum Two Person Duel game

Description

This function returns the expected payoff to Bob for three possible cases for the Quantum Duel game:

1. The game is continued for n rounds and none of the players shoots at the air.

2. The game is continued for 2 rounds and Alice shoots at the air in her second round.

3. The game is continued for 2 rounds and Bob shoots at the air in her second round.

Psi is the initial state of the quantum game, n is the number of rounds, a is the probability of Alice missing the target, b is the probability of Bob missing the target, and alpha1, alpha2, beta1, beta2 are arbitrary phase factors that lie in -pi to pi that control the outcome of a poorly performing player.

Usage

QDuels_Bob_payoffs(Psi, n, a, b, alpha1, alpha2, beta1, beta2)

Arguments

Value

A list consisting of the payoff value to Bob depending on three situations of the quantum duel game: 1) The game is continued for n rounds and none of the players shoots at the air, 2) The game is continued for 2 rounds and Alice shoots at the air in her second round and 3) The game is continued for 2 rounds and Bob shoots at the air in her second round.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0305058.pdf

Examples

init()
QDuels_Bob_payoffs(Q$Q11, 5, 0.666666, 0.5, 0, 0, 0.2, 0.7)
Qs <- (Q$Q0+Q$Q1)/sqrt(2)
Psi <- kronecker(Qs, Qs)
QDuels_Bob_payoffs(Psi, 5, 0.666666, 0.5, 0, 0, 0.2, 0.7)

Quantum Fourier Transform

Description

This function performs Quantum Fourier Transform for a given state |y> from the computational basis to the Fourier basis.

Usage

QFT(y)

Arguments

Value

A vector representing the Quantum Fourier transformation of the state |y> from the computational basis to the Fourier basis.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://books.google.co.in/books?id=66TgFp2YqrAC&pg=PA25&redir_esc=y
https://en.wikipedia.org/wiki/Quantum_Fourier_transform

Examples

init()
QFT(5)

Quantum Hawk and Dove game

Description

This function returns the expected payoffs to Alice and Bob with respect to the probabilities p and q. p+q should equal 1 and moves is a list of two possible strategies for each of the players and v, j, D are the value of resource, cost of injury and cost of displaying respectively.

Usage

QHawkDove(p, q, moves, v, j, D)

Arguments

Value

A vector consisting of the expected payoffs to Alice and Bob as its elements calculated according to the probabilities p and q provided as inputs.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0108075.pdf

Examples

init()
moves <- list(Q$I2, sigmaX(Q$I2))
QHawkDove(0, 1, moves, 50, -100, -10)
QHawkDove(0, 0, moves, 50, -100, -10)

Measurement

Description

This function performs a projective measurement of a quantum state n, in the computational basis and plots the corresponding probability distributions of the qubits.

Usage

QMeasure(n)

Arguments

Value

No return value, plots the probability distributions of the qubits after performing a projective measurement of a quantum state n.

References

https://books.google.co.in/books?id=66TgFp2YqrAC&pg=PA25&redir_esc=y
https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics

Examples

init()
QMeasure(Q$Q10110)

Quantum Monty Hall Problem

Description

This function simulates the quantum version of the Monty Hall problem, by taking in Psi_in as the initial quantum state of the game, gamma lying in 0 to pi/2, Ahat and Bhat as the choice operators in SU(3) for Alice and Bob respectively as the inputs. It returns the expected payoffs to Alice and Bob after the end of the game.

Usage

QMontyHall(Psi_in, gamma, Ahat, Bhat)

Arguments

Value

A vector consisting of the expected payoffs to Alice and Bob as its elements depending on the input parameters.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0109035.pdf

Examples

init()
Psi_in <- kronecker(Q$Qt0, (Q$Qt00+Q$Qt11+Q$Qt22)/sqrt(3))
QMontyHall(Psi_in, pi/4, Q$Identity3, Q$Hhat)

Quantum Newcomb's Paradox

Description

This function simulates the quantum version of the Newcomb's Paradox by taking in the choice of the qubit |0> or |1> by the supercomputer Omega and the probability 'probability' with which Alice plays the spin flip operator. It returns the final state of the quantum game along with plotting the probability densities of the qubits of the final state after measurement.

Usage

QNewcomb(Omega, probability)

Arguments

Value

The final state of the quantum game as a vector along with plotting the probability densities of the qubits of the final state after measurement.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0202074.pdf

Examples

init()
QNewcomb(Q$Q0, 0)
QNewcomb(Q$Q1, 0)
QNewcomb(Q$Q1, 0.7)

Quantum Prisoner's Dilemma game

Description

This function returns the expected payoffs to Alice and Bob, with the strategy moves by Alice and Bob as two of the inputs. w, x, y, z are the payoffs to the players corresponding to the choices available to them with the chain of inequalities, z>w>x>y. This function also plots the probability distribution plots of the qubits for one of all the combinations of the strategies of the players.

Usage

QPD(U_Alice, U_Bob, w, x, y, z)

Arguments

Value

A vector consisting of the expected payoffs to Alice and Bob as its elements according to the strategies played by Alice and Bob and also the payoff values.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/0004076.pdf

Examples

init()
QPD(Hadamard(Q$I2), sigmaZ(Q$I2), 3, 1, 0, 5)

Quantum Penny Flip game

Description

This function simulates the Quantum Penny Flip game by taking in the initial state of the game that is set by Alice and the strategies available to Alice and Bob. It returns the final state of the game along with the plot of the probability distribution of the qubits after measurement of the final state.

Usage

QPennyFlip(initial_state, strategies_Alice, strategies_Bob)

Arguments

Value

The final state of the game along with the plot of the probability distribution of the qubits after measurement of the final state by taking in the initial state of the game that is set by Alice and the strategies available to Alice and Bob as the inputs.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/pdf/quant-ph/9804010.pdf

Examples

init()
psi <- (u+d)/sqrt(2)
S1 <- sigmaX(Q$I2)
S2 <- Q$I2
H <- Hadamard(Q$I2)
SA <- list(S1, S2)
SB <- list(H)
QPennyFlip(psi, SA,SB)

Rotation operation about x-axis of the Bloch sphere

Description

This function operates the Rotation gate about the x-axis of the Bloch sphere by an angle theta on a conformable input matrix n.

Usage

Rx(n, theta)

Arguments

Value

A vector or a matrix after operating the Rotation gate about the x-axis of the Bloch sphere, by an angle theta, on a conformable input matrix or a vector n

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
http://www.physics.udel.edu/~msafrono/650/Lecture%204%20-%205.pdf

Examples

init()
Rx(Q$Q0, pi/6)

Rotation operation about y-axis of the Bloch sphere

Description

This function operates the Rotation gate about the y-axis of the Bloch sphere by an angle theta on a conformable input matrix n.

Usage

Ry(n, theta)

Arguments

Value

A vector or a matrix after operating the Rotation gate about the y-axis of the Bloch sphere, by an angle theta, on a conformable input matrix or a vector n.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
http://www.physics.udel.edu/~msafrono/650/Lecture%204%20-%205.pdf

Examples

init()
Ry(Q$Q1, pi/3)

Rotation operation about z-axis of the Bloch sphere

Description

This function operates the Rotation gate about the z-axis of the Bloch sphere by an angle theta on a conformable input matrix n.

Usage

Rz(n, theta)

Arguments

Value

A vector or a matrix after operating the Rotation gate about the z-axis of the Bloch sphere, by an angle theta, on a conformable input matrix or a vector n.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
http://www.physics.udel.edu/~msafrono/650/Lecture%204%20-%205.pdf

Examples

init()
Rz(Q$Q1, pi)

SWAP gate

Description

This function operates the SWAP gate on a conformable input matrix or a vector.

Usage

SWAP(n)

Arguments

Value

A matrix or a vector after performing the SWAP gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
SWAP(Q$I4)
SWAP(Q$Q10)

T gate

Description

This function operates the T gate on a conformable input matrix or a vector.

Usage

T(n)

Arguments

Value

A matrix or a vector after performing the T gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
T(Q$I2)
T(Q$Q_minus)

Hermitian Transpose of the T gate

Description

This function operates the hermitian transpose of the T gate on a conformable input matrix or a vector.

Usage

TDagger(n)

Arguments

Value

A matrix or a vector after performing the operation of the hermitian transpose of the T gate on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
TDagger(Q$I2)
TDagger(Q$Q_plus)

Toffoli gate

Description

This function operates the Toffoli gate on a conformable input matrix or a vector.

Usage

Toffoli(n)

Arguments

Value

A matrix or a vector after performing the Toffoli gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf

Examples

init()
Toffoli(Q$I8)
Toffoli(Q$Q010)

Walsh-Hadamard gate

Description

This function operates the Walsh-Hadamard gate on a conformable input matrix or a vector.

Usage

Walsh(n)

Arguments

Value

A matrix or a vector after performing the Walsh-Hadamard gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
https://arxiv.org/pdf/quant-ph/0506219.pdf
https://en.wikipedia.org/wiki/Hadamard_transform

Examples

init()
Walsh(Q$I2)
Walsh(Q$Q0)

Walsh-Hadamard gate

Description

This function operates the Walsh-16 gate on a conformable input matrix or a vector.

Usage

Walsh16(n)

Arguments

Value

A matrix or a vector after performing the Walsh-16 gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
https://arxiv.org/pdf/quant-ph/0506219.pdf
https://en.wikipedia.org/wiki/Hadamard_transform

Examples

init()
Walsh16(Q$I16)
Walsh16(Q$Q1001)

Walsh-Hadamard gate

Description

This function operates the Walsh-32 gate on a conformable input matrix or a vector.

Usage

Walsh32(n)

Arguments

Value

A matrix or a vector after performing the Walsh-32 gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
https://arxiv.org/pdf/quant-ph/0506219.pdf
https://en.wikipedia.org/wiki/Hadamard_transform

Examples

init()
Walsh32(Q$I32)
Walsh32(Q$Q10011)

Walsh-Hadamard gate

Description

This function operates the Walsh-4 gate on a conformable input matrix or a vector.

Usage

Walsh4(n)

Arguments

Value

A matrix or a vector after performing the Walsh-4 gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
https://arxiv.org/pdf/quant-ph/0506219.pdf
https://en.wikipedia.org/wiki/Hadamard_transform

Examples

init()
Walsh4(Q$I4)
Walsh4(Q$Q10)

Walsh-Hadamard gate

Description

This function operates the Walsh-8 gate on a conformable input matrix or vector.

Usage

Walsh8(n)

Arguments

Value

A matrix or a vector after performing the Walsh-8 gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
https://arxiv.org/pdf/quant-ph/0506219.pdf
https://en.wikipedia.org/wiki/Hadamard_transform

Examples

init()
Walsh8(Q$I8)
Walsh8(Q$Q000)

Number of columns of a vector/matrix

Description

This function counts the number of columns of a vector or a matrix

Usage

col_count(M)

Arguments

Value

An integer that gives the number of columns in a vector or a matrix.

Examples

init()
col_count(Q$Q11)
col_count(Q$lambda4)
col_count(Q$I2)

Initialization

Description

Builds the parameters in the required environment after initialization

Usage

init()

Value

No return value, generates the required variables/parameters.

References

https://arxiv.org/pdf/Quant-ph/0512125.pdf
https://arxiv.org/pdf/0910.4222.pdf
https://arxiv.org/pdf/Quant-ph/9703032.pdf
https://en.wikipedia.org/wiki/Quantum_computing
https://en.wikipedia.org/wiki/Qubit
https://en.wikipedia.org/wiki/Qutrit
https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients_for_SU(3)

Examples

init()
Q$Q110
Q$Qt12
Q$Q_minus
Q$lambda4

Levi-Civita symbol

Description

This function computes the Levi-Civita symbol depending on the permutations of the three inputs, lying in 0 to 2

Usage

levi_civita(i, j, k)

Arguments

Value

0, 1 or -1 after computing the Levi-Civita symbol depending on the permutations of the three inputs 0, 1 and 2

References

https://en.wikipedia.org/wiki/Levi-Civita_symbol

Examples

init()
levi_civita(0, 2, 1)
levi_civita(1, 2, 0)
levi_civita(1, 2, 1)

Number of rows of a vector/matrix

Description

This function counts the number of rows of a vector or a matrix

Usage

row_count(M)

Arguments

Value

An integer that gives the number of rows in a vector or a matrix.

Examples

init()
row_count(Q$Q01)
row_count(Q$lambda5)
row_count(Q$Qt12)

Pauli-X gate

Description

This function operates the Pauli-X gate on a conformable input matrix or a vector.

Usage

sigmaX(n)

Arguments

Value

A matrix or a vector after performing the Pauli-X gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
http://www.physics.udel.edu/~msafrono/650/Lecture%204%20-%205.pdf

Examples

init()
sigmaX(Q$I2)
sigmaX(Hadamard(Q$I2))
sigmaX(Q$Q1)

Pauli-Y gate

Description

This function operates the Pauli-Y gate on a conformable input matrix or a vector.

Usage

sigmaY(n)

Arguments

Value

A matrix or a vector after performing the Pauli-Y gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
http://www.physics.udel.edu/~msafrono/650/Lecture%204%20-%205.pdf

Examples

init()
sigmaY(Q$I2)
sigmaY(Hadamard(Q$I2))
sigmaY(Q$Q0)

Pauli-Z gate

Description

This function operates the Pauli-Z gate on a conformable input matrix or a vector.

Usage

sigmaZ(n)

Arguments

Value

A matrix or a vector after performing the Pauli-Z gate operation on a conformable input matrix or a vector.

References

https://en.wikipedia.org/wiki/Quantum_logic_gate
http://www2.optics.rochester.edu/~stroud/presentations/muthukrishnan991/LogicGates.pdf
http://www.physics.udel.edu/~msafrono/650/Lecture%204%20-%205.pdf

Examples

init()
sigmaZ(Q$I2)
sigmaZ(Hadamard(Q$I2))
sigmaZ(Q$Q0)