times-ccnotgate-qstate

Description

Applies a CCNOT (or toffoli) gate to a quantum state.

Usage

## S4 method for signature 'ccnotgate,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-ccqgate-qstate

Description

Applies a twice controlled single qubit gate to a quantum state.

Usage

## S4 method for signature 'ccqgate,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-cnotgate-qstate

Description

Applies a CNOT gate to a quantum state.

Usage

## S4 method for signature 'cnotgate,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-cnqgate-qstate

Description

Applies n-fold controlled single qubit gate to a quantum state.

Usage

## S4 method for signature 'cnqgate,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-number-qstate

Description

Multiplies a quantum gate by a global (phase) factor.

Usage

## S4 method for signature 'complex,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-cqgate-qstate

Description

Applies a controlled single qubit gate to a quantum state.

Usage

## S4 method for signature 'cqgate,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-cswapgate-qstate

Description

Applies a CSWAP gate to a quantum state.

Usage

## S4 method for signature 'cswapgate,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-matrix-qstate

Description

Applies a single qubit gate to a quantum state.

Usage

## S4 method for signature 'matrix,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-sqgate-qstate

Description

Applies a single qubit gate to a quantum state.

Usage

## S4 method for signature 'sqgate,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

times-swapgate-qstate

Description

Applies a SWAP gate to a quantum state.

Usage

## S4 method for signature 'swapgate,qstate'
e1 * e2

Arguments

Value

An object of S4 class 'qstate'

The CCNOT or toffoli gate

Description

The CCNOT or toffoli gate

Usage

CCNOT(bits = c(1, 2, 3))

toffoli(bits = c(1, 2, 3))

Arguments

Value

An S4 class 'ccnotgate' object is returned

The CNOT gate

Description

The CNOT gate

Usage

CNOT(bits = c(1, 2))

Arguments

Value

An S4 class 'cnotgate' object is returned

The CSWAP or Fredkin gate

Description

The CSWAP or Fredkin gate

Usage

CSWAP(bits = c(1, 2, 3))

fredkin(bits = c(1, 2, 3))

Arguments

Value

An S4 class 'cswapgate' object is returned

The Hadarmard gate

Description

The Hadarmard gate

Usage

H(bit)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- qstate(nbits=2)
z <- H(1) * x
z

The identity gate

Description

The identity gate

Usage

Id(bit)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- qstate(nbits=2)
z <- Id(1) * x
z

The Ri gate

Description

The Ri gate

Usage

Ri(bit, i, sign = +1)

Arguments

Details

Implements the gate ( 1 0 ) ( 0 exp(+-2pi1i/2^i) )

If 'sign < 0', the inverse of the exponential is used. This gate is up to global phase identical with the 'Rz' gate with specific values of the angle.

Value

An S4 class 'sqgate' object is returned

Examples

x <- X(1) * qstate(nbits=2)
z <- Ri(1, i=2) * x
z

The Rx gate

Description

The Rx gate

Usage

Rx(bit, theta = 0)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- qstate(nbits=2)
z <- Rx(1, pi/4) * x
z

The Ry gate

Description

The Ry gate

Usage

Ry(bit, theta = 0)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- qstate(nbits=2)
z <- Ry(1, pi/4) * x
z

The Rz gate

Description

The Rz gate

Usage

Rz(bit, theta = 0)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- qstate(nbits=2)
z <- Rz(1, pi/4) * x
z

The S gate

Description

The S gate

Usage

S(bit)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- X(1) * qstate(nbits=2)
z <- S(1) * x
z

The SWAP gate

Description

The SWAP gate

Usage

SWAP(bits = c(1, 2))

Arguments

Value

An S4 class 'swapgate' object is returned

The Tgate gate

Description

The Tgate gate

Usage

Tgate(bit)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- X(1)*qstate(nbits=2)
z <- Tgate(1) * x
z

The X gate

Description

The X gate

Usage

X(bit)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- qstate(nbits=2)
z <- X(1) * x
z

The Y gate

Description

The Y gate

Usage

Y(bit)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- qstate(nbits=2)
z <- Y(1) * x
z

The Z gate

Description

The Z gate

Usage

Z(bit)

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- X(1) * qstate(nbits=2)
z <- Z(1) * x
z

The CCNOT gate

Description

This class represents a generic CNOT gate

Slots

bits

Integer vector of length 2. First two bits are the control bits, third the target bit.

Examples

x <- qstate(nbits=3)
z <- CCNOT(c(1,2,3)) * (H(1) * x)

A twice controlled single qubit gate

Description

This class represents a generic controlled gate

Details

The qubits are counted from 1 to nbits starting with the least significant bit.

Slots

bits

Integer. Integer vector of bits. The first two are the control bits, the third the target bit.

gate

sqgate. The single qubit gate.

Examples

x <- H(1) * qstate(nbits=3)
## application of the CCX (CCNOT) gate to bit 1,2,3
z <- ccqgate(bits=c(1L, 2L, 3L), gate=X(3L)) * x
z
## the same, but differently implemented
z <- CCNOT(c(1,2,3)) * x
z

The CNOT gate

Description

This class represents a generic CNOT gate

Slots

bits

Integer vector of length 2. First bit is the control bit, second the target bit.

Examples

x <- qstate(nbits=2)
## A Bell state
z <- CNOT(c(1,2)) * (H(1) * x)

n-fold controlled single qubit gate

Description

This class represents a generic n-fold controlled gate

Details

The qubits are counted from 1 to nbits starting with the least significant bit.

Slots

cbits

Integer. Integer vector of control bits.

tbit

Integer. Target bit.

gate

sqgate. The single qubit gate.

inverse

Logical. Boolean vector of same length as cbits. If TRUE, the corresponding control bit is negated.

Examples

x <- H(1) * qstate(nbits=3)
## application of the CCX (CCNOT) gate to bits 1,2 and 3
z <- cnqgate(cbits=c(1L, 2L), tbit=3L, gate=X(3L)) * x
z
## the same, but differently implemented
z <- CCNOT(c(1,2,3)) * x
z

cqft

Description

performs the controlled quantum Fourier Trafo on the qstate x and the specified list of qubits.

Usage

cqft(c, x, inverse = FALSE, bits)

Arguments

Details

Controlled Quantum Fourier Trafo

The Fourier Trafo is defined as

|j> -> 1/sqrt(N) sum_k=0^N_1 exp(2 pi i j k/N) |k>

the inverse with the oposite sign in the exponential.

Value

a qstate object with the quantum Fourier trafo of input x.

Examples

x <- qstate(3)
y <- cqft(1, x)
z <- cqft(1, y, inverse=TRUE)

A controlled single qubit gate

Description

This class represents a generic controlled gate

Details

The qubits are counted from 1 to nbits starting with the least significant bit.

Slots

bits

Integer. Integer vector of bits. The first is the control bit, the second the target bit.

gate

sqgate. The single qubit gate.

Examples

x <- H(1) * qstate(nbits=2)
## application of the CX (CNOT) gate to bit 1,2
z <- cqgate(bits=c(1L, 2L), gate=X(2L)) * x
z
## the same as, but differently implemented
z <- CNOT(c(1,2)) * x
z

The CSWAP gate

Description

This class represents a generic SWAP gate, also called Fredkin gate

Slots

bits

Integer vector of length 2. First two bits are the control bits, third the target bit.

Examples

x <- qstate(nbits=3)
z <- CSWAP(c(1,2,3)) * (H(1) * x)

export2qiskit

Description

export a circuit to IBM's qiskit python format. Note that only gates can be exported where the correspondence in qiskit is known and well defined. Qiskit can then be used for IBM's QASM to run on real hardware.

Usage

export2qiskit(object, varname = "qc", filename = "circuit.py",
  append = FALSE, import = FALSE)

Arguments

Details

Export to IBM's Qiskit

Currently the following gates can be exported: H, X, Y, Z, S, Tgate, Rz, Rx, Ry, CNOT, SWAP, CCNOT, CSWAP, measure.

note that only standard gates can be exported, not self defined ones. The function will draw a warning in case a gate cannot be exported and indicate it in the output file.

Value

nothing is returned, but a file is created.

References

https://qiskit.org/documentation/

Examples

x <- qstate(2)
x <- H(1) * x
x <- X(2) * x
x <- CNOT(c(1,2)) * x
export2qiskit(measure(x,1)$psi)
cat(readLines("circuit.py"), sep = '\n')
file.remove("circuit.py")

genComputationalBasis

Description

function to generate the basis strings for given number of bits

Usage

genComputationalBasis(nbits, collapse = "")

Arguments

Value

a character vector of length 2^nbits

Examples

genComputationalBasis(4)
genComputationalBasis(2, collapse=">|")

genNoise

Description

function to generate the noise list

Usage

genNoise(nbits, p = 0, bits = 1:nbits, error = "any", ...)

Arguments

Details

See function noise for details.

Value

a list containing p, bits, error and args

Examples

genNoise(4)
genNoise(2, p=1, error="small", sigma=0.1)

genStateNumber

Description

function to generate the bit representation for a specific basis state

Usage

genStateNumber(int, nbits)

Arguments

Value

a integer vector of length nbits

Examples

genStateNumber(5, 4)
genStateNumber(2, 2)

genStateString

Description

function to generate the string for a specific basis state

Usage

genStateString(int, nbits, collapse = "")

Arguments

Value

a character

Examples

genStateString(5, 4)
genStateString(2, 2, collapse=">|")

Plot the histogram of a quantum measurement

Description

Plot the histogram of a quantum measurement

Usage

## S3 method for class 'measurement'
hist(x, only.nonzero = TRUE, by.name = only.nonzero,
  freq = TRUE, ...)

Arguments

Value

No return value.

is.bitset

Description

checks whether or not a bit is set in target

Usage

is.bitset(x, bit)

Arguments

Value

a boolean vector

Method measure

Description

performs a masurement on a qstate object.

Usage

measure(e1, bit = NA, repetitions = NA)

## S4 method for signature 'qstate'
measure(e1, bit = NA, repetitions = 1)

Arguments

Details

measure(e1, bit, repetitions) performs repetitions many projections/measurements of the qubit bit. If bit is not given explicitly, all qubits are projected.

Value

measure(e1, bit, repetitions) returns a list with the measured bit, the number of repetitions, the probability distribution of all states prob and the results vector value. If all bits are measured, the basis is added to the list as basis. The collapsed state is stored as psi if exactly one measurement is performed. In the case of a single qubit measurement value is of length repetitions and contains all the results of this projection. Otherwise value is of length 2^nbits and it contains the counts how often each state has been obtained.

Examples

## measure the separate bits
x <- H(1) * (H(2) * qstate(nbits=2))
summary(measure(x, bit=1))
hist(measure(x, rep=100))

A noise gate

Description

A noise gate

Usage

noise(bit, p = 1, error = "any", type = "ERR", args = list())

Arguments

Value

An S4 class 'sqgate' object is returned

Examples

x <- noise(1, error="X") * qstate(nbits=2)
x
y <- noise(2, p=0.5) * x
y
z <- noise(2, error="small", args=list(sigma=0.1)) * x
z

normalise

Description

Normalises a complex vector to 1

Usage

normalise(x)

Arguments

Value

Returns the normalised complex valued vector

phase_estimation

Description

phase estimation algorithm

Usage

phase_estimation(bitmask, FUN, x, ...)

Arguments

Examples

## NOT^k = Id if k even
cnotwrapper <- function(c, j, x, t) {
  if(j == 1) return(CNOT(c(c, t)) * x)
  return(Id(t) * x)
}
x <- X(1) * qstate(3)
## X has eigenvalues lambda=1 and lambda=-1
## thus phases 0 and 1/2
x <- phase_estimation(bitmas=c(2:3), FUN=cnotwrapper, x=x, t=1)
x

plot-qstate

Description

Plots a circuit corresponding to a qstate object

Usage

## S4 method for signature 'qstate,missing'
plot(x, y, ...)

Arguments

Value

nothing is returned, but a plot created

Examples

x <- qstate(2)
y <- H(1) * x
z <- CNOT(c(1,2)) * y
plot(z)

qft

Description

performs the quantum Fourier Trafo on the qstate x and the specified list of qubits.

Usage

qft(x, inverse = FALSE, bits)

Arguments

Details

Quantum Fourier Trafo

The Fourier Trafo is defined as

|j> -> 1/sqrt(N) sum_k=0^N_1 exp(2 pi i j k/N) |k>

the inverse with the oposite sign in the exponential.

Value

a qstate object with the quantum Fourier trafo of input x.

Examples

x <- qstate(3)
y <- qft(x)
z <- qft(y, inverse=TRUE)

The qsimulatR Package

Description

A simulator for a quantum computer

Details

A quantum computer simulator framework. General single qubit gates and general controlled single qubit gates can be easily defined. For convenience, it currently directly provides most common gates (X, Y, Z, H, Z, S, T, Rx, Ry, Rz, CNOT, SWAP, toffoli or CCNOT, CSWAP). 'qsimulatR' supports plotting of circuits and is able to export circuits into IBM's 'Qiskit' python package, which can be run on IBM's real quantum hardware. 'qsimulatR' currently works for up to 24 qubits (a virtual restriction, which can be lifted).

Author(s)

Johann Ostemeyer, Carsten Urbach, urbach@hiskp.uni-bonn.de

The qstate class

Description

This class represents a quantum state

Details

The qubits are counted from 1 to nbits starting with the least significant bit.

Slots

nbits

The number of qubits

coefs

The 2^nbits complex valued vector of coefficients

basis

String or vector of strings. A single string will be interpreted as the collapse-parameter in genComputationalBasis. A vector of length 2^nbits yields the basis directly.

noise

List containing the probability p some noise is applied to one of the bits after a gate application, the model error of this noise and further arguments args to be passed to the function noise. See function noise for details. The list noise can be generated with genNoise.

circuit

List containing the number of non-quantum bits ncbits and a list of gates gatelist applied to the original state. Filled automatically as gates are applied, required for plotting.

Examples

x <- qstate(nbits=2)
x

x <- qstate(nbits=2, coefs=as.complex(sqrt(rep(0.25, 4))), basis=",")
x

x <- qstate(nbits=1, coefs=as.complex(sqrt(rep(0.5, 2))), basis=c("|dead>", "|alive>"))
x

x <- qstate(nbits=2, noise=genNoise(nbits=2, p=1))
Id(2) * x

x <- qstate(nbits=3, noise=genNoise(p=1, bits=1:2, error="small", sigma=0.1))
Id(2) * x

A single qubit gate

Description

This class represents a generic single qubit gate

Details

The qubits are counted from 1 to nbits starting with the least significant bit.

Slots

bit

Integer. The single bit to act on.

M

complex valued array. The 2x2 matrix representing the gate

type

a character vector representing the type of gate

Examples

x <- qstate(nbits=2)
## application of the X (NOT) gate to bit 1
z <- sqgate(bit=1L, M=array(as.complex(c(0,1,1,0)), dim=c(2,2))) * x
z

Summarize a quantum measurement

Description

Summarize a quantum measurement

Usage

## S3 method for class 'measurement'
summary(object, ...)

Arguments

Value

No return value.

The SWAP gate

Description

This class represents a generic SWAP gate

Slots

bits

Integer vector of length 2. The two bits to swap.

Examples

x <- H(1) * qstate(nbits=2)
z <- SWAP(c(1,2)) * (H(1) * x)

Method truth.table

Description

Method truth.table

Usage

truth.table(e1, nbits, bits, ...)

Arguments

Details

calculates the quantum truth table of the gate e1. If a basis state is transformed to a superposition of basis states by the gate, the result is 'NA'.

Value

returns a data.frame containing the truth table. Each row corresponds to one input-output combination. Each column to one specific bit.

Examples

## truth table for a single bit gate
truth.table(X, 1)
## for a 2-bit gate
truth.table(CNOT, 2)
## for a 2-bit gate with reversed controll and target bits
truth.table(CNOT, bits=2:1)
## for a general controlled gate
truth.table(cqgate, 2, gate=H(2))
## for an arbitrary circuit (here a swap implementation using only CNOTs)
myswap <- function(bits){ function(x){ CNOT(bits) * (CNOT(rev(bits)) * (CNOT(bits) * x))}}
truth.table(myswap, 2)