Welcome to QutiePy’s documentation!¶
Package Description¶
QutiePy is a python3 package designed to provide an easy and practical toolset for simulated quantum computing aimed users with any experience level in quantum theory and a working knowledge of pythonic OOP.
QutiePy is currently a work-in-progress and is being developed by a first-timer. Please report any issues or suggestions on the GitHub repo at <https://github.com/franklinscudder/QutiePy/issues>.
Reference¶
General Notes and Conventions¶
QutiePy assumes that the first bit in a register (reg[0]) is the least significant bit. Thus, if a register is observed as [0,0,1] the resulting output would be 4.
For default controlled gates, the first bit (LSB) is the control bit.
The names used in the package use camelCase as much as possible with the caveat that ‘N’ as in ‘number of’ is capitalised and treated as a word itself (NBits, NStates).
For a pretty representation of a register, just call print(reg).
When calling a gate on a register, the result is returned in a new object, the original register is not modified in any way.
All gate objects implement a __call__ method and are intended to be applied to a register in this way:
# A Hadamard gate
h = hadamard(4)
# A 4-bit register
r = register(4)
# Applying the gate to the register
result = h(r)
Gates can be compounded is series as a new object.
a(b(c))will return a compoundGate object if a, b and c are gates.If reproducability is required, setSeed() can be used to set the RNG seed to a given string so that each run will produce the same results.
QutiePy¶
qutiepy.py¶
The main file containing the core components of QutiePy, including classes for gates and the register class as well as a few functions which handle on gate and register objects:
- class qutiepy.register(NBits)¶
Bases:
objectN-bit quantum register. The initial state is (1+0j)|0>.
- Parameters
NBits (int) – Size of the register in bits.
- NBits¶
Number of bits in the register.
- Type
int
- NStates¶
Number of states the register can occupy (2^NBits).
- Type
int
- amps¶
The complex probability amplitudes of each state of the register.
- Type
list
- probabilities()¶
Return the probability associated with observing each state.
- Returns
probabilities – The probabilities p(X=x_i) of observing each state.
- Return type
numpy array
- observe(bit=- 1, collapseStates=True, fmt='int')¶
‘Observe’ the register and return an integer representation of the observed state according to the probability amplitudes.
If a bit argument is supplied, only that bit will be observed and it’s state returned as an integer (1 or 0).
If collapseStates=True, adjust the amplitudes to reflect the collapsed state.
- Parameters
bit (int, optional) – The index of the bit to be observed.
collapseStates (bool, optional) – Flag to set whether probability amplitudes will be affected by this observation.
fmt (string, optional) – One of “int” (default), “bin” or “hex”
- Returns
state – The observed state of the register or bit.
- Return type
int or string
- prod(B)¶
Return the tensor product of self and B, ‘Joining’ two registers into a single larger register with self at the MSB and ‘B’ at the LSB.
- Parameters
B (register) – The register to be appended to self.
- Returns
result – The resulting joined register.
- Return type
See also
prodEquivalent function
- bloch(eps=1e-12)¶
Return the angles theta and phi used in the Bloch sphere representation of a single qubit register (eps is used to avoid infinite and NaN results, set to 0 to disable).
- Returns
theta (float) – The angle theta = 2*arccos(amps[0]).
phi (float) – The angle phi = Ln[(amps[1]+eps)/(sin(theta/2)+eps)].
- density()¶
Return the density matrix of the register.
- Returns
density – The density matrix.
- Return type
numpy array
- reducedPurities()¶
Return the reduced purity of each bit of the register, i.e.: Tr[Tr_i(D)^2] where D is the full density matrix of the register and Tr_i is the partial trace over the subspace of bit index ‘i’.
- Returns
purities – The reduced purity of each qubit in the register.
- Return type
numpy array
- setAmps(amps)¶
Manually set the qubit probability amplitudes in-place, ensuring they remain properly normalised.
- Parameters
amps (iterable) – The relative complex amplitudes to be applied to the register with normalisation.
- qutiepy.prod(regA, regB)¶
‘Join’ two registers into a single larger register with regA at the MSB and regB at the LSB by performing the Kronecker product between their state vectors |A>|B> = |AB>.
- Parameters
- Returns
result – The resulting joined register.
- Return type
See also
register.prodEquivalent class method.
- class qutiepy.genericGate(NBits)¶
Bases:
objectBase class for callable quantum logic gates.
- Parameters
NBits (int) – Size of the registers that the gate will take as input/output.
- NBits¶
Number of bits that the gate takes as input/output.
- Type
int
- matrix¶
The 2^NBits by 2^NBits matrix representation of the gate.
- Type
2D numpy array
- NControlBits¶
Indicates whether a control bit has been added using .addControlBits().
- Type
bool
- isInverse¶
Indicates whether the object has been created by a call to H().
- Type
bool
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- class qutiepy.compoundGate(NBits)¶
Bases:
qutiepy.genericGateA class returned when gates are compounded. See genericGate attributes.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.hadamard(NBits, skipBits=[])¶
Bases:
qutiepy.genericGateA callable hadamard gate object.
- Parameters
NBits (int) – Number of bits that the gate takes as input/output.
skipBits (list of int, optional, deprecated) – Indices of bits in a register that this gate will not operate on.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.phaseShift(NBits, phi, skipBits=[])¶
Bases:
qutiepy.genericGateA callable phase-shift gate object.
- Parameters
NBits (int) – Number of bits that the gate takes as input/output.
phi (float) – The phase angle through which to shift the amplitudes.
skipBits (list of int, optional, deprecated) – Indices of bits in a register that this gate will not operate on.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.pauliX(NBits, skipBits=[])¶
Bases:
qutiepy.genericGateA callable Pauli-X gate object, AKA the quantum NOT gate.
- Parameters
NBits (int) – Number of bits that the gate takes as input/output.
skipBits (list of int, optional) – Indices of bits in a register that this gate will not operate on.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.pauliY(NBits, skipBits=[])¶
Bases:
qutiepy.genericGateA callable Pauli-Y gate object.
- Parameters
NBits (int) – Number of bits that the gate takes as input/output.
skipBits (list of int, optional, deprecated) – Indices of bits in a register that this gate will not operate on.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.pauliZ(NBits, skipBits=[])¶
Bases:
qutiepy.phaseShiftA callable Pauli-Z gate object.
- Parameters
NBits (int) – Number of bits that the gate takes as input/output.
skipBits (list of int, optional, deprecated) – Indices of bits in a register that this gate will not operate on.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.cNot¶
Bases:
qutiepy.genericGateA callable CNOT gate object.
The first bit (LSB) in the register on which this gate is called is the control bit.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.ccNot¶
Bases:
qutiepy.genericGateA callable CCNOT (Toffoli) gate object.
The first two bits (LSBs) in the register on which this gate is called are the control bits.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.swap¶
Bases:
qutiepy.genericGateA callable SWAP gate object. For two qubits in a register (A,B), outputs (B,A).
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.sqrtSwap¶
Bases:
qutiepy.genericGateA callable sqrt(SWAP) gate object.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.sqrtNot(NBits, skipBits=[])¶
Bases:
qutiepy.genericGateA callable sqrt(not) or sqrt(Pauli-X) gate object.
- Parameters
NBits (int) – Number of bits that the gate takes as input/output.
skipBits (list of int, optional, deprecated) – Indices of bits in a register that this gate will not operate on.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.fredkin¶
Bases:
qutiepy.genericGateA callable Fredkin (CCSWAP) gate object.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.identity(NBits)¶
Bases:
qutiepy.genericGateA callable identity gate object.
- Parameters
NBits (int) – Number of bits that the gate takes as input/output.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.QFT(NBits)¶
Bases:
qutiepy.genericGateA callable quantum Fourier transform (QFT) gate object.
- Parameters
NBits (int) – Number of bits that the gate takes as input/output.
omega (complex) –
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- class qutiepy.parallelGate(gates)¶
Bases:
qutiepy.genericGateA gate class to combine gates in parallel.
- Parameters
gates (array of gate objects) – The gates to be combined in parallel, with the first gate acting on the LSB of an applied register.
- H()¶
- Return an inverse copy of self, i.e. a gate whose matrix representation is
the Hermitian adjoint of self.matrix.
- Returns
gate – The gate performing the inverse operation of self.
- Return type
Gate Object
- addControlBits(controlOffsets)¶
Add control bits to this single bit gate.
- Parameters
controlOffsets (array of int != 0) – The bit index offsets relative to this gate to control off of.
- Returns
result – The resulting controlled gate.
- Return type
gate object
- inverse()¶
Alias of self.H().
See also
genericGate.HThis method maps to self.H()
- qutiepy.serialGate(gates)¶
Combine an iterable of gate objects in series.
- Parameters
gates (iterable of gate objects) – The gate objects to be combined in serial. The operator to be applied first should be at index 0.
- Returns
comp – The result of combining the supplied operators in series.
- Return type
compoundGate object
- qutiepy.setSeed(seed)¶
Set the RNG seed for reproducibility.
- Parameters
seed (string) – The seed to be used by the RNG.
- Returns
result – True if successful.
- Return type
bool
Usage Example¶
This script demonstrates the basic usage of the module, constructing the Bell state ‘Phi+’. A Bell state is a pair of qubits which exhibit maximal entanglement. They are the simplest example of this phenomenon.
This script can be found in the examples folder of your package installation.
import qutiepy as qu
# Create two 1-qubit registers, initialised to 0 by default
r1 = qu.register(1)
r2 = qu.register(1)
# Create a Hadamard and a CNOT gate
h = qu.hadamard(1)
cn = qu.cNot()
# Apply the hadamard operation to r1
r1 = h(r1)
# 'Join' the two bits together into a single register
r = qu.prod(r1,r2)
# Apply the CNOT gate to the new register
r = cn(r)
# Analyse the resulting Bell state
print("The state vector of r:")
print(r)
print()
print("The probabilities of observing each state of r:")
print(r.probabilities())
print()
print("The reduced purities of each qubit in r (0.5 = maximally entangled, 1 = fully unentangled):")
print(r.reducedPurities())
print()
print("The result of observing ten versions of the Bell state r:")
for i in range(10):
print(r.observe(collapseStates=False)),
Entanglement, Parallel Gates and skipBits¶
Entanglement in QutiePy is handled by keeping entangled qubits in the same register as each other. Thus, once registers are combined using prod(), they cannot
be separated. The best way to apply a gate operation to only some bits in a register, you can use a parallelGate object composed of any operations you wish to apply to the gate,
along with identity gates acting on bits you wish to remain unaffected.
A gate can also be specified with a list skipBits of qubit indices to be left
unaltered by the gate. This is no longer the recommended method and is only retained for compatability reasons.
The example below shows how this can be used to transform a register which has been placed in a state of entanglement.
