Operators in Circuit Simulations

Import with using QuantumClifford.Experimental.NoisyCircuits.

Too see a condensed list of all operations check out the API docs.

Unitary Gates

We distinguish between symbolic gates like sCNOT that have specialized (fast) apply! methods (usually just for single and two qubit gates) and general tableau representation of gates like CliffordOperator that can represent any multi-qubit gate.

Predefined unitary gates are available, like sCNOT, sHadamard, etc.

[sCNOT(2,4),sHadamard(2),sCPHASE(1,3),sSWAP(2,4)]

Any arbitrary tableaux can be used as a gate too.

They can be specified by giving a Clifford operator tableaux and the indices on which it acts (particularly useful for gates acting on a small part of a circuit):

SparseGate(tCNOT, [2,4])

The Clifford operator tableaux can be completely arbitrary.

SparseGate(random_clifford(3), [2,4,5])

If the Clifford operator acts on all qubits, we do not need to specify indices, just use the operator.

Noisy Gates

Each gate can be followed by noise applied to the qubits on which it has acted. This is done by wrapping the given gate into a NoisyGate

ε = 0.03 # X/Y/Z error probability
noise = UnbiasedUncorrelatedNoise(ε)
noisy_gate = NoisyGate(SparseGate(tCNOT, [2,4]), noise)

In circuit diagrams the noise is not depicted, but after each application of the gate defined in noisy_gate, a noise operator will also be applied. The example above is of Pauli Depolarization implemented by UnbiasedUncorrelatedNoise.

One can also apply only the noise operator by using NoiseOp which acts only on specified qubits. Or alternatively, one can use NoiseOpAll in order to apply noise to all qubits.

[NoiseOp(noise, [4,5]), NoiseOpAll(noise)]

Coincidence Measurements

Global parity measurements involving single-qubit projections and classical communication are implemented with BellMeasurement. One needs to specify the axes of measurement and the qubits being measured. If the parity is trivial, the circuit continues, if the parity is non-trivial, the circuit ends and reports a detected failure. This operator is frequently used in the simulation of entanglement purification.

BellMeasurement([sMX(1), sMY(3), sMZ(4)])

There is also NoisyBellMeasurement that takes the bit-flip probability of a single-qubit measurement as a third argument.

Stabilizer Measurements

A measurement over one or more qubits can also be performed, e.g., a direct stabilizer measurement on multiple qubits without the use of ancillary qubits. When applied to multiple qubits, this differs from BellMeasurement as it performs a single projection, unlike BellMeasurement which performs a separate projection for every single qubit involved. This measurement is implemented in PauliMeasurement which requires a Pauli operator on which to project and the index of the classical bit in which to store the result. Alternatively, there are sMX, sMZ, sMY if you are measuring a single qubit.

[PauliMeasurement(P"XYZ", 1), sMZ(2, 2)]

TODO: SparseMeasurement, NoisyMeasurement

Verification Operations

At the end of many circuits one might want to check whether they performed correctly. The VerifyOp operation corresponds to an unphysical perfect tomographic operation, checking whether the state of the qubits at the given indices is indeed what is expected. If it is, the operation reports a success, otherwise it reports an undetected error.

desired_state = random_stabilizer(5)
qubit_indices = [1,2,3,4,7]
VerifyOp(desired_state, qubit_indices)

Reset Operations

The Reset operations lets you trace out the specified qubits and set their state to a specific tableau.

new_state = random_stabilizer(3)
qubit_indices = [1,2,3]
Reset(new_state, qubit_indices)

It can be done anywhere in a circuit, not just at the beginning.

Gates Conditioned on Classical Bits

ConditionalGate is a conditional gate that performs one of two provided gates, depending on the value of a given classical bit.

DecisionGate is a conditional gate that performs one of the supplied gates, depending on the output of decisionfunction applied to the entire classical bit register.

gate1 = SparseGate(tCNOT,   [1,2])
gate2 = sCPHASE(1,2)
gate3 = SparseGate(tSWAP,   [1,3])
cg = ConditionalGate(gate1, gate2, 2)
dg = DecisionGate([gate1,gate2,gate3], bit_register->1) # it will always perform gate1
[sMX(4,1), sMZ(5,2), cg, dg]

TODO: Split ConditionalGate into quantum conditional and classical conditional