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| # [Operations - Gates, Measurements, and More](@id all-operations) | ||
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| ```@meta | ||
| DocTestSetup = quote | ||
| using QuantumClifford | ||
| using StableRNGs | ||
| rng = StableRNG(42) | ||
| end | ||
| ``` | ||
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| ## [Operations](@id all-operations) | ||
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| Acting on quantum states can be performed either: | ||
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| - In a "linear algebra" language, where the operators are [Clifford operators](@ref CliffordOperator) represented as tableaux. This is an explicitly deterministic lower-level interface, which provides a great deal of control over how tableaux are manipulated. | ||
| - Or in a "circuit" language, where the operators (and measurements and noise) are represented as circuit gates. This is a higher-level interface in which the outcome of an operation can be stochastic. Particularly useful for [Monte Carlo simulations](@ref noisycircuits_mc) and [Perturbative Expansion Symbolic Results](@ref noisycircuits_perturb) | ||
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| In the circuit language, all operations can be applied on a state with the [`apply!`](@ref) function. Whether they are deterministic and their computational complexity is listed in the table below. A list of lower-level "linear algebra style" functions for more control over how an operation is performed is also given. | ||
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| ```@raw html | ||
| <style> | ||
| td > code { | ||
| white-space: pre; | ||
| } | ||
| </style> | ||
| ``` | ||
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| | Type | Deterministic | 𝒪(nˣ) | Low-level functions | ||
| |:--|:-:|---|---| | ||
| |`AbstractOperation `| | | | | ||
| |` ├─ AbstractCliffordOperator `| | | | | ||
| |` │ ├─ AbstractSymbolicOperator `| | | | | ||
| |` │ │ ├─ AbstractSingleQubitOperator`| | | | | ||
| |` │ │ │ ├─ SingleQubitOperator `|✔️ | n | | | ||
| |` │ │ │ ├─ sHadamard `|✔️ | n | | | ||
| |` │ │ │ ├─ sId1 `|✔️ | n | | | ||
| |` │ │ │ ├─ sInvPhase `|✔️ | n | | | ||
| |` │ │ │ ├─ sPhase `|✔️ | n | | | ||
| |` │ │ │ ├─ sX `|✔️ | n | | | ||
| |` │ │ │ ├─ sY `|✔️ | n | | | ||
| |` │ │ │ └─ sZ `|✔️ | n | | | ||
| |` │ │ └─ AbstractTwoQubitOperator `| | | | | ||
| |` │ │ ├─ sCNOT `|✔️ | n | | | ||
| |` │ │ ├─ sCPHASE `|✔️ | n | | | ||
| |` │ │ └─ sSWAP `|✔️ | n | | | ||
| |` │ │ `| | | | | ||
| |` │ ├─ CliffordOperator `|✔️ | n³| | | ||
| |` │ ├─ PauliOperator `|✔️ | n²| | | ||
| |` │ └─ SparseGate `|✔️ |kn²| | | ||
| |` ├─ AbstractMeasurement `| | | | | ||
| |` │ ├─ PauliMeasurement `|❌ | n²| [`project!`](@ref), [`projectrand!`](@ref) | | ||
| |` │ ├─ sMX `|❌ | n²| [`projectX!`](@ref) | | ||
| |` │ ├─ sMY `|❌ | n²| [`projectY!`](@ref) | | ||
| |` │ └─ sMZ `|❌ | n²| [`projectZ!`](@ref) | | ||
| |` │ `| | | | | ||
| |` ├─ BellMeasurement `|❌ | n²| | | ||
| |` ├─ NoiseOp `|❌ | ?| [`applynoise!`](@ref) | | ||
| |` ├─ NoiseOpAll `|❌ | ?| [`applynoise!`](@ref) | | ||
| |` ├─ NoisyGate `|❌ | ?| [`applynoise!`](@ref) | | ||
| |` └─ Reset `|✔️ |kn²| [`reset_qubits!`](@ref)| | ||
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| ## Details of Operations Supported by [`apply!`](@ref) | ||
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| ### Unitary Gates | ||
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| We distinguish between symbolic gates like [`sCNOT`](@ref) that have specialized (fast) `apply!` methods (usually just for single and two qubit gates) and general tableau representation of gates like [`CliffordOperator`](@ref) that can represent any multi-qubit gate. | ||
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| Predefined unitary gates are available, like [`sCNOT`](@ref), [`sHadamard`](@ref), etc. | ||
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| ```@example 1 | ||
| using QuantumClifford # hide | ||
| using QuantumClifford.Experimental.NoisyCircuits # hide | ||
| using QuantumCliffordPlots # hide | ||
| [sCNOT(2,4),sHadamard(2),sCPHASE(1,3),sSWAP(2,4)] | ||
| ``` | ||
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| Any arbitrary tableaux can be used as a gate too. | ||
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| 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): | ||
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| ```@example 1 | ||
| using QuantumClifford # hide | ||
| using QuantumClifford.Experimental.NoisyCircuits # hide | ||
| using QuantumCliffordPlots # hide | ||
| SparseGate(tCNOT, [2,4]) | ||
| ``` | ||
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| The Clifford operator tableaux can be completely arbitrary. | ||
| ```@example 1 | ||
| SparseGate(random_clifford(3), [2,4,5]) | ||
| ``` | ||
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| If the Clifford operator acts on all qubits, we do not need to specify indices, just use the operator. | ||
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| ### Noisy Gates | ||
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| 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`](@ref) | ||
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| ```@example 1 | ||
| ε = 0.03 # X/Y/Z error probability | ||
| noise = UnbiasedUncorrelatedNoise(ε) | ||
| noisy_gate = NoisyGate(SparseGate(tCNOT, [2,4]), noise) | ||
| ``` | ||
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| 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`](@ref). | ||
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| One can also apply only the noise operator by using [`NoiseOp`](@ref) which acts only on specified qubits. Or alternatively, one can use [`NoiseOpAll`](@ref) in order to apply noise to all qubits. | ||
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| ```@example 1 | ||
| [NoiseOp(noise, [4,5]), NoiseOpAll(noise)] | ||
| ``` | ||
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| The machinery behind noise processes and different types of noise is detailed in [the section on noise](@ref noise) | ||
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| ### Coincidence Measurements | ||
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| Global parity measurements involving single-qubit projections and classical communication are implemented with [`BellMeasurement`](@ref). 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. | ||
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| ```@example 1 | ||
| BellMeasurement([sMX(1), sMY(3), sMZ(4)]) | ||
| ``` | ||
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| There is also [`NoisyBellMeasurement`](@ref) that takes the bit-flip probability of a single-qubit measurement as a third argument. | ||
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| ### Stabilizer Measurements | ||
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| 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`](@ref) 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`](@ref), [`sMZ`](@ref), [`sMY`](@ref) if you are measuring a single qubit. | ||
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| ```@example 1 | ||
| [PauliMeasurement(P"XYZ", 1), sMZ(2, 2)] | ||
| ``` | ||
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| ### Reset Operations | ||
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| The [`Reset`](@ref) operations lets you trace out the specified qubits and set their state to a specific tableau. | ||
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| ```@example 1 | ||
| new_state = random_stabilizer(3) | ||
| qubit_indices = [1,2,3] | ||
| Reset(new_state, qubit_indices) | ||
| ``` | ||
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| It can be done anywhere in a circuit, not just at the beginning. |
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| Original file line number | Diff line number | Diff line change |
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| # [Noise Processes](@id noise) | ||
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| ```@meta | ||
| DocTestSetup = quote | ||
| using QuantumClifford | ||
| using StableRNGs | ||
| rng = StableRNG(42) | ||
| end | ||
| ``` | ||
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| As seen in the list of [possible gates](@id all-operations), | ||
| the simulator is capable of modeling different types of noise. | ||
| If that is your goal, please consider using the available | ||
| [Monte Carlo simulator](@ref noisycircuits_md) or the | ||
| [Symbolic Perturbative Expansion system](@ref noisycircuit_perturb). | ||
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| The implemented types of noise include: | ||
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| - [`UnbiasedUncorrelatedNoise`](@ref) | ||
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| The low-level functionality to work with noise is `applynoise!`, | ||
| but most of the time you would probably just want to use | ||
| [`NoisyGate`](@ref) and [`NoisyOpAll`](@ref). |
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| """A method giving the qubits acted upon by a given operation. Part of the Noise interface.""" | ||
| function affectedqubits end | ||
| affectedqubits(g::AbstractSingleQubitOperator) = [g.q,] | ||
| affectedqubits(g::AbstractTwoQubitOperator) = [g.q1, g.q2] | ||
| affectedqubits(g::NoisyGate) = affectedqubits(g.gate) | ||
| affectedqubits(g::SparseGate) = g.indices | ||
| affectedqubits(b::BellMeasurement) = [m.qubit for m in b.measurements] | ||
| affectedqubits(r::Reset) = r.indices | ||
| affectedqubits(n::NoiseOp) = n.indices | ||
| affectedqubits(g::PauliMeasurement) = 1:length(g.pauli) | ||
| affectedqubits(m::AbstractMeasurement) = [m.qubit] |
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