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Gates

In Quac, gates are symbolic, i.e. they do not store their representation. A gate instance just stores the qubit lane in which it acts and its parameters if needed. Thanks to Julia's multiple-dispatch different representations can be queried lazily from type information.

For example, this is a $Z$ that acts on qubit 4.

julia> gate = Z(4)
Z() on 4

Any gate can be represented by a dense matrix.

julia> Matrix(gate)
2×2 Matrix{ComplexF64}:
 1.0+0.0im   0.0+0.0im
 0.0+0.0im  -1.0+0.0im

You can even specify the eltype!

julia> Matrix{Int}(gate)
2×2 Matrix{Int64}:
 1   0
 0  -1

Furthermore, the $Z$ gate allows a Diagonal representation!

julia> Diagonal{Float32}(gate)
2×2 Diagonal{Float32, Vector{Float32}}:
 1.0    ⋅
  ⋅   -1.0
Quac.Operator — Type
Operator

An abstract type that groups all symbolic expressions of operators.

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Pauli gates

Quac.I — Type
I(lane)

The $σ_0$ Pauli matrix gate.

Note

Due to name clashes with LinearAlgebra.I, Quac.I is not exported by default.

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Hadamard gate

Phase gates

Quac.S — Type
S(lane)

The $S$ gate or $\frac{π}{2}$ rotation around Z-axis.

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Quac.Sd — Type
Sd(lane)

The $S^\dagger$ gate or $-\frac{π}{2}$ rotation around Z-axis.

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Quac.T — Type
T(lane)

The $T$ gate or $\frac{π}{4}$ rotation around Z-axis.

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Quac.Td — Type
Td(lane)

The $T^\dagger$ gate or $-\frac{π}{4}$ rotation around Z-axis.

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Rotation gates

Quac.Rx — Type
Rx(lane, θ)

The $\theta$ rotation around the X-axis gate.

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Quac.Ry — Type
Ry(lane, θ)

The $\theta$ rotation around the Y-axis gate.

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Quac.Rz — Type
Rz(lane, θ)

The $\theta$ rotation around the Z-axis gate.

Notes

  • The U1 gate is an alias of Rz.
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Quac.Rxx — Type
Rxx(lane1, lane2, θ)

The $\theta$ rotation around the XX-axis gate.

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Quac.Ryy — Type
Ryy(lane1, lane2, θ)

The $\theta$ rotation around the YY-axis gate.

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Quac.Rzz — Type
Rzz(lane1, lane2, θ)

The $\theta$ rotation around the ZZ-axis gate.

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General U2, U3 gates

Controlled gates

SWAP gate

Special Unitary gate

Experimental interface

This interface is experimental and may change in the future.

Quac.SU — Type
SU{N}(lane_1, lane_2, ..., lane_N, array)

The SU{N} multi-qubit general unitary gate that can be used to represent any unitary matrix that acts on N qubits. A new random SU{N} can be created with rand(SU{N}, lanes...), where N is the dimension of the unitary matrix and lanes are the qubit lanes on which the gate acts.

Note

Unlike the general notation, N is not the dimension of the unitary matrix, but the number of qubits on which it acts. The dimension of the unitary matrix is $2^N \times 2^N$.

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