BloqadeExpr.N_1 — Constant
N_1
OpN_1 <: YaoBlocks.ConstantGate{1, 3}

Projection operator onto |1⟩ for 3-level Rydberg system.

Matrix expression:

\[n^1 = |1⟩⟨1| = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.N_r — Constant
N_r
OpN_r <: YaoBlocks.ConstantGate{1, 3}

Projection operator onto |r⟩ for 3-level Rydberg system.

Matrix expression:

\[n^{\mathrm{r}} = |r⟩⟨r| = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix}\]

BloqadeExpr.Pd_01 — Constant
Pd_01
OpPd_01 <: YaoBlocks.ConstantGate{1, 3}

Matrix expression:

\[\mathrm{Pd}^{\mathrm{hf}} = \begin{pmatrix} 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.Pd_1r — Constant
Pd_1r
OpPd_1r <: YaoBlocks.ConstantGate{1, 3}

Matrix expression:

\[\mathrm{Pd}^{\mathrm{r}} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix}\]

BloqadeExpr.Pu_01 — Constant
Pu_01
OpPu_01 <: YaoBlocks.ConstantGate{1, 3}

Matrix expression:

\[\mathrm{Pu}^{\mathrm{hf}} = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.Pu_1r — Constant
Pu_1r
OpPu_1r <: YaoBlocks.ConstantGate{1, 3}

Matrix expression:

\[\mathrm{Pu}^{\mathrm{r}} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.X_01 — Constant
X_01
OpX_01 <: YaoBlocks.ConstantGate{1, 3}

Pauli X operator act on |0⟩ and |1⟩ for 3-level Rydberg system.

Matrix expression:

\[\sigma^{x,\mathrm{hf}} = \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.X_1r — Constant
X_1r
OpX_1r <: YaoBlocks.ConstantGate{1, 3}

Pauli X operator act on |1⟩ and |r⟩ for 3-level Rydberg system.

Matrix expression:

\[\sigma^{x,\mathrm{r}} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix}\]

BloqadeExpr.Z_01 — Constant
Z_01
OpZ_01 <: YaoBlocks.ConstantGate{1, 3}

Pauli Z operator act on |0⟩ and |1⟩ for 3-level Rydberg system.

Matrix expression:

\[\sigma^{z,\mathrm{hf}} = \begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.Z_1r — Constant
Z_1r
OpZ_1r <: YaoBlocks.ConstantGate{1, 3}

Pauli Z operator act on |1⟩ and |r⟩ for 3-level Rydberg system.

Matrix expression:

\[\sigma^{z,\mathrm{r}} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1 \end{pmatrix}\]

BloqadeExpr.AbstractTerm — Type
AbstractTerm{D} <: PrimitiveBlock{D}

Abstract term for local hamiltonian terms on D-level system.

BloqadeExpr.Lowlevel.Hamiltonian — Method
Hamiltonian(::Type{Tv}, expr[, space=fullspace])

Create a Hamiltonian from hamiltonian expr that has matrix element of type Tv.

BloqadeExpr.OpN_1 — Type
N_1
OpN_1 <: YaoBlocks.ConstantGate{1, 3}

Projection operator onto |1⟩ for 3-level Rydberg system.

Matrix expression:

\[n^1 = |1⟩⟨1| = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.OpN_r — Type
N_r
OpN_r <: YaoBlocks.ConstantGate{1, 3}

Projection operator onto |r⟩ for 3-level Rydberg system.

Matrix expression:

\[n^{\mathrm{r}} = |r⟩⟨r| = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix}\]

BloqadeExpr.OpPd_01 — Type
Pd_01
OpPd_01 <: YaoBlocks.ConstantGate{1, 3}

Matrix expression:

\[\mathrm{Pd}^{\mathrm{hf}} = \begin{pmatrix} 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.OpPd_1r — Type
Pd_1r
OpPd_1r <: YaoBlocks.ConstantGate{1, 3}

Matrix expression:

\[\mathrm{Pd}^{\mathrm{r}} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix}\]

BloqadeExpr.OpPu_01 — Type
Pu_01
OpPu_01 <: YaoBlocks.ConstantGate{1, 3}

Matrix expression:

\[\mathrm{Pu}^{\mathrm{hf}} = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.OpPu_1r — Type
Pu_1r
OpPu_1r <: YaoBlocks.ConstantGate{1, 3}

Matrix expression:

\[\mathrm{Pu}^{\mathrm{r}} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.OpX_01 — Type
X_01
OpX_01 <: YaoBlocks.ConstantGate{1, 3}

Pauli X operator act on |0⟩ and |1⟩ for 3-level Rydberg system.

Matrix expression:

\[\sigma^{x,\mathrm{hf}} = \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.OpX_1r — Type
X_1r
OpX_1r <: YaoBlocks.ConstantGate{1, 3}

Pauli X operator act on |1⟩ and |r⟩ for 3-level Rydberg system.

Matrix expression:

\[\sigma^{x,\mathrm{r}} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix}\]

BloqadeExpr.OpZ_01 — Type
Z_01
OpZ_01 <: YaoBlocks.ConstantGate{1, 3}

Pauli Z operator act on |0⟩ and |1⟩ for 3-level Rydberg system.

Matrix expression:

\[\sigma^{z,\mathrm{hf}} = \begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.OpZ_1r — Type
Z_1r
OpZ_1r <: YaoBlocks.ConstantGate{1, 3}

Pauli Z operator act on |1⟩ and |r⟩ for 3-level Rydberg system.

Matrix expression:

\[\sigma^{z,\mathrm{r}} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1 \end{pmatrix}\]

BloqadeExpr.RydInteract — Type
struct RydInteract{D} <: AbstractTerm{D}
RydInteract(;atoms, C=2π * 862690MHz⋅μm^6)

Type for Rydberg interactive term.

Expression

\[\sum_{i, j} \frac{C}{|x_i - x_j|^6} n_i n_j\]

Keyword Arguments

  • atoms: a list of atom positions, must be type RydAtom, default unit is μm.
  • C: the interaction strength, default unit is MHz⋅μm^6. default value is 2π * 862690 * MHz*µm^6.
BloqadeExpr.Subspace — Type
Subspace{S <: AbstractVector} <: AbstractSpace

A Dict-like object stores the mapping between subspace and full space.

BloqadeExpr.Subspace — Method
Subspace(nqubits::Int, subspace_v::AbstractVector)

Create a Subspace from given list of subspace indices in the corresponding full space.

BloqadeExpr.SumOfN — Type
struct SumOfN <: AbstractTerm{2}
SumOfN(;nsites[, Δ=1])

Sum of N operators.

The following two expression are equivalent

julia> SumOfN(nsites=5)
∑ n_i

julia> sum([Op.n for _ in 1:5])
nqudits: 1
+
├─ P1
├─ P1
├─ P1
├─ P1
└─ P1

But may provide extra speed up.

Expression

\[\sum_i Δ ⋅ n_i\]

BloqadeExpr.SumOfN_1 — Type
struct SumOfN_1 <: AbstractTerm{3}
SumOfN_1(;nsites[, Δ=1])

Sum of N_1 operators.

Expression

\[\sum_i Δ ⋅ n^r_i\]

BloqadeExpr.SumOfN_r — Type
struct SumOfN_r <: AbstractTerm{3}
SumOfN_1(;nsites[, Δ=1])

Sum of N_r operators.

Expression

\[\sum_i Δ ⋅ n^r_i\]

BloqadeExpr.SumOfX — Type
struct SumOfX <: AbstractTerm{2}
SumOfX(nsites, Ω)

Term for sum of X operators.

The following two expressions are equivalent

julia> SumOfX(nsites=5)
∑ σ^x_i

julia> sum([X for _ in 1:5])
nqudits: 1
+
├─ X
├─ X
├─ X
├─ X
└─ X

Expression

\[\sum_i Ω σ^x_i\]

BloqadeExpr.SumOfXPhase — Type
struct SumOfXPhase <: AbstractTerm{2}
SumOfXPhase(;nsites, Ω=1, ϕ)

Sum of XPhase operators.

The following two expressions are equivalent

julia> SumOfXPhase(nsites=5, ϕ=0.1)
1.0 ⋅ ∑ e^{0.1 ⋅ im} |0⟩⟨1| + e^{-0.1 ⋅ im} |1⟩⟨0|

julia> sum([XPhase(0.1) for _ in 1:5])
nqudits: 1
+
├─ XPhase(0.1)
├─ XPhase(0.1)
├─ XPhase(0.1)
├─ XPhase(0.1)
└─ XPhase(0.1)

But may provide extra speed up.

Expression

\[\sum_i Ω ⋅ (e^{ϕ ⋅ i} |0⟩⟨1| + e^{-ϕ ⋅ i} |1⟩⟨0|)\]

BloqadeExpr.SumOfXPhase_01 — Type
struct SumOfXPhase_01 <: AbstractTerm{3}
SumOfXPhase_01(nsites, Ω, ϕ)

Term for sum of XPhase_01 operators.

Expression

\[\sum_i Ω ⋅ (e^{ϕ ⋅ i} |0⟩⟨1| + e^{-ϕ ⋅ i} |1⟩⟨0|)\]

BloqadeExpr.SumOfXPhase_1r — Type
struct SumOfXPhase_1r <: AbstractTerm{3}
SumOfXPhase_1r(nsites, Ω, ϕ)

Term for sum of XPhase_1r operators.

Expression

\[\sum_i Ω ⋅ (e^{ϕ ⋅ i} |1⟩⟨r| + e^{-ϕ ⋅ i} |r⟩⟨1|)\]

BloqadeExpr.SumOfX_01 — Type
struct SumOfX_01 <: AbstractTerm{3}
SumOfX_01(nsites, Ω)

Term for sum of X_01 operators.

Expression

\[\sum_i Ω σ^{x,\mathrm{hf}}_i\]

BloqadeExpr.SumOfX_1r — Type
struct SumOfX_1r <: AbstractTerm{3}
SumOfX_1r(nsites, Ω)

Term for sum of X_1r operators.

Expression

\[\sum_i Ω σ^{x,\mathrm{r}}_i\]

BloqadeExpr.SumOfZ — Type
struct SumOfZ <: AbstractTerm{2}
SumOfZ(;nsites, Δ=1)

Sum of Pauli Z operators.

The following two expression are equivalent

julia> SumOfZ(nsites=5)
∑ σ^z_i

julia> sum([Z for _ in 1:5])
nqudits: 1
+
├─ Z
├─ Z
├─ Z
├─ Z
└─ Z

Expression

\[\sum_i Δ ⋅ σ^z_i\]

BloqadeExpr.SumOfZ_01 — Type
struct SumOfZ_01 <: AbstractTerm{2}
SumOfZ_01(;nsites, Δ=1)

Sum of Pauli Z_01 operators.

Expression

\[\sum_i Δ ⋅ σ^{z,\mathrm{hf}}_i\]

BloqadeExpr.SumOfZ_1r — Type
struct SumOfZ_1r <: AbstractTerm{2}
SumOfZ_1r(;nsites, Δ=1)

Sum of Pauli Z_1r operators.

Expression

\[\sum_i Δ ⋅ σ^{z,\mathrm{r}}_i\]

BloqadeExpr.XPhase — Type
XPhase{T} <: PrimitiveBlock{2}

XPhase operator for 2-level Rydberg system.

\[e^{ϕ ⋅ i} |0⟩⟨1| + e^{-ϕ ⋅ i} |1⟩⟨0|\]

BloqadeExpr.XPhase_01 — Type
XPhase_01{T} <: PrimitiveBlock{3}

XPhase operator act on |0⟩ and |1⟩ for 3-level Rydberg system.

\[e^{ϕ ⋅ i} |0⟩⟨1| + e^{-ϕ ⋅ i} |1⟩⟨0| = \begin{pmatrix} 0 & e^{ϕ ⋅ im} & 0 \\ e^{-ϕ ⋅ im} & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

BloqadeExpr.XPhase_1r — Type
XPhase_1r{T} <: PrimitiveBlock{3}

XPhase operator act on |1⟩ and |r⟩ for 3-level Rydberg system.

\[e^{ϕ ⋅ i} |1⟩⟨r| + e^{-ϕ ⋅ i} |r⟩⟨1| = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & e^{ϕ ⋅ im} \\ 0 & e^{-ϕ ⋅ im} & 0 \end{pmatrix}\]

BloqadeExpr.attime — Method
attime(h, t)
attime(t)

Return the hamiltonian at time t.

Example

julia> h = rydberg_h(atoms; Ω=sin)
nqudits: 4
+
├─ ∑ 5.42e6/|x_i-x_j|^6 n_i n_j
└─ Ω(t) ⋅ ∑ σ^x_i

julia> h |> attime(0.1)
nqudits: 4
+
├─ ∑ 5.42e6/|x_i-x_j|^6 n_i n_j
└─ 0.0499 ⋅ ∑ σ^x_i
BloqadeExpr.get_rydberg_params — Method
get_rydberg_params(h)

Returns a named tuple containing the fields atoms, ϕ, Ω, and Δ for the RydbergHamiltonian, h.

See also rydberg_h

Example

julia (atoms,ϕ,Ω,Δ) = get_rydberg_params(h)`

BloqadeExpr.is_time_function — Method
is_time_function(f)

Check if a function has method whose signature is of Tuple{Real} or Tuple{T} where {T <: Real}.

BloqadeExpr.matrix_to_positions — Method
matrix_to_positions(locs::AbstractMatrix{T}) -> Vector{NTuple{D, T}}

Convert a dxn location matrix to a list of positions.

BloqadeExpr.rydberg_h — Method
rydberg_h(atoms; [C=2π * 862690 * MHz*µm^6], Ω[, ϕ, Δ])

Create a rydberg hamiltonian

\[∑ \frac{C}{|x_i - x_j|^6} n_i n_j + \frac{Ω}{2} σ_x - Δ σ_n\]

shorthand for

RydInteract(C, atoms) + SumOfXPhase(length(atoms), Ω, ϕ) - SumOfN(length(atoms), Δ)

Arguments

  • atoms: a collection of atom positions.

Keyword Arguments

  • C: optional, default unit is MHz*µm^6, interation parameter, see also RydInteract.
  • Ω: optional, default unit is MHz, Rabi frequencies, divided by 2, see also SumOfX.
  • Δ: optional, default unit is MHz, detuning parameter, see SumOfN.
  • ϕ: optional, does not have unit, the phase, see SumOfXPhase.
Tips

The rabi frequencies are divided by two in the Rydberg hamiltonian unlike directly constructing via SumOfX or SumOfXPhase.

Tips

The parameters of Hamiltonian have their own default units to match hardware, one can use Unitful.jl to specify their units explicitly. If the units are specified explicitly, they will be converted to default units automatically.

Example

julia> using Bloqade

julia> atoms = [(1, ), (2, ), (3, ), (4, )]
4-element Vector{Tuple{Int64}}:
 (1,)
 (2,)
 (3,)
 (4,)

julia> rydberg_h(atoms)
∑ 5.42e6/|x_i-x_j|^6 n_i n_j
julia> rydberg_h(atoms; Ω=0.1)
nqubits: 4
+
├─ ∑ 5.42e6/|x_i-x_j|^6 n_i n_j
└─ 0.05 ⋅ ∑ σ^x_i
BloqadeExpr.rydberg_h_3 — Method
rydberg_h_3(atoms; [C=2π * 862690 * MHz*µm^6, 
    Ω_hf = nothing, ϕ_hf = nothing, Δ_hf = nothing, 
    Ω_r = nothing, ϕ_r = nothing, Δ_r = nothing])

Create a 3-level Rydberg Hamiltonian

\[\sum_{i<j} \frac{C}{|x_i - x_j|^6} n^r_i n^r_j + \sum_{i} \left[\frac{Ω^{\mathrm{hf}}}{2} (e^{iϕ^\mathrm{hf}}|0⟩⟨1| + e^{-iϕ^\mathrm{hf}}|1⟩⟨0|) - Δ^{\mathrm{hf}} n^{1}_i + \frac{Ω^{\mathrm{r}}}{2} (e^{iϕ^\mathrm{r}}|1⟩⟨r| + e^{-iϕ^\mathrm{r}}|r⟩⟨1|) - (Δ^{\mathrm{hf}} + Δ^{\mathrm{r}}) n^{\mathrm{r}}_i \right]\]

shorthand for

RydInteract(C, atoms; nlevel = 3) + 
    SumOfXPhase_01(length(atoms), Ω_hf/2, ϕ_hf) - SumOfN(length(atoms), Δ_hf) +
    SumOfXPhase_1r(length(atoms), Ω_r/2, ϕ_r) - SumOfN(length(atoms), Δ_r + Δ_hf)
BloqadeExpr.Lowlevel.Hamiltonian — Type
struct Hamiltonian

Hamiltonian stores the dynamic prefactors of each term. The actual hamiltonian is the sum of f_i(t) * t_i where f_i and t_i are entries of fs and ts.

BloqadeExpr.Lowlevel.bmul! — Method
bmul!(y::AbstractVector, A::SparseMatrixCSR, x::AbstractVector, alpha::Number, beta::Number)
bmul!(y::AbstractVector, A::SparseMatrixCSR, x::AbstractVector)

Evaluates y = alpha*A*x + beta*y (y = A*x) In-place multithreaded version of sparse csr matrix - vector multiplication, using the threading provided by Polyester.jl