Registers and Observables

Bloqade follows the register interface in Yao. It uses a register to represent a device and its internal quantum state. For Bloqade, the most commonly used register types are ArrayReg and SubspaceArrayReg. They both use a dense array to store the corresponding quantum state. The only difference is that SubspaceArrayReg also stores a subspace object. In this section, we will only cover how to create registers and perform operations on them in the full Hilbert space. For subspace operations, please refer to the subspace page. We will also discuss a few convenient wrappers on commonly used observables for Rydberg systems.

Basic Interface

To create a register with all atoms being in the ground state $| 00..00 \rangle$, we can use the function zero_state by specifying the number of qubits:

julia> using Bloqade
julia> zero_state(5) # creates a 5-qubit registerArrayReg{2, ComplexF64, Array...}
    active qubits: 5/5
    nlevel: 2

To create a more general product state in the computational basis, one can use the product_state function by inputting its bitstring:

julia> product_state(bit"10011")ArrayReg{2, ComplexF64, Array...}
    active qubits: 5/5
    nlevel: 2

where bit"10011" is a special Julia string literal defined for bitstrings.

One can also construct the ArrayReg or SubspaceArrayReg directly from arrays, e.g.:

julia> ArrayReg(rand(ComplexF64, 2^5))ArrayReg{2, ComplexF64, Array...}
    active qubits: 5/5
    nlevel: 2

For a subspace register, one can create in the following way:

julia> space = Subspace(5, [0, 2, 3, 7])5-qubits 4-elements Subspace{Int64, Vector{Int64}}:
──┬──
 1│ 0
 2│ 2
 3│ 3
 4│ 7
julia> state = rand(ComplexF64, length(space))4-element Vector{ComplexF64}:
  0.9909763576732966 + 0.8167070141105562im
  0.5268045800539806 + 0.24439773300296963im
 0.29826002628104553 + 0.7937325814949338im
  0.8005675538678771 + 0.6155620246875098im
julia> reg = SubspaceArrayReg(state, space)SubspaceArrayReg{2, ComplexF64, Vector{ComplexF64}, Subspace{Int64, Vector{Int64}}}(5, ComplexF64[0.9909763576732966 + 0.8167070141105562im, 0.5268045800539806 + 0.24439773300296963im, 0.29826002628104553 + 0.7937325814949338im, 0.8005675538678771 + 0.6155620246875098im], Subspace{Int64, Vector{Int64}}(5, Dict(0 => 1, 7 => 4, 2 => 2, 3 => 3), [0, 2, 3, 7]))

Here, $[0, 2, 3, 7]$ are base-10 integer representations of the corresponding states in bitstrings. For a more detailed guide on how to work in the subspace, please see subspace.

Operations on Registers

You can perform various operations on registers via the standard Yao register interface. This includes, e.g.,

applying operators on quantum states by using apply!,
measuring bitstrings with a projection on the quantum state by using measure!,
calculating the expectation value of certain observables by using expect,
inspecting the internal state of the register by using statevec.

julia> reg = rand_state(3)ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2
julia> measure(reg; nshots=5)5-element Vector{DitStr{2, 3, Int64}}:
 111 ₍₂₎
 011 ₍₂₎
 011 ₍₂₎
 000 ₍₂₎
 001 ₍₂₎
julia> expect(put(3,1=>X), reg)0.20896826361401255
julia> statevec(reg)8-element Vector{ComplexF64}:
  0.32098148612016664 - 0.3027045597687297im
   0.3445379916471652 - 0.15129648720914116im
 0.002213617734381416 - 0.20342225295360214im
  -0.4962941032625858 - 0.1885608372176945im
 0.005937890315291475 - 0.24969864091332164im
 -0.06270521214148751 - 0.11623277813588731im
  -0.2483880006928933 + 0.1135710210377388im
  0.39247145435242276 - 0.1789965100778524im
julia> apply!(reg, put(1=>X))ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2

For a more detailed introduction of the register interface, please refer to Yao:Registers.

Convenient Wrappers

Bloqade also provides a few convenient wrappers on some commonly used observables for Rydberg systems, including the Rydberg density and two-point correlation functions:

Bloqade.rydberg_density — Function

rydberg_density(reg, i::Int) -> Real

Calculates the rydberg density at site i.

\[\langle n_i \rangle\]

Registers and Observables

Basic Interface

Operations on Registers

Convenient Wrappers

Create General Observables using Operator Expressions

References