Quantum Registers

A quantum register is a quantum state or a batch of quantum states. Yao provides two types of quantum registers ArrayReg and BatchedArrayReg.

YaoAPI.AbstractRegister — Type

AbstractRegister{D}

Abstract type for quantum registers. Type parameter D is the number of levels in each qudit. For qubits, D = 2.

Required methods

Optional methods

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Missing docstring.

Missing docstring for AbstractArrayReg. Check Documenter's build log for details.

YaoArrayRegister.ArrayReg — Type

ArrayReg{D,T,MT<:AbstractMatrix{T}} <: AbstractArrayRegister{D}
ArrayReg{D}(raw)
ArrayReg(raw::AbstractVecOrMat; nlevel=2)
ArrayReg(r::ArrayReg)

Simulated full amplitude register type, it uses an array to represent corresponding one or a batch of quantum states. T is the numerical type for each amplitude, it is ComplexF64 by default.

Warning

ArrayReg constructor will not normalize the quantum state. If you need a normalized quantum state remember to use normalize!(register) on the register or normalize the input raw array with normalize or batched_normalize!.

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YaoArrayRegister.BatchedArrayReg — Type

BatchedArrayReg{D,T,MT<:AbstractMatrix{T}} <: AbstractArrayReg{D}
BatchedArrayReg(raw, nbatch; nlevel=2)
BatchedArrayReg{D}(raw, nbatch)

Simulated batched full amplitude register type, it uses an array to represent corresponding one or a batch of quantum states. T is the numerical type for each amplitude, it is ComplexF64 by default.

Warning

BatchedArrayReg constructor will not normalize the quantum state. If you need a normalized quantum state remember to use normalize!(register) on the register or normalize the input raw array with normalize or batched_normalize!.

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We define some shortcuts to create simulated quantum states easier:

YaoArrayRegister.arrayreg — Function

arrayreg(state; nbatch::Union{Integer,NoBatch}=NoBatch(), nlevel::Integer=2)

Create an array register, if nbatch is a integer, it will return a BatchedArrayReg.

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arrayreg([T=ComplexF64], bit_str; nbatch=NoBatch())

Construct an array register from bit string literal. For bit string literal please read @bit_str.

Examples

julia> arrayreg(bit"1010")
ArrayReg{2, ComplexF64, Array...}
    active qubits: 4/4
    nlevel: 2

julia> arrayreg(ComplexF32, bit"1010")
ArrayReg{2, ComplexF32, Array...}
    active qubits: 4/4
    nlevel: 2

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YaoArrayRegister.product_state — Function

product_state([T=ComplexF64], dit_str; nbatch=NoBatch(), no_transpose_storage=false)
product_state([T=ComplexF64], nbits::Int, val::Int; nbatch=NoBatch(), nlevel=2, no_transpose_storage=false)
product_state([T=ComplexF64], vector; nbatch=NoBatch(), nlevel=2, no_transpose_storage=false)

Create an ArrayReg of product state. The configuration can be specified with a dit string, which can be defined with @bit_str or @dit_str. Or equivalently, it can be specified explicitly with nbits, val and nlevel. See also zero_state, rand_state, uniform_state.

Examples

julia> reg = product_state(dit"120;3"; nbatch=2)
BatchedArrayReg{3, ComplexF64, Transpose...}
    active qudits: 3/3
    nlevel: 3
    nbatch: 2

julia> measure(reg)
1×2 Matrix{BitBasis.DitStr64{3, 3}}:
 120 ₍₃₎  120 ₍₃₎

julia> product_state(bit"100"; nbatch=2);

julia> r1 = product_state(ComplexF32, bit"001"; nbatch=2);

julia> r2 = product_state(ComplexF32, [1, 0, 0]; nbatch=2);

julia> r3 = product_state(ComplexF32, 3, 0b001; nbatch=2);

julia> r1 ≈ r2   # because we read bit strings from right to left, vectors from left to right.
true

julia> r1 ≈ r3
true

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YaoArrayRegister.zero_state — Function

zero_state([T=ComplexF64], n::Int; nbatch::Int=NoBatch())

Create an AbstractArrayReg that initialized to state $|0\rangle^{\otimes n}$. See also product_state, rand_state, uniform_state and ghz_state.

Examples

julia> zero_state(4)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 4/4
    nlevel: 2

julia> zero_state(ComplexF32, 4)
ArrayReg{2, ComplexF32, Array...}
    active qubits: 4/4
    nlevel: 2

julia> zero_state(ComplexF32, 4; nbatch=3)
BatchedArrayReg{2, ComplexF32, Transpose...}
    active qubits: 4/4
    nlevel: 2
    nbatch: 3

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YaoArrayRegister.zero_state_like — Function

zero_state_like(register, n) -> AbstractRegister

Create a register initialized to zero from an existing one.

Examples

julia> reg = rand_state(3; nbatch=2);

julia> zero_state_like(reg, 2)
BatchedArrayReg{2, ComplexF64, Array...}
    active qubits: 2/2
    nlevel: 2
    nbatch: 2

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YaoArrayRegister.rand_state — Function

rand_state([T=ComplexF64], n::Int; nbatch=NoBatch(), no_transpose_storage=false)

Create a random AbstractArrayReg with total number of qudits n.

Examples

julia> rand_state(4)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 4/4
    nlevel: 2

julia> rand_state(ComplexF64, 4)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 4/4
    nlevel: 2

julia> rand_state(ComplexF64, 4; nbatch=2)
BatchedArrayReg{2, ComplexF64, Transpose...}
    active qubits: 4/4
    nlevel: 2
    nbatch: 2

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YaoArrayRegister.uniform_state — Function

uniform_state([T=ComplexF64], n; nbatch=NoBatch(), no_transpose_storage=false)

Create a uniform state:

\[\frac{1}{\sqrt{2^n}} \sum_{k=0}^{2^{n}-1} |k\rangle.\]

This state can also be created by applying H (Hadmard gate) on $|00⋯00⟩$ state.

Example

julia> uniform_state(4; nbatch=2)
BatchedArrayReg{2, ComplexF64, Transpose...}
    active qubits: 4/4
    nlevel: 2
    nbatch: 2

julia> uniform_state(ComplexF32, 4; nbatch=2)
BatchedArrayReg{2, ComplexF32, Transpose...}
    active qubits: 4/4
    nlevel: 2
    nbatch: 2

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YaoArrayRegister.ghz_state — Function

ghz_state([T=ComplexF64], n::Int; nbatch::Int=NoBatch())

Create a GHZ state (or a cat state) that defined as

\[\frac{|0\rangle^{\otimes n} + |1\rangle^{\otimes n}}{\sqrt{2}}.\]

Examples

julia> ghz_state(4)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 4/4
    nlevel: 2

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YaoAPI.clone — Function

clone(register, n)

Create an ArrayReg by cloning the original register for n times on batch dimension. This function is only for emulation.

Example

julia> clone(arrayreg(bit"101"; nbatch=3), 4)
BatchedArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2
    nbatch: 12

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In a register, qubits are distinguished as active and inactive (or remaining). The total number of qubits is the number of active qubits plus the number of remaining qubits. Only active qubits are visible to quantum operators and the number of these qubits are the size of a register. Making this distinction of qubits allows writing reusable quantum circuits. For example, Suppose we want to run a quantum Fourier transformation circuit of size 4 on qubits (1, 3, 5, 7), we first set the target qubits to active qubits the reset to inactive, then we apply the circuit on it, finally we unset the inactive qubits.

YaoAPI.nqudits — Function

nqudits(register) -> Int

Returns the total number of qudits in register.

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YaoAPI.nqubits — Function

nqubits(register) -> Int

Returns the (total) number of qubits. See nactive, nremain for more details.

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YaoAPI.nactive — Function

nactive(register) -> Int

Returns the number of active qudits in register. Here, active qudits means the system qubits that operators can be applied on.

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YaoAPI.nremain — Function

nremain(register) -> Int

Returns the number of inactive qudits in register. It equals to subtracting nqudits and nactive.

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Missing docstring.

Missing docstring for nbatch, nlevel, focus!. Check Documenter's build log for details.

YaoAPI.focus — Function

focus(f, register, locs)

Call a callable f under the context of focus. See also focus!.

Examples

To print the focused register

julia> r = arrayreg(bit"101100")
ArrayReg{2, ComplexF64, Array...}
    active qubits: 6/6
    nlevel: 2

julia> focus(x->(println(x);x), r, (1, 2));
ArrayReg{2, ComplexF64, Array...}
    active qubits: 2/6
    nlevel: 2

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YaoAPI.relax! — Function

relax!(register[, locs]; to_nactive=nqudits(register)) -> register
relax!(locs::Int...; to_nactive=nqudits(register)) -> f(register) -> register

Inverse transformation of focus!, where to_nactive is the number of active bits for target register. If the register is not provided, returns a lambda function that takes a register as input.

Examples

julia> reg = product_state(bit"01101")
ArrayReg{2, ComplexF64, Array...}
    active qubits: 5/5
    nlevel: 2

julia> focus!(reg, (1,3,4))
ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/5
    nlevel: 2

julia> relax!(reg, (1,3,4))
ArrayReg{2, ComplexF64, Array...}
    active qubits: 5/5
    nlevel: 2

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Missing docstring.

Missing docstring for zero_state. Check Documenter's build log for details.

YaoArrayRegister.exchange_sysenv — Function

exchange_sysenv(reg::AbstractArrayReg) -> AbstractRegister

Exchange system (focused qubits) and environment (remaining qubits).

julia> reg = rand_state(5)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 5/5
    nlevel: 2

julia> focus!(reg, (2,4))
ArrayReg{2, ComplexF64, Array...}
    active qubits: 2/5
    nlevel: 2

julia> exchange_sysenv(reg)
ArrayReg{2, ComplexF64, Adjoint...}
    active qubits: 3/5
    nlevel: 2

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Storage

Both ArayReg and BatchedArrayReg use matrices as the storage. For example, for a quantum register with $a$ active qubits, $r$ remaining qubits and batch size $b$, the storage is as follows

The first dimension of size $2^a$ is for active qubits, only this subset of qubits are allowed to interact with blocks. Since we reshaped the state vector into a matrix, applying a quantum operator can always be represented as a matrix-matrix multiplication . In practice, most gates have in-place implementation that does not require constructing the operator matrix explicitly.

You can access different views of the storage of an ArrayReg with the following functions:

YaoArrayRegister.state — Function

state(register::AbstractArrayReg) -> Matrix

Returns the raw array storage of register. See also statevec.

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state(ρ::DensityMatrix) -> Matrix

Return the raw state of density matrix ρ.

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BitBasis.basis — Function

basis(register) -> UnitRange

Returns an UnitRange of the all the bits in the Hilbert space of given register.

julia> collect(basis(rand_state(3)))
8-element Vector{DitStr{2, 3, Int64}}:
 000 ₍₂₎
 001 ₍₂₎
 010 ₍₂₎
 011 ₍₂₎
 100 ₍₂₎
 101 ₍₂₎
 110 ₍₂₎
 111 ₍₂₎

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basis(ditstr) -> UnitRange{DitStr{D,N,T}}
basis(DitStr{D,N,T}) -> UnitRange{DitStr{D,N,T}}

Returns the UnitRange for basis in Hilbert Space of qudits.

YaoArrayRegister.statevec — Function

statevec(r::ArrayReg) -> array

Return a state matrix/vector by droping the last dimension of size 1 (i.e. nactive(r) = nqudits(r)). See also state.

Warning

statevec is not type stable. It may cause performance slow down.

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YaoArrayRegister.relaxedvec — Function

relaxedvec(r::AbstractArrayReg) -> AbstractArray

Return a vector representation of state, with all qudits activated. See also state, statevec.

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BitBasis.hypercubic — Function

hypercubic(r::ArrayReg) -> AbstractArray

Return the hypercubic representation (high dimensional tensor) of this register, only active qudits are considered. See also rank3 and state.

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hypercubic(A::Array) -> Array

get the hypercubic representation for an array.

YaoArrayRegister.rank3 — Function

rank3(r::ArrayReg)

Return the rank 3 tensor representation of state, the 3 dimensions are (activated space, remaining space, batch dimension). See also hypercubic and state.

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YaoAPI.viewbatch — Function

viewbatch(register, i::Int) -> AbstractRegister

Returns the i-th single register of a batched register. The returned instance is a view of the original register, i.e. inplace operation changes the original register directly.

Examples

julia> reg = zero_state(5; nbatch=2);

julia> apply!(viewbatch(reg, 2), put(5, 2=>X));

julia> measure(reg; nshots=3)
3×2 Matrix{DitStr{2, 5, Int64}}:
 00000 ₍₂₎  00010 ₍₂₎
 00000 ₍₂₎  00010 ₍₂₎
 00000 ₍₂₎  00010 ₍₂₎

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YaoArrayRegister.transpose_storage — Function

transpose_storage(register) -> register

Transpose the register storage. Sometimes transposed storage provides better performance for batched simulation.

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Operations

The list of arithmetic operations for ArrayReg include

+
-
*
/ (scalar)
adjoint

Then the inner product can be computed as follows.

julia> reg = rand_state(3);

julia> reg' * reg
0.9999999999999998 + 0.0im

Missing docstring.

Missing docstring for AdjointArrayReg. Check Documenter's build log for details.

We also have some faster inplace versions of arithematic operations

Missing docstring.

Missing docstring for regadd!, regsub!, regscale!,. Check Documenter's build log for details.

We also define the following functions for state normalization, and distance measurement.

LinearAlgebra.normalize! — Function

normalize!(r::AbstractArrayReg)

Normalize the register r by its 2-norm. It changes the register directly.

Examples

The following code creates a normalized GHZ state.

julia> reg = product_state(bit"000") + product_state(bit"111");

julia> norm(reg)
1.4142135623730951

julia> isnormalized(reg)
false

julia> normalize!(reg);

julia> isnormalized(reg)
true

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YaoArrayRegister.isnormalized — Function

isnormalized(r::ArrayReg) -> Bool

Returns true if the register r is normalized.

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YaoAPI.fidelity — Function

fidelity(register1, register2) -> Real/Vector{<:Real}
fidelity'(pair_or_reg1, pair_or_reg2) -> (g1, g2)

Return the fidelity between two states. Calcuate the fidelity between r1 and r2, if r1 or r2 is not pure state (nactive(r) != nqudits(r)), the fidelity is calcuated by purification. See also pure_state_fidelity, purification_fidelity.

Obtain the gradient with respect to registers and circuit parameters. For pair input ψ=>circuit, the returned gradient is a pair of gψ=>gparams, with gψ the gradient of input state and gparams the gradients of circuit parameters. For register input, the return value is a register.

Definition

The fidelity of two quantum state for qudits is defined as:

\[F(ρ, σ) = tr(\sqrt{\sqrt{ρ}σ\sqrt{ρ}})\]

Note

This definition is different from the one in Wiki by a square.

Examples

julia> reg1 = uniform_state(3);

julia> reg2 = zero_state(3);

julia> fidelity(reg1, reg2)
0.35355339059327373

References

Jozsa R. Fidelity for mixed quantum states[J]. Journal of modern optics, 1994, 41(12): 2315-2323.
Nielsen M A, Chuang I. Quantum computation and quantum information[J]. 2002.

Note

The original definition of fidelity $F$ was from "transition probability", defined by Jozsa in 1994, it is the square of what we use here.

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YaoAPI.tracedist — Function

tracedist(register1, register2)

Return the trace distance of register1 and register2.

Definition

Trace distance is defined as following:

\[\frac{1}{2} || A - B ||_{\rm tr}\]

Examples

julia> reg1 = uniform_state(3);

julia> reg2 = zero_state(3);

julia> tracedist(reg1, reg2)
1.8708286933869704

References

https://en.wikipedia.org/wiki/Trace_distance

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Resource management and addressing

Missing docstring.

Missing docstring for add_qudits!. Check Documenter's build log for details.

Missing docstring.

Missing docstring for add_qubits!. Check Documenter's build log for details.

YaoAPI.append_qudits! — Function

append_qudits!(register, n::Int) -> register
append_qudits!(n::Int) -> λ(register)

Add n qudits to given register in state |0>. i.e. |psi> -> |000> ⊗ |psi>, increased bits have higher indices.

If only an integer is provided, then returns a lambda function.

Examples

julia> reg = product_state(bit"01101")
ArrayReg{2, ComplexF64, Array...}
    active qubits: 5/5
    nlevel: 2

julia> append_qudits!(reg, 2)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 7/7
    nlevel: 2

julia> measure(reg; nshots=3)
3-element Vector{DitStr{2, 7, Int64}}:
 0001101 ₍₂₎
 0001101 ₍₂₎
 0001101 ₍₂₎

Note here, we read the bit string from right to left.

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YaoAPI.append_qubits! — Function

append_qubits!(register, n::Int) -> register
append_qubits!(n::Int) -> λ(register)

Add n qudits to given register in state |0>. It is an alias of append_qudits! function.

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YaoAPI.reorder! — Function

reorder!(reigster, orders)

Reorder the locations of register by input orders. For a 3-qubit register, an order (i, j, k) specifies the following reordering of qubits

move the first qubit go to i,
move the second qubit go to j,
move the third qubit go to k.

Note

The convention of reorder! is different from the permutedims function, one can use the sortperm function to relate the permutation order and the order in this function.

Examples

julia> reg = product_state(bit"010101");

julia> reorder!(reg, (1,4,2,5,3,6));

julia> measure(reg)
1-element Vector{DitStr{2, 6, Int64}}:
 000111 ₍₂₎

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YaoAPI.invorder! — Function

invorder!(register)

Inverse the locations of the register.

Examples

julia> reg = product_state(bit"010101")
ArrayReg{2, ComplexF64, Array...}
    active qubits: 6/6
    nlevel: 2

julia> measure(invorder!(reg); nshots=3)
3-element Vector{DitStr{2, 6, Int64}}:
 101010 ₍₂₎
 101010 ₍₂₎
 101010 ₍₂₎

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Only a subset of qubits that does not interact with other qubits can be removed, the best approach is first measuring it in computational basis first. It can be done with the measure! function by setting the first argument to RemoveMeasured().

Instruction set

Although we have matrix representation for Yao blocks, specialized instructions are much faster and memory efficient than using the matrix-matrix product. These instructions are specified with the instruct! function listed bellow.

YaoAPI.instruct! — Function

instruct!([nlevel=Val(2), ]state, operator, locs[, control_locs, control_configs, theta])

Unified interface for applying an operator to a quantum state. It modifies the state directly.

Arguments

nlevel is the number of levels in each qudit,
state is a vector or matrix representing the quantum state, where the first dimension is the active qubit dimension, the second is the batch dimension.
operator is a quantum operator, which can be Val(GATE_SYMBOL) or a matrix.
locs::Tuple is a tuple for specifying the locations this gate applied.
control_locs::Tuple and control_configs are tuples for specifying the control locations and control values.
theta::Real is the parameter for the gate, e.g. Val(:Rx) gate takes a real number of its parameter.

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Measurement

We have a true measure function measure! that collapses the state after the measurement. We also have some "cheating" functions to facilitate classical simulation.

YaoAPI.measure! — Function

measure!([postprocess,] [operator, ]register[, locs]; rng=Random.GLOBAL_RNG)

Measure current active qudits or qudits at locs. If the operator is not provided, it will measure on the computational basis and collapse to a product state. Otherwise, the quantum state collapse to the subspace corresponds to the resulting eigenvalue of the observable.

Arguments

postprocess is the postprocessing method, it can be
- NoPostProcess() (default).
- ResetTo(config), reset to result state to config. It can not be used if operator is provided, because measuring an operator in general does not return a product state.
- RemoveMeasured(), remove the measured qudits from the register. It is also incompatible with the operator argument.
operator::AbstractBlock is the operator to measure.
register::AbstractRegister is the quantum state.
locs is the qubits to performance the measurement. If locs is not provided, all current active qudits are measured (regarding to active qudits,

see focus! and relax!).

Keyword arguments

rng is the random number generator.

Examples

The following example measures a random state on the computational basis and reset it to a certain bitstring value.

julia> reg = rand_state(3);

julia> measure!(ResetTo(bit"011"), reg)
110 ₍₂₎

julia> measure(reg; nshots=3)
3-element Vector{DitStr{2, 3, Int64}}:
 011 ₍₂₎
 011 ₍₂₎
 011 ₍₂₎

julia> measure!(RemoveMeasured(), reg, (1,2))
11 ₍₂₎

julia> reg  # removed qubits are not usable anymore
ArrayReg{2, ComplexF64, Array...}
    active qubits: 1/1
    nlevel: 2

Measuring an operator will project the state to the subspace associated with the returned eigenvalue.

julia> reg = uniform_state(3)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2

julia> print_table(reg)
000 ₍₂₎   0.35355 + 0.0im
001 ₍₂₎   0.35355 + 0.0im
010 ₍₂₎   0.35355 + 0.0im
011 ₍₂₎   0.35355 + 0.0im
100 ₍₂₎   0.35355 + 0.0im
101 ₍₂₎   0.35355 + 0.0im
110 ₍₂₎   0.35355 + 0.0im
111 ₍₂₎   0.35355 + 0.0im

julia> measure!(repeat(3, Z, 1:3), reg)
-1.0 + 0.0im

julia> print_table(reg)
000 ₍₂₎   0.0 + 0.0im
001 ₍₂₎   0.5 + 0.0im
010 ₍₂₎   0.5 + 0.0im
011 ₍₂₎   0.0 + 0.0im
100 ₍₂₎   0.5 + 0.0im
101 ₍₂₎   0.0 + 0.0im
110 ₍₂₎   0.0 + 0.0im
111 ₍₂₎   0.5 + 0.0im

Here, we measured the parity operator, as a result, the resulting state collapsed to the subspace with either even or odd parity.

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YaoAPI.measure — Function

measure([, operator], register[, locs]; nshots=1, rng=Random.GLOBAL_RNG) -> Vector{Int}

Measure a quantum state and return measurement results of qudits. This measurement function a cheating version of measure! that does not collapse the input state. It also does not need to recompute the quantum state for performing multiple shots measurement.

Arguments

operator::AbstractBlock is the operator to measure.
register::AbstractRegister is the quantum state.
locs is the qubits to performance the measurement. If locs is not provided, all current active qudits are measured (regarding to active qudits,

see focus! and relax!).

Keyword arguments

nshots::Int is the number of shots.
rng is the random number generator.

Examples

julia> reg = product_state(bit"110")
ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2

julia> measure(reg; nshots=3)
3-element Vector{DitStr{2, 3, Int64}}:
 110 ₍₂₎
 110 ₍₂₎
 110 ₍₂₎

julia> measure(reg, (2,3); nshots=3)
3-element Vector{DitStr{2, 2, Int64}}:
 11 ₍₂₎
 11 ₍₂₎
 11 ₍₂₎

The following example switches to the X basis for measurement.

julia> reg = apply!(product_state(bit"100"), repeat(3, H, 1:3))
ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2

julia> measure(repeat(3, X, 1:3), reg; nshots=3)
3-element Vector{ComplexF64}:
 -1.0 + 0.0im
 -1.0 + 0.0im
 -1.0 + 0.0im

julia> reg = apply!(product_state(bit"101"), repeat(3, H, 1:3))
ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2

julia> measure(repeat(3, X, 1:3), reg; nshots=3)
3-element Vector{ComplexF64}:
 1.0 - 0.0im
 1.0 - 0.0im
 1.0 - 0.0im

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YaoAPI.select! — Function

select!(dest::AbstractRegister, src::AbstractRegister, bits::Integer...) -> AbstractRegister
select!(register::AbstractRegister, bits::Integer...) -> register
select!(b::Integer) -> f(register)

select a subspace of given quantum state based on input eigen state bits. See also select for the non-inplace version. If the register is not provided, it returns a lambda expression that takes a register as the input.

Examples

julia> reg = ghz_state(3)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2

julia> select!(reg, bit"111")
ArrayReg{2, ComplexF64, Array...}
    active qubits: 0/0
    nlevel: 2

julia> norm(reg)
0.7071067811865476

The selection only works on the activated qubits, for example

julia> reg = focus!(ghz_state(3), (1, 2))
ArrayReg{2, ComplexF64, Array...}
    active qubits: 2/3
    nlevel: 2

julia> select!(reg, bit"11")
ArrayReg{2, ComplexF64, Array...}
    active qubits: 0/1
    nlevel: 2

julia> statevec(reg)
1×2 Matrix{ComplexF64}:
 0.0+0.0im  0.707107+0.0im

Tip

Developers should overload select!(r::RegisterType, bits::NTuple{N, <:Integer}) and do not assume bits has specific number of bits (e.g Int64), or it will restrict the its maximum available number of qudits.

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YaoAPI.select — Function

select(register, bits) -> AbstractRegister

The non-inplace version of select!.

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YaoAPI.collapseto! — Function

collapseto!(register, config)

Set the register to bit string literal bit_str (or an equivalent integer). About bit string literal, see more in @bit_str. This interface is only for emulation.

Examples

The following code collapse a random state to a certain state.

julia> measure(collapseto!(rand_state(3), bit"001"); nshots=3)
3-element Vector{DitStr{2, 3, Int64}}:
 001 ₍₂₎
 001 ₍₂₎
 001 ₍₂₎

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YaoAPI.probs — Function

probs(register) -> Vector

Returns the probability distribution of computation basis, aka $|<x|ψ>|^2$.

Examples

julia> reg = product_state(bit"101");

julia> reg |> probs
8-element Vector{Float64}:
 0.0
 0.0
 0.0
 0.0
 0.0
 1.0
 0.0
 0.0

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Missing docstring.

Missing docstring for most_probable,. Check Documenter's build log for details.

Density matrices

YaoAPI.DensityMatrix — Type

DensityMatrix{D,T,MT<:AbstractMatrix{T}} <: AbstractRegister{D}
DensityMatrix{D}(state::AbstractMatrix)
DensityMatrix(state::AbstractMatrix; nlevel=2)

Density matrix type, where state is a matrix. Type parameter D is the number of levels, it can also be specified by a keyword argument nlevel.

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YaoAPI.density_matrix — Function

density_matrix(register_or_rho[, locations])

Returns the reduced density matrix for qubits at locations (default: all qubits).

Examples

The following code gets the single site reduce density matrix for the GHZ state.

julia> reg = ghz_state(3)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2

julia> density_matrix(reg, (2,)).state
2×2 Matrix{ComplexF64}:
 0.5+0.0im  0.0+0.0im
 0.0-0.0im  0.5+0.0im

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YaoArrayRegister.rand_density_matrix — Function

rand_density_matrix([T=ComplexF64], n::Int; nlevel::Int=2, pure::Bool=false)

Generate a random density matrix by partial tracing half of the pure state.

Note

The generated density matrix is not strict hermitian due to rounding error. If you need to check hermicity, do not use ishermitian consider using isapprox(dm.state, dm.state') or explicit mark it as Hermitian.

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YaoArrayRegister.completely_mixed_state — Function

completely_mixed_state([T=ComplexF64], n::Int; nlevel::Int=2)

Generate the completely mixed state with density matrix I(n) ./ nlevel^n.

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YaoAPI.partial_tr — Function

partial_tr(ρ, locs) -> DensityMatrix

Return a density matrix which is the partial traced on locs.

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YaoAPI.purify — Function

purify(r::DensityMatrix; nbit_env::Int=nactive(r)) -> ArrayReg

Get a purification of target density matrix.

Examples

The following example shows how to measure a local operator on the register, reduced density matrix and the purified register. Their results should be consistent.

julia> reg = ghz_state(3)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 3/3
    nlevel: 2

julia> r = density_matrix(reg, (2,));

julia> preg = purify(r)
ArrayReg{2, ComplexF64, Array...}
    active qubits: 1/2
    nlevel: 2

julia> isapprox(expect(Z + Y, preg), 0.0; atol=1e-10)
true

julia> isapprox(expect(Z + Y, r), 0.0; atol=1e-10)
true

julia> isapprox(expect(put(3, 2=>(Z + Y)), reg), 0.0; atol=1e-10)
true

source

Missing docstring.

Missing docstring for von_neumann_entropy, mutual_information,. Check Documenter's build log for details.