YaoToEinsum

Convert Yao circuit to OMEinsum notation for tensor network based simulation.

Installation

YaoToEinsum is a   Julia Language   package. To install YaoToEinsum, please open Julia's interactive session (known as REPL) and press ] key in the REPL to use the package mode, then type the following command

For stable release

pkg> add YaoToEinsum

For current master

pkg> add YaoToEinsum#master

If you have problem to install the package, please file us an issue.

Example

This package contains one main function yao2einsum(circuit; initial_state=Dict(), final_state=Dict()). It transform a Yao circuit to a generalized tensor network (einsum) notation. This function returns a 2-tuple of (einsum code, input tensors). initial_state and final_state specifies the initial state and final state. They can specified as a dictionary with integer keys, with value either integer or a single qubit register. If a qubit of initial state or final state is not specified, the circuit will have open edges.

julia> import Yao, YaoToEinsum

julia> using YaoExtensions: qft_circuit

julia> n = 10;

julia> circuit = qft_circuit(n);

# convert circuit (open in both left and right) to einsum notation (code) and tensors.
julia> code, tensors = YaoToEinsum.yao2einsum(circuit);

# optimize contraction order, for more algorithms, please check `OMEinsumContractionOrders`.
julia> optcode = optimize_code(code, uniformsize(code, 2), TreeSA(ntrials=1));

julia> reshape(optcode(tensors...; size_info=uniformsize(code, 2)), 1<<n, 1<<n) ≈ Yao.mat(circuit)
true

# convert circuit (applied on product state `initial_state` and projected to output state `final_state`)
julia> code, tensors = YaoToEinsum.yao2einsum(circuit;
        initial_state=Dict([i=>0 for i=1:n]), final_state=Dict([i=>0 for i=1:n]));

julia> optcode = optimize_code(code, uniformsize(code, 2), TreeSA(ntrials=1));

julia> optcode(tensors...; size_info=uniformsize(code, 2))[] ≈ Yao.zero_state(n)' * (Yao.zero_state(n) |> circuit)
true

References

• Simulating quantum computation by contracting tensor networks https://arxiv.org/abs/quant-ph/0511069

• Simulating the Sycamore quantum supremacy circuits https://arxiv.org/abs/2103.03074

• Solving the sampling problem of the Sycamore quantum supremacy circuits https://arxiv.org/abs/2111.03011