Clifford circuits and other quantum Stabilizer formalism tools.
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A Julia package for working with quantum stabilizer states and Clifford circuits
that act on them. Graphs states are also supported. The package is already very fast for the majority of common operations, but there are still many low-hanging fruits performance-wise. See the detailed suggested readings & references page for background on the various algorithms.
To install it use:
] add QuantumClifford
Works efficiently with
pure and
mixed stabilizer
states of thousands of qubits
as well as
sparse or dense Clifford operations
acting upon them.
Implements Pauli frames for fast sampling.
Provides
canonicalization,
projection, and
generation operations,
as well as
partial traces.
julia> P"X" * P"Z"-iYjulia> P"X" ⊗ P"Z"+ XZjulia> S"-XX+ZZ"- XX+ ZZjulia> tCNOT * S"-XX+ZZ"- X_+ _Z
The code is vectorized and multithreaded.
Fast, in-place, allocation free implementations.
jldoctest
julia> a = random_pauli(1_000_000_000);
julia> b = random_pauli(1_000_000_000);
julia> @benchmark QuantumClifford.mul_left!(a,b)
BenchmarkTools.Trial: 373 samples with 1 evaluation.
Range (min … max): 13.209 ms … 14.304 ms ┊ GC (min … max): 0.00% … 0.00%
Time (median): 13.355 ms ┊ GC (median): 0.00%
Time (mean ± σ): 13.427 ms ± 173.503 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
Memory estimate: 0 bytes, allocs estimate: 0.jldoctest
julia> @benchmark canonicalize!(s) setup=(s=random_stabilizer(1000))
BenchmarkTools.Trial: 6 samples with 1 evaluation.
Range (min … max): 8.516 ms … 8.614 ms ┊ GC (min … max): 0.00% … 0.00%
Time (median): 8.536 ms ┊ GC (median): 0.00%
Time (mean ± σ): 8.550 ms ± 35.883 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
Memory estimate: 0 bytes, allocs estimate: 0.jldoctest
julia> @benchmark apply!(s, gate) setup=(s=random_stabilizer(1000); gate=tensor_pow(tCNOT,500))
BenchmarkTools.Trial: 6 samples with 1 evaluation.
Range (min … max): 16.879 ms … 17.064 ms ┊ GC (min … max): 0.00% … 0.00%
Time (median): 17.010 ms ┊ GC (median): 0.00%
Time (mean ± σ): 16.997 ms ± 63.050 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
Memory estimate: 800 bytes, allocs estimate: 4.jldoctest
julia> @benchmark apply!(s, sCNOT(32,504)) setup=(s=random_stabilizer(1000))
BenchmarkTools.Trial: 6 samples with 8 evaluations.
Range (min … max): 2.867 μs … 3.228 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 3.043 μs ┊ GC (median): 0.00%
Time (mean ± σ): 3.049 μs ± 119.106 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
Memory estimate: 0 bytes, allocs estimate: 0.jldoctest
julia> s=random_destabilizer(1000); p=random_pauli(1000);
julia> @benchmark project!(_s,_p) setup=(_s=copy(s);_p=copy(p)) evals=1
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 17.753 μs … 39.444 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 21.971 μs ┊ GC (median): 0.00%
Time (mean ± σ): 21.893 μs ± 2.234 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
Memory estimate: 480 bytes, allocs estimate: 4.jldoctest
julia> s=MixedDestabilizer(random_destabilizer(1000));
julia> @benchmark projectY!(_s,42) setup=(_s=copy(s)) evals=1
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 15.379 μs … 37.630 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 16.912 μs ┊ GC (median): 0.00%
Time (mean ± σ): 17.120 μs ± 1.335 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
Memory estimate: 464 bytes, allocs estimate: 5.julia> versioninfo()
Julia Version 1.9.1
Commit 147bdf428cd (2023-06-07 08:27 UTC)
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 32 × AMD Ryzen 9 7950X 16-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-14.0.6 (ORCJIT, znver3)
Threads: 1 on 32 virtual cores