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 QuantumCliffordWorks efficiently with pure and mixed stabilizer states of thousands of qubits as well as sparse or dense Clifford operations acting upon them.
Provides canonicalization, projection, and generation operations, as well as partial traces.
julia> P"X" * P"Z"
-iY
julia> P"X" ⊗ P"Z"
+ XZ
julia> S"-XX
+ZZ"
- XX
+ ZZ
julia> CNOT * S"-XX
+ZZ"
- X_
+ _Z
The code is vectorized and multithreaded.
Fast, in-place, allocation free implementations.
The only other simulator of similar performance I know of is Stim. In particular, Stim implements convenient tracking of Pauli frames, that makes simulating the performance of error correcting codes blazingly fast (which are possible in QuantumClifford.jl, but no convenient interface is provided for that yet).
The "low level" functionality is of similar performance in Stim and QuantumClifford but different tradeoffs are made at the higher levels: to multiply in-place 1M-qubit Pauli operators Stim needs 16us while QuantumClifford.jl needs 20us.
Of note is that Stim achieved this performance through high-quality C++ SIMD code of significant sophistication, while QuantumClifford.jl is implemented in pure Julia.
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: 155 samples with 1 evaluation.
Range (min … max): 32.074 ms … 32.425 ms ┊ GC (min … max): 0.00% … 0.00%
Time (median): 32.246 ms ┊ GC (median): 0.00%
Time (mean ± σ): 32.247 ms ± 63.427 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
▃ ▃▃ ▄ ▆▄▄▄██▃ ▃▄▁▆█▃▃ ▃ ▁
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32.1 ms Histogram: frequency by time 32.4 ms <
Memory estimate: 0 bytes, allocs estimate: 0.
julia> @benchmark canonicalize!(s) setup=(s=random_stabilizer(1000))
BenchmarkTools.Trial: 226 samples with 1 evaluation.
Range (min … max): 21.938 ms … 22.680 ms ┊ GC (min … max): 0.00% … 0.00%
Time (median): 22.025 ms ┊ GC (median): 0.00%
Time (mean ± σ): 22.057 ms ± 115.247 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
▂▂ █▃▃▂
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21.9 ms Histogram: frequency by time 22.6 ms <
Memory estimate: 32 bytes, allocs estimate: 1.
julia> @benchmark apply!(s, gate) setup=(s=random_stabilizer(1000); gate=tensor_pow(CNOT,500))
BenchmarkTools.Trial: 564 samples with 1 evaluation.
Range (min … max): 6.602 ms … 17.719 ms ┊ GC (min … max): 0.00% … 0.00%
Time (median): 8.411 ms ┊ GC (median): 0.00%
Time (mean ± σ): 8.865 ms ± 1.836 ms ┊ GC (mean ± σ): 0.00% ± 0.00%
▂ ▁ █
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6.6 ms Histogram: frequency by time 13.7 ms <
Memory estimate: 13.84 KiB, allocs estimate: 111.
julia> @benchmark apply!(s, sCNOT(32,504)) setup=(s=random_stabilizer(1000))
BenchmarkTools.Trial: 10000 samples with 9 evaluations.
Range (min … max): 3.373 μs … 252.630 μs ┊ GC (min … max): 0.00% … 53.27%
Time (median): 3.766 μs ┊ GC (median): 0.00%
Time (mean ± σ): 3.892 μs ± 2.525 μs ┊ GC (mean ± σ): 0.35% ± 0.53%
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3.37 μs Histogram: frequency by time 6.07 μs <
Memory estimate: 96 bytes, allocs estimate: 2.
Benchmarks executed on a Ryzen Zen1 8-core CPU.