Profiling Howto

To choose an appropriate propagation method and parameters for a given problem, it is essential to benchmark and profile the propagation.

Consider the following simple example:

using QuantumPropagators: hamiltonian
using QuantumControlTestUtils.RandomObjects: random_dynamic_generator, random_state_vector

tlist = collect(range(0, step=1.0, length=101));
N = 200;  # size of Hilbert space
H = hamiltonian(random_dynamic_generator(N, tlist)...);
Ψ₀ = random_state_vector(N);

BenchmarkTools

The first line of defense is the use of BenchmarkTools. The @benchmark macro allows to generate statistics on how long a call to propagate takes.

Chebychev propagation

For example, we can time the propagation with the Chebychev method:

using BenchmarkTools
using QuantumPropagators
using QuantumPropagators: Cheby

@benchmark propagate($Ψ₀, $H, $tlist; method=Cheby, check=false) samples=10

BenchmarkTools.Trial: 10 samples with 1 evaluation per sample.
 Range (min … max):  19.385 ms …  21.783 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     20.229 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   20.329 ms ± 739.784 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▁  ▁          ▁  ▁  ▁█     ▁                     ▁         ▁  
  █▁▁█▁▁▁▁▁▁▁▁▁▁█▁▁█▁▁██▁▁▁▁▁█▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█▁▁▁▁▁▁▁▁▁█ ▁
  19.4 ms         Histogram: frequency by time         21.8 ms <

 Memory estimate: 1023.66 KiB, allocs estimate: 3263.

Newton propagation

Or, the same propagation with the Newton method:

using QuantumPropagators: Newton

@benchmark propagate($Ψ₀, $H, $tlist; method=Newton, check=false) samples=10

BenchmarkTools.Trial: 10 samples with 1 evaluation per sample.
 Range (min … max):  86.430 ms … 90.946 ms  ┊ GC (min … max): 0.00% … 2.58%
 Time  (median):     89.540 ms              ┊ GC (median):    2.57%
 Time  (mean ± σ):   89.193 ms ±  1.389 ms  ┊ GC (mean ± σ):  1.60% ± 1.37%

  █        █                        ██   █  █ ██     █      █  
  █▁▁▁▁▁▁▁▁█▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁██▁▁▁█▁▁█▁██▁▁▁▁▁█▁▁▁▁▁▁█ ▁
  86.4 ms         Histogram: frequency by time        90.9 ms <

 Memory estimate: 13.09 MiB, allocs estimate: 60295.

The result in this case illustrates the significant advantage of the Chebychev method for systems of moderate to small size and unitary dynamics.

When using custom data structures for the dynamical generators or states, @benchmark should also be used to optimize lower-level operations as much as possible, e.g. the application of the Hamiltonian to the state.

TimerOutputs

A lot more insight into the internals of a propagate call can be obtained by collecting timing data. This functionality is integrated in QuantumPropagators and uses the TimerOutputs package internally.

Enabling the collection of timing data

To enable collecting internal timing data, call QuantumPropagators.enable_timings:

QuantumPropagators.enable_timings()

The status of the data collection can be verified with QuantumPropagators.timings_enabled.

Chebychev propagation

Since the call to QuantumPropagators.enable_timings invalidates existing compiled code, and to avoid the compilation overhead showing up in the timing data, we call propagate once to ensure compilation:

propagate(Ψ₀, H, tlist; method=Cheby);

In any subsequent propagation, we could access the timing data in a callback to propagate:

function show_timing_data(propagator, args...)
    if propagator.t == tlist[end]
        show(propagator.timing_data, compact=true)
    end
end

propagate(Ψ₀, H, tlist; method=:cheby, callback=show_timing_data);

─────────────────────────────────────────────────────────────────────
                                        Time           Allocations
                                   ──────────────    ───────────────
        Tot / % measured:           1.16s / 1.7%     26.8MiB / 0.5%
 ────────────────────────────────  ──────────────    ───────────────
 Section                   ncalls    time    %tot      alloc    %tot
─────────────────────────────────────────────────────────────────────
 prop_step!                   100  19.7ms  100.0%     127KiB  100.0%
 └─ matrix-vector product   1.20k  18.5ms   94.2%          ∅       ∅
─────────────────────────────────────────────────────────────────────

See the TimerOutputs documentation for details on how to print the timing_data.

Alternatively, without a callback:

propagator = init_prop(Ψ₀, H, tlist; method=Cheby)
for step ∈ 1:(length(tlist)-1)
    prop_step!(propagator)
end
show(propagator.timing_data, compact=true)

─────────────────────────────────────────────────────────────────────
                                        Time           Allocations
                                   ──────────────    ───────────────
        Tot / % measured:          38.7ms / 52.7%    472KiB / 26.9%
 ────────────────────────────────  ──────────────    ───────────────
 Section                   ncalls    time    %tot      alloc    %tot
─────────────────────────────────────────────────────────────────────
 prop_step!                   100  20.4ms  100.0%     127KiB  100.0%
 └─ matrix-vector product   1.20k  19.3ms   94.4%          ∅       ∅
─────────────────────────────────────────────────────────────────────

The reported runtimes here are less important than the number of function calls and the runtime percentages. In this case, the timing data shows that the propagation is dominated by the matrix-vector products (applying the Hamiltonian to the state), as it should. The percentage would go to 100% for larger Hilbert spaces.

Newton propagation

For the Newton method:

propagate(Ψ₀, H, tlist; method=Newton);   # recompilation
propagate(Ψ₀, H, tlist; method=Newton, callback=show_timing_data);

─────────────────────────────────────────────────────────────────────────────
                                                Time           Allocations
                                           ──────────────    ───────────────
            Tot / % measured:              135ms / 61.4%     14.9MiB / 87.4%
 ────────────────────────────────────────  ──────────────    ───────────────
 Section                           ncalls    time    %tot      alloc    %tot
─────────────────────────────────────────────────────────────────────────────
 prop_step!                           100  83.0ms  100.0%    13.0MiB  100.0%
 ├─ arnoldi!                          200  30.3ms   36.5%       224B    0.0%
 │  └─ matrix-vector product        2.00k  28.1ms   33.8%          ∅       ∅
 ├─ diagonalize_hessenberg_matrix     200  25.7ms   31.0%    9.38MiB   71.9%
 ├─ get Leja points                   200  24.3ms   29.2%          ∅       ∅
 ├─ evaluate polynomial               200   813μs    1.0%    2.47MiB   19.0%
 └─ get Newton coeffs                 200   204μs    0.2%          ∅       ∅
─────────────────────────────────────────────────────────────────────────────

We see here that the Newton propagation requires more matrix-vector products (2000 compared to 1200 for Chebychev), partly because the Newton propagator is "chunked" to m_max applications in each "restart" (10 by default, with 2 restarts required to reach machine precision in this case). Moreover, there is significant overhead beyond just matrix-vector multiplication, which will disappear only for significantly larger Hilbert spaces.

Disabling the collection of timing data

There there is a small overhead associated with collecting the timing data, it should not be enabled "in production". To QuantumPropagators.disable_timings function undoes the previous QuantumPropagators.enable_timings:

QuantumPropagators.disable_timings()

This again will trigger recompilation of any method that was collecting timing data, removing the associated overhead.