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 QuantumControlTestUtils.RandomObjects: random_dynamic_generator, random_state_vector

tlist = collect(range(0, step=1.0, length=101));
N = 200;  # size of Hilbert space
H = 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.
 Range (min … max):  25.089 ms … 28.454 ms  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     25.295 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   25.796 ms ±  1.092 ms  ┊ GC (mean ± σ):  0.00% ± 0.00%

    █▃                                                         
  ▇▁██▇▁▁▁▁▁▁▇▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▇▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▇ ▁
  25.1 ms         Histogram: frequency by time        28.5 ms <

 Memory estimate: 1.00 MiB, allocs estimate: 3464.

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.
 Range (min … max):  95.104 ms … 108.760 ms  ┊ GC (min … max): 0.00% … 7.40%
 Time  (median):     96.138 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   97.934 ms ±   4.132 ms  ┊ GC (mean ± σ):  0.82% ± 2.34%

  ▁▁ █▁▁  ▁      ▁       ▁                                   ▁  
  ██▁███▁▁█▁▁▁▁▁▁█▁▁▁▁▁▁▁█▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█ ▁
  95.1 ms         Histogram: frequency by time          109 ms <

 Memory estimate: 17.25 MiB, allocs estimate: 83298.

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
                                  ───────────────   ───────────────
         Total measured:               389ms            26.4MiB

Section                   ncalls     time    %tot     alloc    %tot
───────────────────────────────────────────────────────────────────
prop_step!                   100   25.2ms  100.0%    132KiB  100.0%
  matrix-vector product    1.20k   23.5ms   93.5%     0.00B    0.0%
───────────────────────────────────────────────────────────────────

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
                                  ───────────────   ───────────────
         Total measured:              57.2ms             432KiB

Section                   ncalls     time    %tot     alloc    %tot
───────────────────────────────────────────────────────────────────
prop_step!                   100   26.2ms  100.0%    132KiB  100.0%
  matrix-vector product    1.20k   24.6ms   93.9%     0.00B    0.0%
───────────────────────────────────────────────────────────────────

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
                                          ───────────────   ───────────────
             Total measured:                   186ms            19.5MiB

Section                           ncalls     time    %tot     alloc    %tot
───────────────────────────────────────────────────────────────────────────
prop_step!                           100    133ms  100.0%   17.2MiB  100.0%
  diagonalize_hessenberg_matrix      200   57.3ms   42.9%   9.37MiB   54.5%
  arnoldi!                           200   44.6ms   33.4%   16.3KiB    0.1%
    matrix-vector product          2.00k   41.4ms   31.0%     0.00B    0.0%
  get Leja points                    200   26.2ms   19.6%   6.25KiB    0.0%
  evaluate polynomial                200   2.52ms    1.9%   6.41MiB   37.3%
  get Newton coeffs                  200    246μs    0.2%   3.12KiB    0.0%
───────────────────────────────────────────────────────────────────────────

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.