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Updated controlled ApproximatelyMultiplexZ, added test #2749

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Updated controlled ApproximatelyMultiplexZ, added test #2749

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10 changes: 10 additions & 0 deletions library/src/tests/resources/src/state_preparation.qs
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Original file line number Diff line number Diff line change
Expand Up @@ -124,4 +124,14 @@ namespace Test {
}
}

operation TestControlledPreparation() : Unit {
use qs = Qubit[2];
let coeffs = [0.5, 0.5, 0.5, 0.5];
use c = Qubit();
H(c);
Controlled Std.StatePreparation.PreparePureStateD([c], (coeffs, qs));
Std.Diagnostics.DumpMachine();
ResetAll(qs + [c]);
}

}
19 changes: 19 additions & 0 deletions library/src/tests/state_preparation.rs
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Expand Up @@ -307,3 +307,22 @@ fn check_uniform_superposition_invalid_state_count() {

expect!["program failed: Number of basis states must be positive."].assert_eq(&out);
}

#[test]
fn check_controlled_state_preparation() {
let out = test_expression_with_lib(
"Test.TestControlledPreparation()",
STATE_PREPARATION_TEST_LIB,
&Value::Tuple(vec![].into(), None),
);

expect![[r#"
STATE:
|000⟩: 0.7071+0.0000𝑖
|001⟩: 0.3536+0.0000𝑖
|011⟩: 0.3536+0.0000𝑖
|101⟩: 0.3536+0.0000𝑖
|111⟩: 0.3536+0.0000𝑖
"#]]
.assert_eq(&out);
}
4 changes: 3 additions & 1 deletion library/std/src/Std/StatePreparation.qs
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Expand Up @@ -13,6 +13,7 @@ import
Std.Arithmetic.ApplyIfGreaterLE,
Std.Arithmetic.ApplyIfGreaterL,
Std.Arithmetic.ReflectAboutInteger,
Std.ArithmeticUtils.ApplyAsSinglyControlled,
Std.Convert.IntAsBigInt,
Std.Math.*,
Std.Arrays.*;
Expand Down Expand Up @@ -351,7 +352,8 @@ operation ApproximatelyMultiplexZ(
ApproximatelyMultiplexZ(tolerance, coefficients0, control, target);
if AnyOutsideToleranceD(tolerance, coefficients1) {
within {
Controlled X(controlRegister, target);
// Reduce circuit complexity by using aux qubits.
Controlled ApplyAsSinglyControlled(controlRegister, (X, target));
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@msoeken msoeken Oct 21, 2025

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One can still save a factor of 2x by only doing the forward direction of the multi-controlled X gate (chain of computing ANDs) and then the backward direction (chain of uncomputing ANDs) afterwards. However, this will require to allocate the helper qubits in this operation.

For a 3-qubit controlRegister the trace would be as follows:

use helper = Qubit[1];

And(controlRegister[0], controlRegister[1], helper[0]);
And(controlRegister[1], helper[0], target);

ApproximatelyMultiplexZ(tolerance, coefficients1, control, target);

Adjoint And(controlRegister[1], helper[0], target);
Adjoint And(controlRegister[0], controlRegister[1], helper[0]);

} apply {
ApproximatelyMultiplexZ(tolerance, coefficients1, control, target);
}
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