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//! (public for pedagogical reasons).
/// Convenience macros for qubit module.
mod macros {
#![macro_use]
/// Square a numeric value efficiently by multiplying it with itself.
#[macro_export]
macro_rules! square {
($x:expr) => {
$x * $x
};
}
/// Compute a complex number's absolute value, i.e. _|x + iy|^2_.
#[macro_export]
macro_rules! abs_square {
($re:expr, $im:expr) => {
square!($re) + square!($im)
};
}
}
/// Single qubit library code.
pub mod qubit {
use float_cmp::ApproxEqUlps;
/// Represents a single (pure, not entangled) qubit state of the form `a|0> + b|1>`.
///
/// The qubit is the linear superposition of the computational basis of `|0>_ and _|1>`.
///
/// We encode the complex coeffients as tuples of their real and imaginary parts,
/// each represented as a 64-bit floating points. This gives high accuracy, while
/// allowing word-size arithmetic on 64-bit systems.
///
/// The theoretical state should always satisfy the equations:
///
/// - `a = a_re + i * a_im`
/// - `b = b_re + i * b_im`
/// - `1 = |a|^2+ |b|^2`
///
/// This representation of that state should approximately satisfy them, subject to floating
/// point imprecision.
#[derive(Clone, Copy, Debug)]
pub struct NonEntangledQubit {
a_re: f64,
a_im: f64,
b_re: f64,
b_im: f64,
}
impl NonEntangledQubit {
/// Safely construct a qubit, given the real and imaginary parts of both coefficients.
///
/// This function validates that the given state is possible.
pub fn new(a_re: f64, a_im: f64, b_re: f64, b_im: f64) -> NonEntangledQubit {
let candidate = NonEntangledQubit {
a_re: a_re,
a_im: a_im,
b_re: b_re,
b_im: b_im,
};
assert!(candidate.validate());
candidate
}
/// Validate that this qubit's state is possible.
///
/// In our imperfect floating point model, this means computing `|a|^2+ |b|^2` and
/// comparing it to `1` with some leeway.
///
/// That leeway is arbitrarily chosen as 10 units of least precision.
#[cfg(not(feature = "optimize"))]
pub fn validate(&self) -> bool {
let sample_space_sum: f64 = abs_square!(self.a_re, self.a_im) +
abs_square!(self.b_re, self.b_im);
sample_space_sum.approx_eq_ulps(&1.0f64, 10)
}
/// Skip state validation for speed.
#[cfg(feature = "optimize")]
#[inline(always)]
pub fn validate(&self) -> bool {
true
}
}
#[test]
fn initialization_test() {
let sqrt2inv = 2.0f64.sqrt().recip();
let q1: NonEntangledQubit = NonEntangledQubit::new(0.5, 0.5, 0.5, 0.5);
let q2: NonEntangledQubit = NonEntangledQubit::new(sqrt2inv, sqrt2inv, 0.0, 0.0);
let q3: NonEntangledQubit = NonEntangledQubit::new(0.0, 0.0, sqrt2inv, sqrt2inv);
assert!(q1.validate());
assert!(q2.validate());
assert!(q3.validate());
}
#[test]
#[should_panic(expected = "assertion failed")]
#[cfg(not(feature = "optimize"))]
fn bad_initialization_test() {
NonEntangledQubit::new(0.0, 0.0, 0.0, 0.0);
}
}