cpx-coords

To power the rust-quantum project, this library provides a robust Cpx type, specifically optimized for the intensive complex number multiplications required for quantum gate applications and tensor product operations. It supports various coordinate representations to maximize performance.

Usage

Add the following to your Cargo.toml:

[dependencies]
cpx-coords = "0.1.4"

Features

• Multiple Coordinate Representations: To optimize performance, particularly for multiplication, this library supports logarithmic coordinates. Multiplication in logarithmic form reduces to addition, which is faster than Cartesian multiplication. Additionally, common-case optimizations further improve time complexity.
• Regularization: Implements a regularize() method to normalize complex numbers, ensuring consistent representations and handling numerical edge cases.
• Precision: Uses f32 or f64 for floating-point precision.
• Comprehensive Operations: Implements standard arithmetic operations (addition, subtraction, multiplication, division), negation, conjugation, i-th root, exponentiation, logarithm, powi, powf, powc and more.
• Constants: Provides a suite of predefined constants for common complex numbers.

Coordinate Representations

This library uses the following coordinate representations for complex numbers:

• Zero {}: Represents the additive identity (0).
• One {}: Represents the multiplicative identity (1).
• NegOne {}: Represents the negation of One (-1).
• J {}: Represents the imaginary unit (j), a square root of -1.
• NegJ {}: Represents the negation of J (-j).
• Real { re: f32 or f64 }: Represents a real number (re).
• Imag { im: f32 or f64 }: Represents a purely imaginary number (im * j).
• Phase { ph: f32 or f64 }: Represents a complex number with a radius of 1 and a phase angle (ph) in the interval (-π, π].
• Ccs { re: f32 or f64, im: f32 or f64 }: Represents a complex number in Cartesian coordinates (re + j * im).
• Ln { re: f32 or f64, im: f32 or f64 }: Represents a complex number in logarithmic form (exp (re + j * im)).
• PL { rad: f32 or f64, ph: f32 or f64 }: Represents a complex number in polar coordinates (rad * exp(j * ph)).

License

This project is licensed under either of

• MIT license
• Apache License, Version 2.0

at your option.

Contributions

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in this project by you shall be licensed as above, without any additional terms or conditions.