Zixy

Zixy is a high performance library for the manipulation of Pauli strings and other quantum algebraic objects.

Installation

From PyPI

The package is available via PyPI and can be installed using the preferred package manager, such as pip.

pip install zixy

From source

Developers may wish to install from source. The recommended method is by using maturin from the top level directory.

git clone https://github.com/quantinuum/zixy
cd zixy
maturin develop

Usage

Overview

The package is written in Rust, with Python bindings enabled via PyO3. The base containers in the Python interface are defined in a general fashion. The user-facing API separates these objects into three important classes:

• Coeff: a coefficient, defining a scalar value of varying types.
• Cmpnt: a component, defining a basic algebraic building block.
• Term: a term, consisting of a Cmpnt scaled by a Coeff.

Coefficients are separated into built-in Python types such as float or complex, symbolic sympy expressions, and roots of unity such as Sign and ComplexSign, which have custom implementations.

Additionally, each such class has associated containers for collections of that type. Implementations of these base classes may narrow their implementation depending on the coefficient type.

Example

These general building blocks are sufficient to define many different quantum algebraic objects. An example of one such specification of the objects in Zixy is Pauli strings. These are made available in the zixy.qubit.pauli submodule, with the qubits forming a basis for their definition available in zixy.qubit.

import zixy.qubit as zq
import zixy.qubit.pauli as zqp

qubits = zq.Qubits.from_count(4)
print(len(qubits))  # 4

strings = zqp.Strings.from_str("X0 Y1 Z3", qubits)
print(str(strings))  # X0 Y1 Z3

terms = zqp.RealTerms.from_str("X0 Y1 Z3")
print(str(terms))  # (1, X0 Y1 Z3)

For other specifications such as computational basis vectors, further example notebooks are available.

Rust

The trait NumRepr (meaning "number representation") is implemented by all types that can represent the numbers multiplying components. In collections, these are stored contiguously in vector-like structures. Values of NumRepr types are closed under multiplication, but do not implement addition. Implementers of NumRepr are

• Unity: a unit type representing +1 and only +1. The corresponding collection container UnityVec only stores a length, the number of unit values.
• Sign: the square roots of unity (+1, -1). The corresponding collection container, SignVec is implemented as a bitset.
• ComplexSign: the fourth roots of unity (+1, +i, -1, -i). The corresponding collection container, ComplexSignVec is implemented as a paired bitset.

The FieldElem subtrait of NumRepr is implemented by types whose values form a field with multiplication and addition. Implementers of both NumRepr and FieldElem use Vec<T> for collection storage, and are

• Real: Floating point value f64
• Complex: Complex floating point value Complex64 from num_complex crate.

The Python interface further supports symbolic types via SymPy, which are not currently available within the Rust library.

On the Rust side, components are stored contiguously in CmpntList types. These implement the business logic applicable to their elements. There are three main kinds of container that encapsulate CmpntList with generic coefficient type C

• Terms<C: NumRepr>: stores a C::Vector of the same length as the CmpntList, offers mutable access to the components and coefficients.
• TermSet<C: NumRepr>: stores a C::Vector of the same length as the CmpntList and via an indirect hash map, provides constant complexity lookup and enforces uniqueness among components. Offers mutable access only to the coefficients.
• TermSum<C: FieldElem>: works like Set<C> but with linear combination semantics and is only defined for FieldElem-implementing coefficient types.