Unitaria: Quantum Linear Algebra via Block Encodings

TL;DR

Unitaria is a Python library that simplifies the implementation and analysis of quantum linear algebra algorithms using block encodings, enabling classical verification and resource estimation.

Contribution

It introduces a user-friendly, array-like interface for quantum block encodings, allowing direct classical computation and analysis of quantum linear algebra operations.

Findings

Supports classical verification of quantum algorithms.

Enables resource estimation without circuit execution.

Provides a composable interface for quantum matrix operations.

Abstract

We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on block encodings, a general-purpose abstraction in which a matrix is embedded as a sub-block of a larger unitary operator. Their implementation has so far required deep knowledge of low-level circuit construction, which Unitaria aims to eliminate. The library provides a composable, array-like interface through which users can define block encodings of matrices and vectors, combine them through standard operations such as addition, multiplication, tensor products, and the Quantum Singular Value Transformation, and extract the resulting quantum circuits automatically. A key feature is a matrix-arithmetic evaluation path in which every operation can be computed directly on encoded vectors and matrices without dependence on ancilla qubits or circuit simulation. This enables correctness verification and classical simulation that scale well beyond what state vector simulation permits and also allows resource estimation, including gate counts, qubit counts, and normalization constants, without executing any circuit. Together, these capabilities allow researchers to develop, verify, and analyze quantum linear algebra algorithms today, ahead of the availability of error-corrected hardware. Unitaria is open source and available at https://github.com/tequilahub/unitaria.