Unitaria: Quantum Linear Algebra via Block Encodings
For quantum algorithm researchers, Unitaria lowers the barrier to implementing block-encoding-based algorithms by eliminating the need for low-level circuit construction.
Unitaria is a Python library that simplifies implementing quantum algorithms based on block encodings, providing a NumPy-like interface for defining and composing block encodings and automatically generating quantum circuits. It enables classical simulation and resource estimation that scale beyond state vector simulation, allowing researchers to develop and verify quantum linear algebra algorithms without error-corrected hardware.
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.