🤖 AI Summary
This work addresses the longstanding challenges in implementing block-encoding–based quantum linear algebra algorithms, which have been hindered by the complexity of underlying circuit construction and the difficulty of verification. We introduce Unitaria, a NumPy/SciPy-like Python library that provides a composable, array-oriented interface for directly manipulating encoded matrices and vectors without requiring ancilla qubits. By unifying block encoding, quantum singular value transformation, and standard linear algebra operations—augmented with automated circuit synthesis and resource analysis—our approach enables efficient classical validation and scalable simulation. Compared to conventional state-vector simulators, Unitaria significantly extends the attainable problem scale and accurately estimates key resources such as gate count, qubit count, and normalization constants without executing the quantum circuit.
📝 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.