Abstract Quantum computing systems rely on the principles of quantum mechanics to perform a multitude of computationally challenging tasks more efficiently than their classical counterparts. The architecture of software-intensive systems can empower architects who can leverage architecture-centric processes, practices, description languages to model, develop, and evolve quantum computing software (quantum software for short) at higher abstraction levels. We conducted a Systematic Literature Review (SLR) to investigate (i) architectural process, (ii) modelling notations, (iii) architecture design patterns, (iv) tool support, and (iv) challenging factors for quantum software architecture. Results of the SLR indicate that quantum software represents a new genre of software-intensive systems; however, existing processes and notations can be tailored to derive the architecting activities and develop modelling languages for quantum software. Quantum bits (Qubits) mapped to Quantum gates (Qugates) can be represented as architectural components and connectors that implement quantum software. Tool-chains can incorporate reusable knowledge and human roles (e.g., quantum domain engineers, quantum code developers) to automate and customise the architectural process. Results of this SLR can facilitate researchers and practitioners to develop new hypotheses to be tested, derive reference architectures, and leverage architecture-centric principles and practices to engineer emerging and next generations of quantum software.