Abstract: An apparatus can include at least a controller, quantum hardware, and an interface. The controller can be configured to generate command signals. The quantum hardware can include at least a plurality of qubits. The interface can be connected to the controller and the quantum hardware, the interface being configured to control the quantum hardware based on the command signals to implement a quantum circuit configured to simulate a boundary operator that creates a mapping of boundaries of a given graph having nodes and edges. For example, the quantum circuit can be configured to simulate a boundary operator that creates a mapping of simplices of orders, e.g., of all orders, in a given simplicial complex. A method can include creating a boundary operator on a quantum computer, where a quantum circuit is built using Pauli spin operators.