Hardware emulation of quantum circuits based on Toffoli gates

This work presents the design of a hardware architecture for the emulation of quantum circuits based on Toffoli gates allowing the emulation of more than 50 qubits. The state of the system is obtained processing each basis state by means of the functions determined by the quantum gates for each qubit; the time required to execute the emulation grows exponentially only with the number of qubits that are used to generate a superposition of states, but not with the total amount of qubits of the system as occurs when the conventional matrix representation is used. Additionally, an array of processing units was designed to decrease the execution time. The synthesis results allow concluding that 9.35 seconds are required to emulate the 8-bit modular exponentiation, which uses 48 qubits, 155,312 quantum gates and requires processing 131,072 basis states. Furthermore these results allow estimating that 256 processing units of 52 qubits can be implemented in the FPGA EP3C120F780I7.