Extending UNIQuE: Quantum Simulation Speedup for the HHL Algorithm
For researchers simulating quantum algorithms classically, this provides a more efficient emulation of HHL for small linear systems.
This work extends the UNIQuE emulator to classically emulate the HHL algorithm for linear systems, achieving exponential scaling in qubits rather than system size and eigenvalue magnitude. Benchmarks show a runtime advantage over the Intel Quantum Simulator for small systems.
In an extension of the Unconventional Noiseless Intermediate Quantum Emulator, this work introduces a classical emulation of the quantum Harrow-Hassidim-Lloyd algorithm for sampling from the solution space of linear systems. The emulated HHL algorithm scales exponentially with the number of qubits required to represent the linear system, which is an advantage over the state vector simulation of the HHL algorithm, which scales exponentially as a function of both the size of the linear system and the magnitude of its largest (scaled) eigenvalue. We benchmark our emulator by comparing it with the Intel Quantum Simulator and demonstrate a runtime advantage for small linear systems.