Speaker
Description
Shor’s factorization algorithm which factors integers in time polynomial to their bit-length, is a major milestone in the race to demonstratable quantum advantage because of its exponential speedup over currently available classical algorithms. It also provides an ideal testbed for benchmarking classical simulations of quantum algorithms and is particularly interesting as a stress test for tensor-network simulations because of the entanglement generated within its quantum circuit representation. In this talk I will present our work on benchmarking the Shor’s algorithm on RSA-like semi-primes using the full gate-level Vedral, Barenco and Ekert (VBE) modular exponentiation circuit instead of a high-level arithmetic oracle on a tensor network powered quantum emulator and quantify its performance with three complementary figures of merit: a fidelity estimate derived from truncated singular values, a divergence metric comparing the distance between the true output distribution and the simulated one, and the normalized factoring success probability. In addition to illustrating how each of them behave with the bond dimension of the tensor network, I will also highlight how the simulation complexity relates to the bit-length and the multiplicative order for a particular semi-prime for ideal, noiseless circuits. This serves as the premise for the core of the talk: benchmarking under the effect of coherent errors, which is modelled using systematic unitary over-rotations applied stochastically, mimicking gate miscalibrations in quantum hardware. I will present the noise model in detail which rely on two main parameters: the over-rotation angle and the per-gate probability. Sweeping both, we map how the figures of merit behave, locate the thresholds where factoring fails, and find that coherent errors tend to drive the required bond dimension upward; thus establishing Shor's algorithm as a verifiable, tuneable probe of classical simulability at the edge of tractability.