Identity Check Problem for Shallow Quantum Circuits

Learn about a groundbreaking quantum computing research presentation that explores the identity check problem for shallow quantum circuits. Discover a new classical algorithm for approximating the diamond-norm distance between quantum circuits and identity channels, specifically designed for shallow geometrically local D-dimensional circuits. Explore how this algorithm achieves linear runtime scaling with qubit count for constant circuit depth and spatial dimension, and understand its practical implementation in 1D Trotter circuits with up to 100 qubits. Delve into the theoretical findings showing efficient approximation of operator-norm distance to identity for shallow 1D circuits and D-dimensional circuits under specific conditions. This talk, presented at the prestigious 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024) by researchers Sergey Bravyi, Natalie Parham, and Minh Tran, advances our understanding of quantum circuit equivalence verification.