In a recent publication in EPJ Quantum Technology, Le Bin Ho of Tohoku University’s Frontier Institute for Interdisciplinary Sciences has introduced a groundbreaking technique known as “time-dependent stochastic parameter shift” in the realm of quantum computing and quantum machine learning. This innovative approach is set to transform the way we estimate gradients or derivatives of functions, a critical step in numerous computational tasks.
Traditionally, computing derivatives involves dissecting a function and calculating its rate of change over small intervals. However, classical computers face limitations when it comes to endless subdivisions. In contrast, quantum computers offer a unique advantage. They can achieve this task without needing to discretize the function. This ability arises from quantum computers operating in the “quantum space,” characterized by periodicity and the absence of the need for infinite subdivisions.
To better understand this concept, consider comparing the sizes of two elementary schools on a map. One approach would involve printing out maps of the schools and cutting them into smaller pieces. After cutting, these pieces are aligned in a line, and their total length is compared (see Figure 1a). However, these pieces may not form a perfect rectangle, leading to inaccuracies. Achieving high accuracy would require an impractical, infinite subdivision, even for classical computers.
A more straightforward method is to weigh the paper pieces representing the two schools and compare their weights (see Figure 1b). This method provides accurate results as long as the paper sizes are large enough to detect the mass difference. This concept bears similarity to the parameter shift technique but operates in spaces that do not necessitate endless intervals (as depicted in Figure 1c).
Le explains, “Our time-dependent stochastic method is versatile and can be applied to compute higher-order derivatives and the quantum Fisher information matrix (QFIM). The QFIM is a fundamental concept in quantum information theory and quantum metrology, with intricate connections to various disciplines, including quantum metrology, phase transitions, entanglement witness, Fubini-Study metric, and quantum speed limits. Calculating the QFIM on quantum computers opens doors to utilizing quantum computing across diverse fields such as cryptography, optimization, drug discovery, materials science, and more.”
Le also demonstrates how this method can be applied in various scenarios, including quantum metrology involving single and multiple magnetic fields and Hamiltonian tomography for complex many-body systems. A meticulous comparison between the new approach and the exact theoretical method, as well as an approximation model known as the Suzuki-Trotter, reveals that the method aligns closely with the theoretical approach. In contrast, the Suzuki-Trotter approximation deviates from the true value, emphasizing the need for infinite subdivisions in enhancing its results.
Source: Tohoku University