Certain of Heisenberg's Arts

Friedrich Katscher

Yinuo Shao

As a matter of fact, the Heisenberg’s uncertainty principle has important significance and extensive application in microcosmic particle science, is one of the cornerstones of quantum mechanics, proposed by Heisenberg in 1927. The uncertainty principle means that it is impossible to measure a particle’s speed and position at the same time. The uncertainty of particle, i.e., the product of uncertainty of position (∆Q) and uncertainty of momentum (∆P), is inevitable greater than or equal to Plank’s constant, it expresses the inconsistency between particle behavior in microcosm and macroscopic substance. This study is going to set forth the uncertainty meaning, the research progress of uncertainty principle from the angle of physics, and further exploring the physical significance of Heisenberg’s uncertainty principle. According to the analysis, the state-of-art applications will be demonstrated as well as the current limitations and prospects will be discussed. Overall, these results pave a novel path for further investigation in regarding to Heisenberg’s uncertainty.

Changhao Yi, Cunlu Zhou, Jun Takahashi

As a signal recovery algorithm, compressed sensing is particularly effective when the data has low complexity and samples are scarce, which aligns natually with the task of quantum phase estimation (QPE) on early fault-tolerant quantum computers. In this work, we present a new Heisenberg-limited, robust QPE algorithm based on compressed sensing, which requires only sparse and discrete sampling of times. Specifically, given multiple copies of a suitable initial state and queries to a specific unitary matrix, our algorithm can recover the phase with a total runtime of O ( ϵ − 1 poly log ⁡ ( ϵ − 1 ) ) , where ϵ is the desired accuracy. Additionally, the maximum runtime satisfies T max ϵ ≪ π , making it comparable to state-of-the-art algorithms. Furthermore, our result resolves the basis mismatch problem in certain cases by introducing an additional parameter to the traditional compressed sensing framework.

Hrishikesh Belagali, Ryan LaRose

We introduce Propaq, a performant and flexible Python package implementing Heisenberg propagation techniques for classically simulating quantum circuits. Propaq is compatible with major quantum software packages like Qiskit and Cirq, and matches or outperforms similar state-of-the-art packages for Heisenberg propagation. Beyond this, Propaq has multiple distinguishing features for simulation and research. These include Heisenberg propagation in any basis, hybrid Schrödinger-Heisenberg simulation, custom truncation and noisy simulation methods, and detailed logging information for analyzing simulation accuracy, runtime, and memory usage. We describe these features, how to use Propaq for research, and its backend implementation.

Abner Shimony