Applied Quantum Technologies (United States)

This paper presents a probabilistic, multi-layered framework designed to forecast the longevity and security of cryptographic systems under the dual pressures of classical and quantum computational threats. The model integrates thermodynamic decay analogies, stochastic transitions via Hidden Markov Models, and an adapted financial option pricing method to quantify cryptographic degradation, strategic risk, and transition readiness. This framework can guide standardization roadmaps, cipher retirement, or quantum-migration planning, guiding proactive, instead of reactive, crypto agility. Furthermore, it provides a quantitative methodology to complement the current opinions expressed in surveys, as well as a qualitative approach to cryptographic security risk projections.

Abstract A major challenge in fault-tolerant quantum computation is to reduce both the space overhead, that is, the large number of physical qubits per logical qubit, and the time overhead, that is, the long physical gate sequences needed to implement a logical gate. Here we prove that a protocol using non-vanishing-rate quantum low-density parity-check (QLDPC) codes, combined with concatenated Steane codes, achieves constant space overhead and polylogarithmic time overhead, even when accounting for the required classical processing. This protocol offers an improvement over existing constant-space-overhead protocols. To prove our result, we develop a technique that we call partial circuit reduction, which enables error analysis for the entire fault-tolerant circuit by examining smaller parts composed of a few gadgets. With this approach, we resolve a logical gap in the existing arguments for the threshold theorem for the constant-space-overhead protocol with QLDPC codes and complete its proof. Our work establishes that the QLDPC-code-based approach can realize fault-tolerant quantum computation with a negligibly small slowdown and a bounded overhead of physical qubits.

The accurate and efficient energy estimation of quantum Hamiltonians consisting of Pauli observables is an essential task in modern quantum computing. We introduce a Resource-Optimized Grouping Shadow (ROGS) algorithm, which optimally allocates measurement resources by minimizing the estimation error bound through a novel overlapped grouping strategy and convex optimization. Our numerical experiments demonstrate that ROGS requires significantly fewer unique quantum circuits for accurate estimation accuracy compared to existing methods given a fixed measurement budget, addressing a major cost factor for compiling and executing circuits on quantum computers.

Mesoscopic systems, which lie between microscopic and macroscopic scales, are pivotal in understanding quantum transport phenomena. These systems, typically comprising a few hundred to thousand atoms, exhibit quantum effects that are not observable in either the macroscopic or microscopic regimes. Theoretical models of quantum transport in mesoscopic systems, such as the Landauer-Büttiker formalism, the tight-binding model, and the Lippmann-Schwinger equation, provide crucial insights into electron behavior, resistance, and conductance in these systems. This article presents an overview of key theoretical models used to describe quantum transport, discusses their applications, and examines the experimental validation of these models in modern mesoscopic systems.

We describe microsystems approach to realizing a scalable quantum information processor in trapped ions and atoms. A flexible, MEMS-based beam steering system is demonstrated that enables random access of qubits in a 2D array.