Towards an Operational Quantum Memory

Wolfgang Tittel, Mikael Afzelius, Nicolas Gisin +2 more

Xiao Yuan, Yunchao Liu, Qi Zhao +3 more

Quantum memory -- the capacity to store and faithfully recover unknown quantum states -- is essential for any quantum technology to exhibit operational advantage. There is thus great value in identifying physically meaningful means to benchmark candidate quantum memories against each other across diverse operational settings. Here we introduce the robustness of quantum memory, and prove that it satisfies all the mathematical properties we expect of a bona-fide resource-theoretic measure of a system's capacity to retain non-classical information. We demonstrate its operational meaning as a resource in three different settings: (1) the resource cost of synthesising the memory with idealised qubit memories, (2) the resource cost of simulating the memory's observational statistics with classical resources, and (3) the performance of the memory in discriminating different input states. We illustrate an efficient semi-definite program to estimate the robustness of quantum memory, and show that it can be lower bounded with a single witness or purity measurement. Our results thus provide an experimentally accessible and operationally meaningful quantifier of the resources behind preserving quantum information.

Tai Tsun Wu

To a large extent, the power of a quantum computer comes from the possibility of operating on a number of quantum memories simultaneously. For example, if there are n linearly independent quantum states in each of N quantum memories, then the number of linearly independent quantum states is n^N when they are taken together. This exponential increase is the basis of the present interest in quantum computing. In the context of quantum mechanics as described by the Schrodinger equation (which is a partial differential equation), the most explicit model of the quantum memory is one with two linearly independent quantum states described in terms of the Fermi pseudo-potential at one point. In this model, operations on the quantum memory are accomplished through scattering with both symmetrical and anti-symmetrical incident waves. As a first step toward operating on more than one quantum memory, this model is generalized in two directions. (1) With the Fermi pseudo-potential at one point retained, three linearly independent quantum states are used for the quantum memory. This model of the quantum memory requires three external connections. (2) With a more general potential, operations on the quantum memory with two states are accomplished through scattering with either symmetrical or anti-symmetrical incident waves. This second generalization is important because it is not practical to keep the number of external connections equal to the number of linearly independent quantum states.

Jincheng Zhang

This paper proposes a novel approach to biological information processing by leveraging the principles of quantum memory. The core idea is to mimic the memory function of biological neurons using quantum memory models, thereby accelerating and enhancing the efficiency of biological information handling. This research explores the potential of quantum memory to emulate key aspects of neuronal operation, specifically focusing on the rapid processing and storage of biological information. The theoretical framework developed herein outlines a computational model based on quantum memory interactions, demonstrating a pathway towards achieving significant improvements in biological information processing speed and capacity. This work presents a fundamental investigation into the intersection of quantum mechanics and neuroscience, offering a new perspective on the mechanisms underlying biological memory and potentially paving the way for advanced bio-computing architectures. The presented model utilizes the following key equations to illustrate the core concepts: (Δs) = (H(s) * ∇s) + (G(s, s') * s') where: Δs represents the change in state of the quantum memory. H(s) is the Hamiltonian operator describing the quantum memory's energy levels. ∇s is the gradient operator, representing the influence of external stimuli. G(s, s') is the coupling strength between neighboring quantum memories. s and s' represent the states of the quantum memories. Further equations exploring the dynamics include: (ds/dt) = (H(s) * s) - (∑G(s, s') * s') and the state update rule: s(t+Δt) = U(Δt) * s(t) where: U(Δt) is the time evolution operator, describing the quantum dynamics over a small time interval Δt. This research contributes to the nascent field of quantum biology and provides a foundational model for future investigations into quantum-enhanced biological systems. ---