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Abstract:

In this Letter, we show how Euclidean three-space uniquely emerges from the structure of quantum temporal correlations associated with sequential measurements of Pauli observables on a single qubit. Quite remarkably, the quantum temporal correlations which give rise to geometry are independent of the initial state of the qubit, which we show enables an observer to extract geometric data from sequential measurements without the observer having any knowledge of initial conditions. Such results suggest the plausibility that space itself may emerge from quantum temporal correlations, and we formulate a toy model of such a hypothetical phenomenon.

Abstract:

Solving quantum molecular systems presents a significant challenge for classical computation. The advent of early fault‐tolerant quantum computing devices offers a promising avenue to address these challenges, leveraging advanced quantum algorithms with reduced hardware requirements. This review surveys the latest developments in quantum computing algorithms for quantum molecular systems in the fault‐tolerant quantum computing era, covering encoding schemes, advanced Hamiltonian simulation techniques, and ground‐state energy estimation methods. We highlight recent progress in overcoming practical barriers, such as reducing circuit depth and minimizing the use of ancillary qubits. Special attention is given to the potential quantum advantages achievable through these algorithms, as well as the limitations imposed by dequantization and classical simulation techniques. The review concludes with a discussion of future directions, emphasizing the need for optimized algorithms and experimental validation to bridge the gap between theoretical developments and practical implementation for quantum molecular systems.

Abstract:

We propose a collision model to investigate the information dynamics of a system coupled to an environment with varying degrees of non-Markovianity. We control the degree of non-Markovianity by applying a depolarising channel to a fixed and rigid reservoir of qubits. We characterise the effect of the depolarising channel and apply the model to study the coherent transport of information on a chain of three interacting qubits. We show how the system-environment coupling probability and the degree of non-Markovianity affect the process. Interestingly, in some cases a Markovian environment is preferable to reduce information loss and enhance the coherent transport.