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Abstract Our study evaluates the limitations and potentials of Quantum Random Access Memory (QRAM) within the principles of quantum physics and relativity. QRAM is crucial for advancing quantum algorithms in fields like linear algebra and machine learning, purported to efficiently manage large data sets with$${{{\mathcal{O}}}}(\log N)$$ $O\left(\log N\right)$circuit depth. However, its scalability is questioned when considering the relativistic constraints on qubits interacting locally. Utilizing relativistic quantum field theory and Lieb–Robinson bounds, we delve into the causality-based limits of QRAM. Our investigation introduces a feasible QRAM model in hybrid quantum acoustic systems, capable of supporting a significant number of logical qubits across different dimensions-up to ~10⁷in 1D, ~10¹⁵to ~10²⁰in 2D, and ~10²⁴in 3D, within practical operation parameters. This analysis suggests that relativistic causality principles could universally influence quantum computing hardware, underscoring the need for innovative quantum memory solutions to navigate these foundational barriers, thereby enhancing future quantum computing endeavors in data science. 

Abstract Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in devices without quantum error correction. To address these challenges simultaneously, we develop a quantum error-mitigation strategy calledsymmetry-adjusted classical shadows, by adjusting classical-shadow tomography according to how symmetries are corrupted by device errors. As a concrete example, we highlight global U(1) symmetry, which manifests in fermions as particle number and in spins as total magnetization, and illustrate their group-theoretic unification with respective classical-shadow protocols. We establish rigorous sampling bounds under readout errors obeying minimal assumptions, and perform numerical experiments with a more comprehensive model of gate-level errors derived from existing quantum processors. Our results reveal symmetry-adjusted classical shadows as a low-cost strategy to mitigate errors from noisy quantum experiments in the ubiquitous presence of symmetry. 

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions1. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter2,3. Our preparation relies on simultaneous control over an array of tightly focused individual addressing laser beams, generating long-range spin–spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.