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Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as {importance sampling,} observable…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
Accurately estimating the overlap between quantum states is a fundamental task in quantum information processing. While various strategies using distinct quantum measurements have been proposed for overlap estimation, the lack of…
The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…
Characterising large-scale quantum systems is central to fundamental physics and essential for applications of quantum technologies. While a full characterisation requires exponentially increasing resources, focusing on application-relevant…
Partial tomography, which focuses on reconstructing reduced density matrices (RDMs), has emerged as a promising approach for characterizing complex quantum systems, particularly when full state tomography is impractical. Recently,…
Achieving chemical accuracy in quantum simulations is often constrained by the measurement bottleneck: estimating operators requires a large number of shots, which remains costly even on fault-tolerant devices and is further exacerbated on…
Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For…
Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital…
Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms. For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the…
Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
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…
The practical application of quantum technologies to chemical problems faces significant challenges, particularly in the treatment of realistic basis sets and the accurate inclusion of electron correlation effects. A direct approach to…
The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems…
Large-scale overlapping problems are prevalent in practical engineering applications, and the optimization challenge is significantly amplified due to the existence of shared variables. Decomposition-based cooperative coevolution (CC)…
Scalable quantum technologies will present challenges for characterizing and tuning quantum devices. This is a time-consuming activity, and as the size of quantum systems increases, this task will become intractable without the aid of…
Quantum technologies are developing powerful tools to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we explore how coherence can be…
Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…