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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…
Recent advances in quantum computers and simulators are steadily leading us towards full-scale quantum computing devices. Due to the fact that debugging is necessary to create any computing device, quantum tomography (QT) is a critical…
Quantum tomography is a critically important tool to evaluate quantum hardware, making it essential to develop optimized measurement strategies that are both accurate and efficient. We compare a variety of strategies using nearly pure test…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a…
The manipulation of quantum states through linear maps beyond quantum operations has many important applications in various areas of quantum information processing. Current methods simulate unphysical maps by sampling physical operations…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
The ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point,…
We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an…
Even with the recent rapid developments in quantum hardware, noise remains the biggest challenge for the practical applications of any near-term quantum devices. Full quantum error correction cannot be implemented in these devices due to…
Given the state of a quantum system, one can calculate the expectation value of any observable of the system. However, the inverse problem of determining the state by performing different measurements is not a trivial task. In various…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
In the absence of experimental constraints, optimal measurement schemes for quantum state tomography are well understood. We consider the scenario where the experimenter doesn't have arbitrary freedom to construct their measurement set, and…
In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in…
Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. We propose a novel scheme where identical copies of a quantum state are measured jointly so that all Pauli…