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Since model quantization helps to reduce the model size and computation latency, it has been successfully applied in many applications of mobile phones, embedded devices and smart chips. The mixed-precision quantization model can match…
Classically simulating quantum systems is challenging, as even noiseless $n$-qubit quantum states scale as $2^n$. The complexity of noisy quantum systems is even greater, requiring $2^n \times 2^n$-dimensional density matrices. Various…
Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…
In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate the system trough a finite element reduction, by composing…
In this paper, we present a general framework to solve a fundamental problem in Random Matrix Theory (RMT), i.e., the problem of describing the joint distribution of eigenvalues of the sum $\bsA+\bsB$ of two independent random Hermitian…
The dissociation of $\rm N_2$ and $\rm N_2^+$ has been studied by using the \emph{ab initio} Density Matrix Renormalization Group (DMRG) method. Accurate Potential Energy Surfaces (PES) have been obtained for the electronic ground states of…
Noise characterization methods such as randomized benchmarking (RB) are critical for the development of scalable quantum computers. Modern RB protocols for multiqubit systems extract physically relevant error rates by exploiting the…
The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here we review some methods that may be used for performing that task. We start by presenting a simple…
Linear response (LR) is an important tool in the computational chemist's toolbox. It is therefore no surprise that the emergence of quantum computers has led to a quantum version, quantum LR (qLR). However, the current quantum era of…
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory…
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…
The construction and operation of large scale quantum information devices presents a grand challenge. A major issue is the effective control of coherent evolution, which requires accurate knowledge of the system dynamics that may vary from…
Reconstruction of a quantum state is of prime importance for quantum-information science. Specifically, means of efficient determination of a state of atoms of room-temperature vapor may enable applications in quantum computations and…
The Density Matrix Renormalization Group (DMRG) algorithm is a powerful tool for solving eigenvalue problems to model quantum systems. DMRG relies on tensor contractions and dense linear algebra to compute properties of condensed matter…
The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more…
Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve…
We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the…
The quest for effective quantum feature maps for data encoding presents significant challenges, particularly due to the flat training landscapes and lengthy training processes associated with parameterised quantum circuits. To address these…