Related papers: Numerical investigation of the quantum inverse alg…
Matrix square roots and their inverses arise frequently in machine learning, e.g., when sampling from high-dimensional Gaussians $\mathcal{N}(\mathbf 0, \mathbf K)$ or whitening a vector $\mathbf b$ against covariance matrix $\mathbf K$.…
In this brief, we improve the Broad Learning System (BLS) [7] by reducing the computational complexity of the incremental learning for added inputs. We utilize the inverse of a sum of matrices in [8] to improve a step in the pseudoinverse…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
The exact evaluation of the molecular ground state in quantum chemistry requires an exponentially increasing computational cost. Quantum computation is a promising way to overcome the exponential problem using polynomial-time quantum…
Invertible Neural Networks (INN) have become established tools for the simulation and generation of highly complex data. We propose a quantum-gate algorithm for a Quantum Invertible Neural Network (QINN) and apply it to the LHC data of…
Quantum simulations of molecular systems on quantum computers often employ minimal basis sets of Gaussian orbitals. In comparison with more realistic basis sets, quantum simulations employing minimal basis sets require fewer qubits and…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
We present a novel, computationally efficient approach to accelerate quantum optimal control calculations of large multi-qubit systems used in a variety of quantum computing applications. By leveraging the intrinsic symmetry of finite…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Quantum chemistry simulations that accurately predict the properties of materials are among the most highly anticipated applications of quantum computing. It is widely believed that simulations running on quantum computers will allow for…
We assess the performance of the Quantum Flow (QFlow) algorithm employing cost-effective solvers based on the unitary coupled-cluster ansatz with single and double excitations (QFlow-SD). The resulting energies are benchmarked against those…
The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
The proposal for quantum computing with rare-earth-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding to radiation in selected…
We propose the regularized compressed double factorization (RC-DF) method to classically compute compressed representations of molecular Hamiltonians that enable efficient simulation with noisy intermediate scale (NISQ) and error corrected…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Quantum integrable systems have very strong mathematical properties that allow an exact description of their energetic spectrum. From the Bethe equations, I formulate the Baxter "T-Q" relation, that is the starting point of two…