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Over the past three decades significant reductions have been made to the cost of estimating ground-state energies of molecular Hamiltonians with quantum computers. However, comparatively little attention has been paid to estimating the…
Dynamical correlation functions are essential for characterizing the response of the quantum many-body systems to the external perturbation. As their calculation is classically intractible in general, quantum algorithms are promising in…
Reconstructing the state of quantum many-body systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present an efficient quantum tomography protocol…
Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we design optimal probe states for detector estimation based on the minimum upper bound of the…
The calculation of dynamic response functions is expected to be an early application benefiting from rapidly developing quantum hardware resources. The ability to calculate real-time quantities of strongly-correlated quantum systems is one…
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum…
Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting…
Quantum Phase Estimation (QPE) is a cornerstone algorithm in quantum computing, with applications ranging from integer factorization to quantum chemistry simulations. However, the resource demands of standard QPE, which require a large…
Classification is at the core of data-driven prediction and decision-making, representing a fundamental task in supervised machine learning. Recently, several quantum machine learning algorithms that use quantum kernels as a measure of…
Noisy intermediate-scale quantum (NISQ) computers could solve quantum-mechanical simulation problems that are beyond the capabilities of classical computers. However, NISQ devices experience significant errors which, if not corrected, can…
Recent advances in quantum computing devices have brought attention to hybrid quantum-classical algorithms like the Variational Quantum Eigensolver (VQE) as a potential route to practical quantum advantage in chemistry. However, it is not…
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…
Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of…
Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation. In this work, we present a protocol for estimating the ground-state energy using only global time…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
Simulating quantum many-body systems is a highly demanding task since the required resources grow exponentially with the dimension of the system. In the case of fermionic systems, this is even harder since nonlocal interactions emerge due…
Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the Superfast Encoding introduced by Kitaev and one of the authors. This encoding maps…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…