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Some of the most problematic issues that limit the implementation of applications on Noisy Intermediate Scale Quantum (NISQ) machines are the adverse impacts of both incoherent and coherent errors. We conducted an in-depth study of coherent…
Quantum Error Correction (QEC) is the process of detecting and correcting errors in quantum systems, which are prone to decoherence and quantum noise. QEC is crucial for developing stable and highly accurate quantum computing systems,…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
Quantum defect embedding theory (QDET) is a many-body embedding method designed to describe condensed systems with correlated electrons localized within a given region of space, for example spin defects in semiconductors and insulators.…
Quantum computational experiments exploiting Noisy Intermediate-Scale Quantum (NISQ) devices to demonstrate violation of a Bell inequality are proposed. They consist of running specified quantum algorithms on few-qubit computers. If such a…
Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data…
Noisy intermediate-scale quantum (NISQ) devices are valuable platforms for testing the tenets of quantum computing, but these devices are susceptible to errors arising from de-coherence, leakage, cross-talk and other sources of noise. This…
This article quantifies the uncertainty reduction achievable for \textit{counterfactual} estimand, and cautions against potential bias when the estimand uses Digital Twins. Posed by Neyman (1923a) who showed unbiased \textit{point…
The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if…
Quantum computers promise transformative speedups, but environmental noise destroys their fragile states. Conventional quantum error correction (QEC) encodes information redundantly across physical qubits, yet fails above a threshold of…
Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE)…
We outline a proposal to test quantum mechanics in the high-complexity regime using noisy intermediate-scale quantum (NISQ) devices. The procedure involves simulating a non-Clifford random circuit, followed by its inverse, and then checking…
Progress in fault-tolerant quantum computation (FTQC) has driven the pursuit of practical applications with early fault-tolerant quantum computers (EFTQC). These devices, limited in their qubit counts and fault-tolerance capabilities,…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
Out-of-equilibrium fermionic quantum impurity models (QIM), describing a small interacting system coupled to a continuous fermionic bath, play an important role in condensed matter physics. Solving such models is a computationally demanding…
Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the…
Quantum reservoir computers (QRC) and quantum extreme learning machines (QELM) aim to efficiently post-process the outcome of fixed -- generally uncalibrated -- quantum devices to solve tasks such as the estimation of the properties of…
Practical quantum computing holds clear promise in addressing problems not generally tractable with classical simulation techniques, and some key physically interesting applications are those of real-time dynamics in strongly coupled…
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian…
For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors which occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum…