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Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
Quantum error correction (QEC) underpins practical fault-tolerant quantum computing (FTQC) by addressing the fragility of quantum states and mitigating decoherence-induced errors. As quantum devices scale, integrating robust QEC protocols…
Quantum computing roadmaps predict the availability of 10,000 qubit devices within the next 3-5 years. With projected two-qubit error rates of 0.1%, these systems will enable certain operations under quantum error correction (QEC) using…
Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…
The key obstacle to the realization of a scalable quantum computer is overcoming environmental and control errors. Topological quantum computation has attracted great attention because it has emerged as one of the most promising approaches…
Quantum error correction (QEC) is a crucial step towards long coherence times required for efficient quantum information processing (QIP). One major challenge in this direction concerns the fast real-time analysis of error syndrome…
In the era of noisy intermediate-scale quantum computing, it is of crucial importance to verify quantum processes and extract information. Quantum process tomography is a typical approach, however, both resource-intensive and vulnerable to…
We establish rigorous error bounds for prime counting using a truncated Gaussian (TG) kernel in the explicit formula framework. Our main theorem proves that the approximation error remains globally below 1/2 for all sufficiently large…
Quantum process tomography (QPT) methods aim at identifying a given quantum process. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the…
We consider experimentally feasible chains of trapped ions with pseudo-spin 1/2, and find models that can potentially be used to implement error-resistant quantum computation. Similar in spirit to classical neural networks, the…
Fixed-point quantum search algorithms succeed at finding one of $M$ target items among $N$ total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster…
Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings, but their fault-tolerant advantage over qubit encodings remains unclear. We compare the non-Clifford cost…
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…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls,…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits (PQCs) with classical optimization, they…
Quantum error correction (QEC) is essential for practical quantum computing, as it protects fragile quantum information from errors by encoding it in high-dimensional Hilbert spaces. Conventional QEC protocols typically require repeated…
Quantum computing is one of the most promising technology advances of the latest years. Once only a conceptual idea to solve physics simulations, quantum computation is today a reality, with numerous machines able to execute quantum…