Related papers: Rare Event Simulation of Quantum Error-Correcting …
Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and…
Quantum error correction (QEC) requires the execution of deep quantum circuits with large numbers of physical qubits to protect information against errors. Designing protocols that can reduce gate and space-time overheads of QEC is…
Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms. However, realizing practical quantum error correction (QEC) requires resolving many…
Continuous-time quantum error correction (CTQEC) is an approach to protecting quantum information from noise in which both the noise and the error correcting operations are treated as processes that are continuous in time. This chapter…
With quantum devices rapidly approaching qualities and scales needed for fault tolerance, the validity of simplified error models underpinning the study of quantum error correction needs to be experimentally evaluated. In this work, we have…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum…
Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…
The use of analog classical systems for computation is generally thought to be a difficult proposition due to the susceptibility of these devices to noise and the lack of a clear framework for achieving fault-tolerance. We present…
Experimental implementations of quantum information processing have now reached a level of sophistication where quantum process tomography is impractical. The number of experimental settings as well as the computational cost of the data…
When modeling the effects of noise on quantum circuits, one often makes the assumption that these effects can be accounted for by individual decoherence events following an otherwise noise-free gate. In this work, we address the validity of…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model.…
We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using…
Quantum error mitigation (QEM) protocols have provably exponential bounds on the cost scaling; however, exploring which regimes QEM can recover usable results is still of sizable interest. The expected absence of complete error correction…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
Quantum error correction (QEC) is essential for achieving fault-tolerant quantum computing. While superconducting qubits are among the most promising candidates for scalable QEC, their limited nearest-neighbor connectivity presents…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied…