Related papers: Efficient simulation of quantum error correction u…
As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully…
This paper aims to give an overview of the current state of fault-tolerant quantum computing, by surveying a number of results in the field. We show that thresholds can be obtained for a simple noise model as first proved in [AB97, Kit97,…
Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are…
We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by $\sigma_x^{\otimes n}$, $\sigma_y^{\otimes…
Quantum error-correcting codes, such as subspace, subsystem, and Floquet codes, are typically constructed within the stabilizer formalism, which does not fully capture the idea of fault-tolerance needed for practical quantum computing…
We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
While the power of quantum computers is commonly acknowledged to rise exponentially, it is often overlooked that the complexity of quantum noise mechanisms generally grows much faster. In particular, quantifying whether the instructions on…
Quantum error correcting (QEC) codes protect quantum information against environmental noise. Computational errors caused by the environment change the quantum state within the qubit subspace, whereas quantum erasures correspond to the loss…
Quantum processors can already execute tasks beyond the reach of classical simulation, albeit for artificial problems. At this point, it is essential to design error metrics that test the experimental accuracy of quantum algorithms with…
Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computers. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits…
The error model of a quantum computer is essential for optimizing quantum algorithms to minimize the impact of errors using quantum error correction or error mitigation. Noise with temporal correlations, e.g. low-frequency noise and…
Standard approaches to quantum error correction (QEC) require active maintenance using measurements and classical processing. Passive QEC, by contrast, has so far been established only in unphysical spatial dimensions. Here, we give an…
We consider the problem of devising a suitable Quantum Error Correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction…
The effects of noise are one of the most important factors to consider when it comes to quantum computing in the noisy intermediate-scale quantum computing (NISQ) era that we are currently in. Therefore, it is important not only to gain…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on…
Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum…