Related papers: Tutorial on Quantum Error Correction for 2024 Quan…
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
We propose a method for applying the quantum error-correction method for errors that occur during quantum gates. Using a perturbation treatment of the noise that allows us to separate it from the ideal evolution of the quantum gate, we…
An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one…
The existence of quantum error correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum information theory. However, standard error correction refers to abstract quantum…
We present an experimental procedure to determine the usefulness of a measurement scheme for quantum error correction (QEC). A QEC scheme typically requires the ability to prepare entangled states, to carry out multi-qubit measurements, and…
This is the text for a one quarter or one semester undergraduate course on quantum computing that has been given at the University of California Santa Cruz. It is intended for students in the physical sciences who have already studied…
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…
To implement fault-tolerant quantum computation with continuous variables, the Gottesman--Kitaev--Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing…
Fault-tolerant quantum error correction is a necessity for any quantum architecture destined to tackle interesting, large-scale problems. Its theoretical formalism has been well founded for nearly two decades. However, we still do not have…
Executing quantum applications with quantum error correction (QEC) faces the gate non-universality problem imposed by the Eastin-Knill theorem. As one resource-time-efficient solution, code switching changes the encoding of logical qubits…
As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…
Quantum computing (QC) seems to show potential for application in machine learning (ML). In particular quantum kernel methods (QKM) exhibit promising properties for use in supervised ML tasks. However, a major disadvantage of kernel methods…
Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
Any quantum computing application, once encoded as a quantum circuit, must be compiled before being executable on a quantum computer. Similar to classical compilation, quantum compilation is a sequential process with many compilation steps…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes.…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…