Quantum error correction Research Papers (original) (raw)

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- Physical sciences, Profitability, Quantum error correction, Bang-Bang Control

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to NpiN\piNpi, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the quantum correction is an invariant, independent of the number of nodes in the wave function. In those systems, the energy levels of all the bound states can be easily calculated from the exact quantization rule and the solution for the ground state, which can be obtained by solving the Riccati equation. With this new method, we re-calculate the energy levels for the one-dimensional systems with a finite square well, with the Morse potential, with the symmetric and asymmetric Rosen-Morse potentials, and with the first and the second P\"{o}schl-Teller potentials, for the harmonic oscillators both in one dimension and in three dimensions, and for the hydrogen atom.

- by Mas Eple
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- Mathematical Sciences, Physical sciences, Quantum error correction, Riccati Equation
- by Paulo Mendonca
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- Measure Theory, Control Theory, Mathematical Sciences, Physical sciences
- by Hans-heinrich Limbach
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- Molecular Dynamics, Macrocycle, Isotope Effects, Quantum error correction
- by Jirong Ren
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- Mathematical Physics, Quantum Physics, Black Holes, Entropy
- by Jungsang Kim and +1
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- Quantum Physics, Quantum error correction, Quantum Computer, Quantum Dot

Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation appeared justified when Peter Shor described a polynomial time quantum algorithm for factoring integers. In quantum systems, the computational space increases exponentially with the size of

- by Martin Plenio
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- Quantum Logic, Quantum error correction, Quantum Computer, Optical physics
- by Charles Bennett
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- Information Theory, Communication Theory, Matrix Inversion, Mathematical Sciences
- by Yi Song
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- Materials Engineering, Condensed Matter Physics, Nanowires, Numerical Simulation
- by Philip Candelas
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- Mathematical Physics, Quantum Physics, Geometry, Quantum error correction

We propose a scheme for quantum Brownian motion of a particle in a fermionic bath. Based on the spin coherent-state representation of the noise operators and a canonical thermal distribution of the associated c numbers, we derive a quantum analog of generalized Langevin equation for quantum-mechanical mean position of the particle subjected to an external force field. The approach allows us to map the quantum problem on a classical setting. The quantum dispersion around the mean can be estimated order by order by a set of quantum correction equations up to a desired degree of accuracy for a given nonlinear potential. We derive a quantum diffusion equation for free particle and show that quantization, in general, enhances the mean-square displacement. Increase in temperature leads to suppression of mean-square displacement. The method is based on canonical quantization procedure and may be used for understanding diffusive transport and thermally activated processes in a fermionic bath.

- by debasish deb
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- Engineering, Quantum Mechanics, Quantum Transport, Mathematical Sciences
- by Riccardo Sacco and +1
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- Engineering, Computational Physics, Finite element method, Semiconductor Devices

We implement the DiVincenzo-Shor 5 qubit quantum error correcting code into a solid-state quantum register. The quantum register is a multi charge-qubit system in a semiconductor environment, where the main sources of noise are phase decoherence and relaxation. We evaluate the decay of the density matrix for this multi-qubit system and perform regular quantum error corrections. The performance of the error correction in this realistic system is found to yield an improvement of the fidelity. The fidelity can be maintained arbitrarily close to one by sufficiently increasing the frequency of error correction. This opens the door for arbitrarily long quantum computations.

- by Haleemur Ali
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- Quantum Physics, Quantum error correction, Error Correction, Quantum Computer
- by Todd Brun
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- Mathematical Sciences, Physical sciences, Quantum error correction, Error Correction

The correlated motion of electrons in multi-orbital metallic ferromagnets is investigated in terms of a realistic Hubbard model with {\cal N}-fold orbital degeneracy and arbitrary intra- and inter-orbital Coulomb interactions U and J using a Goldstone-mode-preserving non-perturbative scheme. An effective quantum parameter '\hbar'=\frac{U^2+({\cal N}-1)J^2}{(U+({\cal N}-1)J)^2} is obtained which determines, in analogy with 1/S for quantum spin systems and 1/N for the N-orbital Hubbard model, the strength of correlation-induced quantum corrections to magnetic excitations. The rapid suppression of this quantum parameter with Hund's coupling J, especially for large {\cal N}, provides fundamental insight into the phenomenon of strong stabilization of metallic ferromagnetism by orbital degeneracy and Hund's coupling. This approach is illustrated for the case of ferromagnetic iron and the half metallic Heusler alloy Co_2 Mn Si. For realistic values for iron, the calculated spin stiffness and Curie temperature values obtained are in quantitative agreement with measurements. Significantly, the contribution of long wavelength modes is shown to yield a nearly ~25% reduction in the calculated Curie temperature. Finally, an outline is presented for extending the approach to generic multi-band metallic ferromagnets including realistic band-structure features of non-degenerate orbitals and inter-orbital hopping as obtained from LDA calculations.

- by Bhaskar Kamble
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- Materials Engineering, Condensed Matter Physics, Nanotechnology, Band Structure
- by Gianluca Calcagni
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- Quantum Cosmology, High Energy Physics, Early Universe, Multidisciplinary

In this presentation, we give a basic introduction to Stabilizer Code and how one can formulate Shor's Code using it.

- by E. Novais
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- Mathematical Sciences, Physical sciences, Quantum error correction, CHEMICAL SCIENCES
- by Mark Wilde
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- Quantum error correction

The global white-noise model is proposed as a coarse-grained description of the noise dynamics occurring in Noisy Intermediate-Scale Quantum (NISQ) hardware. The adherence of NISQ hardware to the global white-noise model is used to... more

- by Amro M. Farid
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- Engineering, Quantum Information, Nuclear Magnetic Resonance, Quantum Mechanics

We propose an entanglement generation scheme that requires neither the coherent evolution of a quantum system nor the detection of single photons. Instead, the desired state is heralded by a {\em macroscopic} quantum jump. Macroscopic quantum jumps manifest themselves as a random telegraph signal with long intervals of intense fluorescence (light periods) interrupted by the complete absence of photons (dark periods). Here we show that a system of two atoms trapped inside an optical cavity can be designed such that a dark period prepares the atoms in a maximally entangled ground state. Achieving fidelities above 0.9 is possible even when the single-atom cooperativity parameter C is as low as 10 and when using a photon detector with an efficiency as low as eta = 0.2.

- by Jeremy Metz and +1
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- Quantum nonlocality, Physical sciences, Quantum error correction, Quantum Fluctuation
- by Lorenza Viola
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- Coding Theory, Quantum Physics, Multidisciplinary, Biological Sciences
- by Gerard Collins
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- Measure Theory, Thermodynamics, Data Mining, Quantum Information

Basic concepts of quantum information theory, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are concerned. The main blocks of quantum logic, schemes of quantum calculations implementation, as well as some known today effective quantum algorithms, called to realize advantages of quantum calculations upon classical, are presented here. Among them special place is taken by Shor’s algorithm of number factorization and Grover’s algorithm of unsorted database search. Phenomena of decoherence, its influence on quantum computer stability and methods of quantum errors correction are described.
More recent by Steven Duplij: "Innovative Quantum Computing" (IOP Publishing, Bristol-London) 2023, 178 pages) https://iopscience.iop.org/book/mono/978-0-7503-5281-9
https://www.amazon.com/gp/product/0750352795

- by Steven Duplij
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- Quantum Physics, Nuclear Magnetic Resonance, Quantum Chaos, Quantum Logic
- by Philip Candelas
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- Quantum error correction, Modular group
- by Frank Wilczek
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- Quantum Field Theory, String Theory, Ultraviolet, Quantum error correction

In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and fusion rules of emergent anyonic excitations and thus serve as a diagnostic of topological order. Moreover, modular transformations of higher genus surfaces, e.g. a torus with multiple handles, can enhance the computational power of a topological state, in many cases providing a universal fault-tolerant set of gates for quantum computation. However, due to the intrusive nature of modular transformations, which abstractly involve global operations and manifold surgery, physical implementations of them in local systems have remained elusive. Here, we show that by folding manifolds, modular transformations can be applied in a single shot by independent local unitaries, providing a novel class of transversal logic gates for fault-tolerant quantum computation. Specifically, we demonstrate that multi-layer topological states with appropriate boundary conditions and twist defects allow modular transformations to be effectively implemented by a finite sequence of local SWAP gates between the layers. We further provide methods to directly measure the modular matrices, and thus the fractional statistics of anyonic excitations, providing a novel way to directly measure topological order.

A full-band Cellular Monte Carlo (CMC) approach is applied to the simulation of electron transport in AlGaN/GaN HEMTs with quantum corrections included via the effective potential method. The best fit Gaussian parameters of the effective potential method for different Al contents and gate biases are calculated from the equilibrium electron density. The extracted parameters are used for quantum corrections included in the full-band CMC device simulator. The charge set-back from the interface is clearly observed. However, the overall current of the device is close to the classical solution due to the dominance of polarization charge.

- by Shela Aboud
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- Monte Carlo Simulation, Monte Carlo, Crystal structure, Dislocations
- by Wim Ubachs
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- Measure Theory, Thermodynamics, Data Mining, Quantum Information

Recent one-loop calculations of certain supergravity-mediated quantum corrections in supersymmetric brane-world models employ either the component formulation (hep-th/0305184) or the superfield formalism with only half of the bulk supersymmetry manifestly realized (hep-th/0305169 and hep-th/0411216). There are reasons to expect, however, that 5D supergraphs provide a more efficient setup to deal with these and more involved (in particular, higher-loop) calculations. As

- by Lorenza Viola
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- Quantum Information, Communication Theory, Mathematical Sciences, Physical sciences

We study the evolution of purity, entanglement, and total correlations of general two-mode continuous variable Gaussian states in arbitrary uncorrelated Gaussian environments. The time evolution of purity, von Neumann entropy, logarithmic negativity, and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.

- by Silvio Siena
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- Quantum Mechanics, Mathematical Sciences, Physical sciences, Mutual Information

In this paper we study supersymmetric Chern-Simons-matter (CSM) theories with several Higgs branches. Two such theories at small Chern-Simons level are conjectured to describe the superconformal field theory at the infrared fixed point of N = 4 QED with N_f = 2, 3. In particular, the mirror symmetry which exchanges the Coulomb and Higgs branches of N = 4 QED

- by X. Yin and +1
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- Mirror Symmetry, High Energy Physics, Fixed Point Theory, Strongly Correlated Electrons

In this paper we describe connections among extraspecial 2-groups, unitary representations of the braid group and multi-qubit braiding quantum gates. We first construct new representations of extraspecial 2-groups. Extending the latter by the symmetric group, we construct new unitary braid representations, which are solutions to generalized Yang-Baxter equations and use them to realize new braiding quantum gates. These gates generate

- by Mo-lin Ge and +1
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- Quantum Physics, High Energy Physics, Symmetric group, Quantum error correction