Experimental implementation of a concatenated quantum error-correcting code

Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information processing. We report the implementation of a concatenated quantum error-correcting code able to correct phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error correction is a practical tool to handle realistic noise involving both independent and correlated errors.     

Nonadditive quantum error-correcting code

We report the first nonadditive quantum error-correcting code, namely, a ((9, 12, 3)) code which is a 12-dimensional subspace within a 9-qubit Hilbert space, that outperforms the optimal stabilizer code of the same length by encoding more levels while correcting arbitrary single-qubit errors. Taking advantage of the graph states, we construct explicitly a complete encoding-decoding circuit for the proposed nonadditive error-correcting code.     

Capabilities of a perturbed toric code as a quantum memory

We analyze the effect of typical, unknown perturbations on the 2D toric code when acting as a quantum memory, incorporating the effects of error correction on readout. By transforming the system into a 1D transverse Ising model undergoing an instantaneous quench, and making extensive use of Lieb-Robinson bounds, we prove that for a large class of perturbations, the survival time of stored information grows at least logarithmically with the system size. A uniform magnetic field saturates this scaling behavior. We show that randomizing the stabilizer strengths gives a polynomial survival time with a degree that depends on the strength of the perturbation.     

Helium trimer calculations with a public quantum three-body code

We present an illustration of using a quantumthree-body code being prepared for public release. The code is based on iterative solving of the three-dimensional Faddeev equations. The code is easy to use and allows users to perform highly-accurate calculations of quantum three-body systems. The previously known results for He₃ ground state are well reproduced by the code.     

Finite-dimensional spin glass and quantum error correcting code

We study a variety of spin systems with randomness in order to investigate the performance of the quantum error correcting codes. We show that the duality formalism is useful to search the locations of the critical points for the random spin systems, which gives us the clue to the exact values of the accuracy thresholds for the topological error correcting codes.     

Experimentally feasible quantum erasure-correcting code for continuous variables

We devise a scheme that protects quantum coherent states of light from probabilistic losses, thus achieving the first continuous-variable quantum erasure-correcting code. If the occurrence of erasures can be probed, then the decoder enables, in principle, a perfect recovery of the original light states. Otherwise, if supplemented with postselection based on homodyne detection, this code can be turned into an efficient erasure-filtration scheme. The experimental feasibility of the proposed protocol is carefully addressed.     

Description of quantum systems by the collective behavior method

Optics and Spectroscopy - We develop the constructive viewpoint to quantum theory, which means the using of constructive mathematics as the basic formalism. It is shown how the heuristic of...     

A small error-correction code for protecting three-qubit quantum information

We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. The present code has a high encoding efficiency, since only one auxiliary qubit is needed for one message qubit on average. In addition, we note that the code can also work even in a worse case that the interaction with the environment causes a leakage out of the qubit space. The code may have some applications in the storage of quantum information for small-scale quantum computing, quantum information processing, and quantum communication.     

Deformed quantum double realization of the toric code and beyond

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Z_n${\mathbb{Z}}_n$ and S₃$S_3$. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z₂${\mathbb{Z}}_2$ phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.     

Benchmarking quantum computers: the five-qubit error correcting code.

The smallest quantum code that can correct all one-qubit errors is based on five qubits. We experimentally implemented the encoding, decoding, and error-correction quantum networks using nuclear magnetic resonance on a five spin subsystem of labeled crotonic acid. The ability to correct each error was verified by tomography of the process. The use of error correction for benchmarking quantum networks is discussed, and we infer that the fidelity achieved in our experiment is sufficient for preserving entanglement.     

A compact program code for simulations of quantum algorithms in classical computers

A general quantum simulation language on a classical computer provides the opportunity to compare an experiential result from the development of quantum computers with mathematical theory. The intention of this research is to develop a program language that is able to make simulations of all quantum algorithms in same framework. This study examines the simulation of quantum algorithms on a classical computer with a symbolic programming language. We use the language Mathematica to make simulations of well-known quantum algorithms. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. This gives us an uncomplicated and clear language for the implementations of algorithms. The computational language includes essential formulations such as quantum state, superposition and quantum operator. This symbolic programming language provides a universal framework for examining the existing as well as future quantum algorithms. This study contributes with an implementation of a quantum algorithm in a program code where the substance is applicable in other simulations of quantum algorithms.     

Literate programming in quantum chemistry: a collaborative approach to the development of theory and computer code

Literate programming has not so far found widespread application in quantum chemistry. Here we suggest that literate programming would do much to enhance the communication of the methods and algorithms of computational quantum chemistry. We argue that literate programming can foster a collaborative approach to the development of theory and code in quantum chemistry. We consider a collaborative approach to computational quantum chemistry via a collaborative virtual environment involving literate programming methods and contrast this with the more traditional approaches, such as the UK's Collaborative Computational Project 1. A sample literate program for the evaluation of the incomplete gamma function is presented using C and the literate programming conventions introduced by Knuth. This demonstrates the application of literate programming methodology to the heart of the molecular integral problem when Gaussian basis sets are employed. We briefly indicate how literate programming techniques may prove useful more generally in other computational sciences.     

Quantitative gas sensing by backscatter-absorption measurements of a pseudorandom code modulated lambda ~ 8-microm quantum cascade laser

We have demonstrated quantitative chemical vapor detection with a multimode quantum cascade (QC) laser. Experiments incorporated pseudorandom code (PRC) modulation of the laser intensity to permit sensitive absorption measurements of isopropanol vapor at 8.0micro . The demonstration shows the practicality of one technical approach for implementing low-peak-power QC lasers in the transmitter portion of a differential absorption lidar (DIAL) system. With a 31-chip, 300-ns/chip PRC sequence, the measured isopropanol detection limit was 12 parts in 10(6) by volume times meters (~3x10(-3) absorption) for a simple backscatter-absorption measurement configuration.     

Output of a neuronal population code

In the population coding framework, we consider how the response distributions affect output distribution. A general theory for the output of neuronal population code is presented when the spike train is a renewal process. Under a given condition on the response distribution, the most probable value of the output distribution is the center of input-preferred values, whereas in the other cases the most improbable value of the output distribution is the center of input-preferred values or there are no most probable states. Depending on the exact form of the response distributions, the variance of the output distributions can either enlarge or reduce the tuning width of the tuning curves.     

Global receptive field transformer decoder method on quantum surface code data and syndrome error correction

Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation. However, the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution. Therefore, quantum error correction technology is crucial to achieving reliable quantum computing. In this work, we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors. However, errors can occur not only in data qubits but also in syndrome qubits, and different types of errors may generate the same syndromes, complicating the decoding task and creating a need for more efficient decoding methods. To address this challenge, we used a transformer decoder based on an attention mechanism. By mapping the surface code lattice, the decoder performs a self-attention process on all input syndromes,thereby obtaining a global receptive field. The performance of the decoder was evaluated under a phenomenological error model. Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%. Additionally, we obtained decoding thresholds of 5% and 6.05% at maximum code distances of 7 and 9, respectively. These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.     

Description of the π-meson form factor in the covariant Hamiltonian formulation of quantum field theory

An expression is obtained for the π-meson form factor in terms of the quasipotential wave functions. As an example, a system of quarks with a Coulomb interaction potential is considered.     

The quantum field as a quantum computer

It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than c=a/τ, a and τ being the minimum space and time distances between gates, respectively. For one space dimension it is shown that the information flow satisfies a Dirac equation, with speed v=ζc and ζ=ζ(m) mass-dependent. For c the speed of light ζ−1 is a vacuum refraction index that increases monotonically from ζ−1(0)=1 to ζ−1(M)=∞, M being the Planck mass for 2a the Planck length. The Fermi anticommuting field can be entirely qubitized, i.e. it can be written in terms of local Pauli matrices and with the field interaction remaining local on qubits. Extensions to larger space dimensions are discussed.     

Benchmarking of a flux compression generator code

Science Applications International Corporation and the Air Force Research Laboratory are continuing development of a graphical design/simulation code for explosive flux compression generators (FCGs). “FCGSCA” is written in FORTRAN and Visual Basic and targets the Windows O/S (Microsoft, Chicago, IL). Basic physics principles and well-known circuit analysis techniques simulate generator-to-load performance; furthermore, FCGSCA incorporates an armature/stator inductance model, a “flux-loss” model, and a fairly detailed treatment of the stator winding resistance. FCGSCA includes a capability for modeling transformer coupling and fuze switching as part of various load configurations; additionally, the user can view overlays of time-history plots from one- or two-parameter variation studies. With reasonable costs in fidelity, this approximation permits quick system-level simulations that expedite FCG design and development. Herein, we primarily explain the ease-of-use of the FCGSCA interface and report on some benchmarking against the “Ranchito” generator that has been designed and tested by Los Alamos National Laboratory (LANL)