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arXiv:1912.07486 · Revista Mexicana de Física

Performance and error modeling of Deutsch's algorithm in IBM Q

Efrain Buksman, A. L. Fonseca de Oliveira, C. Allende

Published Mar 1, 2020• 2 citations
arXivHTMLPDF

Abstract

The performance of quantum computers today can be studied by analyzing theeect of errors in the result of simple quantum algorithms. The modeling and char-acterization of these errors is relevant to correct them, for example, with quantumcorrecting codes. In this article we characterize the error of the ve qubits quantumcomputer ibmqx4 (IBM Q), using a Deutsch algorithm and modeling the error byGeneralized Amplitude Damping (GAD) and a unitary misalignment operation.

DOI
10.31349/revmexfis.66.239

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The performance of quantum computers today can be studied by analyzing theeect of errors in the result of simple quantum algorithms. The modeling and char-acterization of these errors is relevant to correct them, for example, with quantumcorrecting codes. In this article we characterize the error of the ve qubits quantumcomputer ibmqx4 (IBM Q), using a Deutsch algorithm and modeling the error byGeneralized Amplitude Damping (GAD) and a unitary misalignment operation.
The performance of today's quantum computers are affected by noise. This effect can be analyzed in the result of simple quantum algorithms in real quantum computers. The noise can be characterized as a decoherence error or a systematic error, the last could be corrected by a unitary rotation. In this article we propose two methods to model a systematic error, in the Quantum Fourier Transform algorithm (QFT). The first method uses the isotropic index presented in `` [1] and needs to reconstruct the density matrix of the experimental state, while the second method, although less general, only needs to reconstruct the reduced density matrices for each qubit. In both methods, a unitary transformation is proposed, which approximates the experimental result to the expected theoretical state. As an example, the QFT algorithm is analyzed for two qubit states, in quantum IBM Q computer ibmq\_santiago.
We reexamine a non-Gaussian quantum error-correction code designed to protect optical coherent-state qubits against errors due to an amplitude-damping channel. We improve on a previous result [R. Wickert, N. K. Bernardes, and P. van Loock, Phys. Rev. A 81, 062344 (2010)] by providing a tighter upper bound on the performance attained when considering realistic assumptions, which constrain the operation of the gates employed in the scheme. The quantitative characterization is performed through measures of fidelity and concurrence, the latter obtained by employing the code as an entanglement distillation protocol. We find that, when running the code in fully deterministic error-correction mode, direct transmission can only be beaten for certain combinations of channel and input state parameters. In contrast, in error-detection mode, the usage of higher repetition encodings remains beneficial throughout, however, at the expense of diminishing success probabilities.
Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC) codes, which are generally designed to correct independent errors. To address this, we have developed a computational model to simulate the effects of radiation impacts on QEC performance. This is achieved by building from recently developed models of quasiparticle density, mapping radiation-induced qubit error rates onto a quantum error channel and simulation of a simple surface code. We also provide a performance metric to quantify the resilience of a QEC code to radiation impacts. Additionally, we sweep various parameters of chip design to test mitigation strategies for improved QEC performance. Our model approach is holistic, allowing for modular performance testing of error mitigation strategies and chip and code designs.
Abstract This practical guide presents methods for constructing noise models using the Qiskit Aer noise module within the IBM Q ecosystem. The objective is to simulate quantum circuits under realistic error conditions, enabling accurate emulation of noisy quantum processors. The guide demonstrates how to: Use the Qiskit Aer noise module to define custom noise models. Incorporate gate errors, readout errors, and decoherence effects into simulations. Apply noise channels (e.g., depolarizing, amplitude damping, phase damping). Attach noise models to quantum circuit simulations. Analyze how noise affects algorithm performance and output distributions. Building noise models is essential for studying the behavior of quantum algorithms in the NISQ (Noisy Intermediate-Scale Quantum) era. It allows researchers to evaluate algorithm robustness, optimize circuit depth, and test error mitigation strategies before execution on real IBM Quantum hardware. This approach provides a bridge between ideal theoretical circuits and physically realistic quantum devices, enhancing the reliability and applicability of quantum computing experiments.
Recently, there has been a rapid increase in interest in quantum computers. Their work isbased on the use of quantum-mechanical phenomena such as superposition and entanglement forcomputing input data into output data that can actually provide effective performance 3 to 4 orders ofmagnitude higher than any modern computing devices, which will solve the above and others tasks ina natural and accelerated time scale. This article is devoted to solving the problem of research anddevelopment of corrective codes for correcting several types of quantum errors that appear duringcomputational processes in quantum algorithms and models of quantum computing devices. The aimof the work is to study existing methods for correcting various types and types of quantum errors andto create a 3-qubit corrective code for quantum error correction. The work touches upon the tasks ofresearch and development of the functioning methods of quantum circuits and models of quantumcomputing devices. The relevance of these studies lies in the mathematical and software modelingand implementation of corrective codes for correcting several types of quantum errors as part of thedevelopment and implementation of quantum algorithms for solving classes of classical problems.The scientific novelty of this area is expressed in the exclusion of one of the shortcomings of thequantum computing process. The scientific novelty of this area is primarily expressed in the constantupdating and addition of the field of quantum research in a number of areas, and computer simulation of quantum physical phenomena and features is poorly illuminated in the world. The aim of the work is computer simulation of a quantum computing process using the method of correctingphase types of errors, which allows one to evaluate the own phase of a unitary gate that hasgained access to the quantum state in proportion to its own vector.