Detecting and Eliminating Quantum Noise of Quantum Measurements (original) (raw)

Demonstrating elements of measurement-based quantum error correction

Physical Review A, 2014

In measurement-based quantum computing an algorithm is performed by measurements on highly-entangled resource states. To date, several implementations were demonstrated, all of them assuming perfect noise-free environments. Here we consider measurement-based information processing in the presence of noise and demonstrate quantum error detection. We implement the protocol using a four-qubit photonic cluster state, where we first encode a general qubit non-locally such that phase errors can be detected. We then read out the error syndrome and analyze the output states after decoding. Our demonstration shows a building block for measurement-based quantum computing which is crucial for realistic scenarios.

Measurement-based quantum error correction

2015

Measurement-based (or one-way) quantum error correction (MBQEC) is a method with the capability to detect and correct any errors present in a measurement-based quantum computation (MBQC) setup [1]. There are a variety of methods and protocols we can use to perform QEC, although few that have been successfully implemented experimentally [2, 3]. An MBQC protocol requires a resource state and will inevitably experience errors, which may be caused by a wide variety of factors, including coherent, systematic control errors, environmental decoherence, channel loss and measurement errors [4]. This essay will discuss the theoretical methods utilised for MBQEC and how these may be implemented. Our long-term aim is to create a quantum computation setup that successfully corrects against a reasonable threshold percentage of errors. Such a thing is said to be fault tolerant. Before leaping straight into the process of MBQC, it seems prudent to first discuss the finer details of QEC. We know tha...

Mitigation of Crosstalk Errors in a Quantum Measurement and Its Applications

2021

In practical realizations of quantum information processing, there may exist noise in a measurement readout stage where errors appear not only on individual qubits but also on multiple ones collectively, the latter of which is called crosstalk errors. In this work, we present a framework for mitigating measurement errors, for both individual and crosstalk errors. The mitigation protocol consists of two steps, firstly quantum pre-processing, which applies local unitary transformations before a measurement, and classical post-processing that manipulates measurement outcomes to recover noiseless data. The local unitaries in quantum pre-processing can be constructed by characterizing a noisy measurement via quantum detector tomography. We show that the mitigation protocol can maintain a measurement error on multiple qubits as much as that in a single-qubit readout, i.e., the error rates for measurements on multiple qubits are suppressed up to a percent level. The mitigation protocol is ...

Efficient error characterization in quantum information processing

Physical Review A, 2007

We describe how to use the fidelity decay as a tool to characterize the errors affecting a quantum information processor through a noise generator Gτ . For weak noise, the initial decay rate of the fidelity proves to be a simple way to measure the magnitude of the different terms in Gτ . When the generator has only terms associated with few-body couplings, our proposal is scalable. We present the explicit protocol for estimating the magnitude of the noise generators when the noise consists of only one and two-body terms, and describe a method for measuring the parameters of more general noise models. The protocol focuses on obtaining the magnitude with which these terms affect the system during a time step of length τ ; measurement of this information has critical implications for assesing the scalability of fault-tolerant quantum computation in any physical setup.

Error Estimation in Current Noisy Quantum Computers

One of the main important features of the noisy intermediate-scale quantum (NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyze the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover's algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator's results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the 99% of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.

The MMEQ with Quantum Error Analysis for Advancing Quantum Computing and Quantum Sensing

International Journal of Theoretical & Computational Physics, 2023

This paper delves into the profound significance and farreaching impact of the Modified McGinty Equation (MMEQ) with Quantum Error Analysis in pushing the boundaries of quantum computing and quantum sensing. Quantum error analysis plays a pivotal role in these domains due to the innate vulnerability of quantum systems to errors and decoherence. The Modified McGinty Equation (MMEQ) extends the original equation by introducing the term ΨErrorAnalysis(x,t), which encapsulates the repercussions of error analysis on the quantum field. This extension opens doors to the exploration of error mitigation strategies, elevating the performance of quantum technologies to new heights. The contributions of the MMEQ with Quantum Error Analysis are monumental, because it equips researchers with the tools to tackle the challenges posed by errors in quantum information processing tasks. By accounting for error rates, identifying error sources, and analyzing error propagation, researchers gain invaluable insights into the behavior of quantum systems. This new equation provides a structured framework for error characterization, error modeling, and error correction, thereby enabling the creation of quantum technologies that are more resilient and dependable. The potential impact of this research transcends boundaries, with ramifications spanning across various industries and technological frontiers. In the realm of quantum computing, the ability to comprehend and mitigate errors is the linchpin for achieving precise and dependable quantum computations. This will usher in revolutionary breakthroughs in fields such as cryptography, optimization, materials science, and drug discovery. In the arena of quantum sensing, error analysis facilitates the development of high-precision measurement techniques and quantum-enhanced sensing applications, revolutionizing transformations in metrology, imaging, and sensing technology.

Experimental quantum error correction with high fidelity

Physical Review A, 2011

More than ten years ago a first step toward quantum error correction (QEC) was implemented [Phys. Rev. Lett. 81, 2152 (1998)]. The work showed there was sufficient control in nuclear magnetic resonance to implement QEC, and demonstrated that the error rate changed from to ∼ 2. In the current work we reproduce a similar experiment using control techniques that have been since developed, such as the pulses generated by gradient ascent pulse engineering algorithm. We show that the fidelity of the QEC gate sequence and the comparative advantage of QEC are appreciably improved. This advantage is maintained despite the errors introduced by the additional operations needed to protect the quantum states.

Effects of noise on quantum error correction algorithms

Physical Review A, 1997

It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation, however, are limited by decoherence, in which the effect of an external environment causes random errors in the quantum calculation. To combat this problem, quantum error correction schemes have been proposed, in which a single quantum bit (qubit) is "encoded" as a state of some larger number of qubits, chosen to resist particular types of errors. Most such schemes are vulnerable, however, to errors in the encoding and decoding itself. We examine two such schemes, in which a single qubit is encoded in a state of n qubits while subject to dephasing or to arbitrary isotropic noise. Using both analytical and numerical calculations, we argue that error correction remains beneficial in the presence of weak noise, and that there is an optimal time between error correction steps, determined by the strength of the interaction with the environment and the parameters set by the encoding.

Quantum Circuit Engineering for Correcting Coherent Noise

ArXiv, 2022

Crosstalk and several sources of operational interference are invisible when qubit or a gate is calibrated or benchmarked in isolation. These are unlocked during the execution of full quantum circuit applying entangling gates to several qubits simultaneously. Unwanted Z-Z coupling on superconducting cross-resonance CNOT gates, is a commonly occurring unitary crosstalk noise that severely limits the state fidelity. This work presents (1) method of tracing unitary errors, which exploits their sensitivity to the arrangement of CNOT gates in the circuit and (2) correction scheme that modifies original circuit by inserting carefully chosen compensating gates (singleor two-qubit) to possibly undo unitary errors. On two vastly different types of IBMQ processors offering quantum volume 8 and 32, our experimental results show up to 25% reduction in the infidelity of [[7, 1, 3]] code |+〉 state. Our experiments aggressively deploy forced commutation of CNOT gates to obtain low noise state-prep...

Quantum error correction without measurement and an efficient recovery operation

2011

It is known that one can do quantum error correction without syndrome measurement, which is often done in operator quantum error correction (OQEC). However, the physical realization could be challenging, especially when the recovery process involves high-rank projection operators and a superoperator. We use operator theory to improve OQEC so that the implementation can always be done by unitary gates followed by a partial trace operation. Examples are given to show that our error correction scheme outperforms the existing ones in various scenarios.