Bit-flip Noise Research Articles

Multi-hop Quantum Teleportation Based on HSES via GHZ-like States

Abstract Implementing quantum wireless multi-hop network communication is essential to improve the global quantum network system. In this paper, we employ eight-level GHZ states as quantum channels to realize multi-hop quantum communication, and utilize the logical relationship between the measurements of each node to derive the unitary operation performed by the end node. The Hierarchical Simultaneous Entanglement Switching (HSES) method is adopted, resulting in a significant reduction in the consumption of classical information compared to the multi-hop quantum teleportation (QT) based on general Simultaneous Entanglement Switching (SES). In addition, the proposed protocol is simulated on the IBM Quantum Experiment Platform (IBM QE). Then, the data obtained from the experiment is analyzed using quantum state tomography, which verifies the protocol's good fidelity and accuracy. Finally, by calculating fidelity, we analyze the impact of four different types of noise (phase-damping, amplitude-damping, phase-flip, and bit-flip noise) in this protocol.

A hybrid protocol by a single measurement in noisy environment with simulation

In this paper, a hybrid protocol for teleportation and remote state preparation of an unknown and a known qubits is introduced. The suggested protocol depends on only a single measurement and a single entangled channel which makes the protocol operationally convenient. The protocol has been implemented on the IBM platform. Moreover, a quantum circuit is designed to generate the quantum channel between the sender and the receivers. The fidelity of the receiver’s channel is investigated in the presence of different types of noises which are Bit-flip noise, Phase-flip noise, Bit-phase-flip noise, Depolarizing noise and Two-Pauli noise. It is shown that the fidelities decrease gradually with the strength of the noise.

Effects of quantum noise on teleportation of arbitrary two-qubit state via five-particle Brown state

Abstract We propose a new protocol for quantum teleportation (QT) which adopts the Brown state as the quantum channel. This work focuses on the teleportation of a single unknown two-qubit state via a Brown state channel in an ideal environment. To validate the effectiveness of our proposed scheme, we conduct experiments by using the quantum circuit simulator Quirk. Furthermore, we investigate the effects of four noisy channels, namely, the phase damping noise, the bit-flip noise, the amplitude damping noise, and the phase-flip noise. Notably, we employ Monte Carlo simulation to elucidate the fidelity density under various noise parameters. Our analysis demonstrates that the fidelity of the protocol in a noisy environment is influenced significantly by the amplitude of the initial state and the noise factor.

Quantum teleportation of W-type states in the presence of a controller

In this paper, we discuss a proposal for the transfer of states belonging to the W-type states by executing a controlled teleportation protocol. A 7-qubit quantum entangled resource shared between the sender, receiver and controller is utilized in this protocol. The scheme proposed here is a perfect communication scheme where the task of quantum state transfer is performed with certainty. Further, a protocol for the generation of the quantum resource used here is designed and run on IBM platform. Additionally, we consider the effect of four types of noises, namely, amplitude-damping noise, bit-flip noise, phase-flip noise and phase-damping noise on our protocol. The efficiency of the protocol is compared with other similar protocols which shows that the present one is better performing.

Efficient color code decoders in d≥2 dimensions from toric code decoders

We introduce an efficient decoder of the color code in d≥2 dimensions, the Restriction Decoder, which uses any d-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the Restriction Decoder successfully corrects errors in the color code if and only if the corresponding toric code decoding succeeds. We also numerically estimate the Restriction Decoder threshold for the color code in two and three dimensions against the bit-flip and phase-flip noise with perfect syndrome extraction. We report that the 2D color code threshold p2D≈10.2% on the square-octagon lattice is on a par with the toric code threshold on the square lattice.

A secure deterministic remote state preparation via a seven-qubit entangled channel of a two-qubit entangled state under the impact of quantum noise

In this study, a deterministic remote state preparation protocol is presented for the preparation of arbitrary two-qubit entangled states through a seven-qubit entangled channel prepared from the state proposed by Borras et al. (2007). The implementation of any protocol for quantum communication is inherently susceptible to quantum noise, presenting a challenge to the reliability and security of quantum communication systems. The introduction of noise results in a transition from a pure to a mixed quantum state. This paper examines six distinct noise models, including bit-flip noise, phase-flip noise, bit-phase-flip noise, amplitude damping, phase damping, and depolarizing noise, and analyzes their impact on the entangled channel. The alterations to the density matrices resulting from the introduction of noise are evaluated. The fidelity between the original and remotely prepared quantum states is also analyzed and visually represented. Additionally, a thorough security analysis is conducted to demonstrate the robustness of the protocol against both internal and external attacks.

Multi-hop quantum teleportation of an arbitrary two-qubit state based on hierarchical simultaneous entanglement swapping

Combined with hierarchy simultaneous entanglement swapping, the scheme of the multi-hop quantum teleportation (QT) is proposed by using multi-pair Bell states. The scheme consists of two levels based on simultaneous entanglement swapping, namely Level-1 and Level-2. The former realizes simultaneous entanglement swapping of the inner segment, while the latter completes simultaneous entanglement swapping of the inter segment. Besides, the effect of four different types of noise (phase-damping, amplitude-damping, phase-flip, and bit-flip noise) on our scheme is analyzed by calculating the fidelity and concurrence. The results indicate that the fidelity and concurrence are related to the amplitude parameter, decoherence rate and number of nodes. Furthermore, compared with the scheme of the multi-hop QT adopting simultaneous entanglement swapping, our scheme can greatly reduce classical communication cost, and shows that the optimal classical communication cost can be obtained by selecting different segmentation methods.

Complexity analysis of quantum teleportation via different entangled channels in the presence of noise

Quantum communication is one of the hot topics in quantum computing, where teleportation of a quantum state has a slight edge and gained significant attention from researchers. A large number of teleportation schemes have already been introduced so far. Here, we compare the teleportation of a single qubit message among different entangled channels such as the two-qubit Bell channel, three-qubit GHZ channel, two- and three-qubit cluster states, the highly entangled five-qubit Brown \emph{et al.} state and the six-qubit Borras \emph{et al.} state. We calculate and compare the quantum costs in each of the cases. Furthermore, we study the effects of six noise models, namely bit-flip noise, phase-flip noise, bit-phase flip noise, amplitude damping, phase damping and the depolarizing error that may affect the communication channel used for the teleportation. An investigation on the variation of the initial state's fidelity with respect to the teleported state in the presence of the noise model is performed. A visual representation of the variation of fidelity for various values of the noise parameter $\eta$ is done through a graph plot. It is observed that as the value of noise parameter in the range $\eta \in [0,0.5]$, the fidelity decreases in all the entangled channels under all the noise models. After that, in the Bell channel, GHZ channel and three-qubit cluster state channel, the fidelity shows an upward trend under all the noise models. However, in the other three channels, the fidelity substantially decreases in the case of amplitude damping, phase damping and depolarizing noise, and even it reaches zero for $\eta = 1$ in Brown \emph{et al.} and Borras \emph{et al.} channels.

Enhancing the fidelity of joint remote state preparation by weak measurement

In this paper, the technique of weak measurement is employed in order to enhance the fidelity of joint remote state preparation (JRSP) protocol under decoherence. We design a quantum circuit of joint remote preparation of a single-qubit state through a GHZ state. Then, we analytically derive the average fidelity of the JRSP protocol under four types of noise usually encountered in real-world implementations of quantum communication protocols, i.e. the phase-flip, depolarizing, amplitude-damping and bit-flip noise. Our study shows that the application of weak measurement and measurement reversal could enhance the average fidelity of the JRSP process under the influence of phase-flip, depolarizing, amplitude-damping noise for most values of the decoherence parameters. If the JRSP process suffers from the bit-flip noise, the weak measurement technique is not useful for increasing the average fidelity.

Total Ionizing Dose Effects on Read Noise of MLC 3-D NAND Memories

This article analyzes the total ionizing dose (TID) effects on noise characteristics of commercial multi-level-cell (MLC) 3-D NAND memory technology during the read operation. The chips were exposed to a Co-60 gamma-ray source for up to 100 krad(Si) of TID. We find that the number of noisy cells in the irradiated chip increases with TID. Bit-flip noise was more dominant for cells in an erased state during irradiation compared to programmed cells.

Noise-Robust Quantum Teleportation With Counterfactual Communication

Direct counterfactual communication (DCC) based on the dynamic quantum Cheshire cat effect is an interesting protocol for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">particle-less</i> information transfer. In this paper, we propose a noise-robust, completely counterfactual, teleportation scheme based on the modified DCC. We show that our scheme does not require any <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> shared phase reference; an essential requirement for conventional teleportation schemes. For our modified DCC, we investigate the noise acting on the remotely controlled properties of a photon, i.e., path and polarization. We show that our proposed modification and resulting teleportation scheme are robust against channel delay and dephasing noise. While for photonic loss, depolarizing, and bit-flip noise, it is possible to obtain the correct state given only the channel state information.

Fast charging of a quantum battery assisted by noise

We investigate the performance of a quantum battery exposed to local Markovian and non-Markovian dephasing noises. The battery is initially prepared as the ground state of a one-dimensional transverse $XY$ model with open boundary condition and is charged (discharged) via interactions with local bosonic reservoirs. We show that in the transient regime, the quantum battery (QB) can store energy faster and has a higher maximum extractable work, quantified via ergotropy, when it is affected by local phase-flip or bit-flip Markovian noise compared to the case when there is no noise in the system. In both the charging and discharging processes, we report the enhancement in work output as well as in ergotropy when all the spins are affected by a non-Markovian Ohmic bath in both the transient and the steady-state regimes, thereby showing a counterintuitive advantage of decoherence in the QB. In both Markovian and non-Markovian cases, we identify the system parameters and the corresponding noise models which lead to maximum enhancement of work output and ergotropy. Moreover, we show that the benefit due to noise persists even with the initial state being prepared at a moderate temperature.

Entropy analysis of the discrete-time quantum walk under bit-flip noise channel

We study the behavior of tunable one-dimensional discrete-time quantum walk (DTQW) in the presence of decoherence modeled by the flip-bit noise channel. By varying the noise intensity, we obtain a wide range of probability distributions of noisy walks, which can be loosely characterized as pure quantum walk, quantum-like walk, semi-classical like walk, and classical-like walk. We show the maximum Shannon entropy of the walk is not obtained under maximum decoherence, but instead at a lower degree of decoherence. This result may be useful for the implementation of quantum error correction, quantum cryptography, and quantum communication protocol, where one might expect the qubit internal state to be flipped due to noise.

Statistical mechanical models for quantum codes with correlated noise

We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl, and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or subsystem codes subject to correlated Pauli noise models, including models of fault tolerance. This mapping connects the error correction threshold of the quantum code to a phase transition in the statistical mechanical model. Thus, any existing method for finding phase transitions, such as Monte Carlo simulations, can be applied to approximate the threshold of any such code, without having to perform optimal decoding. By way of example, we numerically study the threshold of the surface code under mildly correlated bit-flip noise, showing that noise with bunching correlations causes the threshold to drop to p_{\textup{corr}}=10.04(6)\% , from its known iid value of p_{\text{iid}}=10.917(3)\% . Complementing this, we show that the mapping also allows us to utilise any algorithm which can calculate/approximate partition functions of classical statistical mechanical models to perform optimal/approximately optimal decoding. Specifically, for 2D codes subject to locally correlated noise, we give a linear-time tensor network-based algorithm for approximate optimal decoding which extends the MPS decoder of Bravyi, Suchara and Vargo.

Efficient and Robust Certification of Genuine Multipartite Entanglement in Noisy Quantum Error Correction Circuits

Ensuring the correct functioning of quantum error correction (QEC) circuits is crucial to achieve fault tolerance in realistic quantum processors subjected to noise. The first checkpoint for a fully operational QEC circuit is to create genuine multipartite entanglement across all subsystems of physical qubits. We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) that is efficient in the number of subsystems and, importantly, robust against experimental noise and imperfections. Specifically, we prove that the detection of entanglement in a linear number of bipartitions by a number of measurements that also scales linearly, suffices to certify GME. Moreover, our method goes beyond the standard procedure of separating the state from the convex hull of biseparable states, yielding an improved finesse and robustness compared to previous techniques. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version. In particular, we subject the circuits to combinations of three types of noise, namely, uniform depolarizing noise, two-qubit gate depolarizing noise, and bit-flip measurement noise. We numerically compare our method with the standard, yet generally inefficient, fidelity test and to a pair of efficient witnesses, verifying the increased robustness of our method. Last but not least, we provide the full translation of our analysis to a trapped-ion native gate set that makes it suitable for experimental applications.

Correcting Spanning Errors With a Fractal Code

The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators - such as the cubic code - to be robust to highly correlated, one-dimensional errors that span their lattice. The challenge remains to design decoding algorithms that utilise the high distance of these codes. Here, we begin the development of such algorithms by proposing an efficient decoder for the `Fibonacci code'; a two-dimensional classical code that mimics the fractal nature of the cubic code. Our iterative decoder finds a correction through repeated use of minimum-weight perfect matching by exploiting symmetries of the code. We perform numerical experiments that show our decoder is robust to one-dimensional, correlated errors. First, using a bit-flip noise model at low error rates, we find that our decoder demonstrates a logical failure rate that scales super exponentially in the linear size of the lattice. In contrast, a decoder that could not tolerate spanning errors would not achieve this rapid decay in failure rate with increasing system size. We also find a finite threshold using a spanning noise model that introduces string-like errors that stretch along full rows and columns of the lattice. These results provide direct evidence that our decoder is robust to one-dimensional, correlated errors that span the lattice.

Enhancing teleportation of a single-qubit state by the unitary transformation in arbitrary decoherence rate

The proposal of the quantum teleportation(QT) is to transfer an unknown quantum state from one place to another through local operations and classical communication. However, the efficiency of standard QT will be significantly reduced due to the influence of the inevitable noise in environments. In this work, we propose two schemes to improve the efficiency of the QT protocol when quantum channel is subjected to bit-flip or phase-flip noise. We find that the so-called more entanglement means low efficiency in the performance of the standard teleportation protocol, and the optimal fidelity is obtained only by using the appropriate unitary operation. Specially, we show that the optimal averaged fidelity to our schemes is always more than the best classically achievable fidelity 2/3. We also provide a physical explanation of the obtained conclusions and our results will be helpful for improving quantum communication with real implementation.

Determination of the semion code threshold using neural decoders

We compute the error threshold for the semion code, the companion of the Kitaev toric code with the same gauge symmetry group $\mathbb{Z}_2$. The application of statistical mechanical mapping methods is highly discouraged for the semion code, since the code is non-Pauli and non-CSS. Thus, we use machine learning methods, taking advantage of the near-optimal performance of some neural network decoders: multilayer perceptrons and convolutional neural networks (CNNs). We find the values $p_{\text {eff}}=9.5\%$ for uncorrelated bit-flip and phase-flip noise, and $p_{\text {eff}}=10.5\%$ for depolarizing noise. We contrast these values with a similar analysis of the Kitaev toric code on a hexagonal lattice with the same methods. For convolutional neural networks, we use the ResNet architecture, which allows us to implement very deep networks and results in better performance and scalability than the multilayer perceptron approach. We analyze and compare in detail both approaches and provide a clear argument favoring the CNN as the best suited numerical method for the semion code.

Exploring classical correlations in noise to recover quantum information using local filtering

A general quantum channel consisting of a decohering and a filtering element carries one qubit of an entangled photon pair. As we apply a local filter to the other qubit, some mutual quantum information between the two qubits is restored depending on the properties of the noise mixed into the signal. We demonstrate a drastic difference between channels with bit-flip and phase-flip noise and further suggest a scheme for maximal recovery of the quantum information.

Sharp bounds for population recovery

The population recovery problem is a basic problem in noisy unsupervised learning that has attracted significant research attention in recent years [WY12,DRWY12, MS13, BIMP13, LZ15,DST16]. A number of different variants of this problem have been studied, often under assumptions on the unknown distribution (such as that it has restricted support size). In this work we study the sample complexity and algorithmic complexity of the most general version of the problem, under both bit-flip noise and erasure noise model. We give essentially matching upper and lower sample complexity bounds for both noise models, and efficient algorithms matching these sample complexity bounds up to polynomial factors.