A Novel Framework to Construct S-Box Quantum Circuits Using System Modeling: Application to 4-Bit S-Boxes

Quantum computers accelerate many algorithms based on the superposition principle of quantum mechanics.The Grover algorithm provides significant performance to malicious users attacking symmetric key systems.Since the performance of attacks using quantum computers depends on the efficiency of the quantum circuit of the encryption algorithms,research research on the implementation of quantum circuits is essential.This paper presents a new framework to construct quantum circuits of substitution boxes(S-boxes)using system modeling.We model the quantum circuits of S-boxes using two layers:Toffoli and linear layers.We generate vector spaces based on the values of qubits used in the linear layers and apply them to find quantum circuits.The framework finds the circuit bymatching elements of vector spaces generated fromthe input and output of a given S-box,using the forward search or themeet-in-the-middle strategy.We developed a tool to apply this framework to 4-bit S-boxes.While the 4-bit S-box quantum circuit construction tool LIGHTER-R only finds circuits that can be implemented with four qubits,the proposed tool achieves the circuits with five qubits.The proposed tool can find quantum circuits of 4-bit odd permutations based on the controlled NOT,NOT,and Toffoli gates,whereas LIGHTER-R is unable to perform this task in the same environment.We expect this technique to become a critical step toward optimizing S-box quantum circuits.

Phase-controlled coherent population trapping in superconducting quantum circuits

We investigate the influences of the-applied-field phases and amplitudes on the coherent population trapping behavior in superconducting quantum circuits. Based on the interactions of the microwave fields with a single A-type three-level fluxonium qubit, the coherent population trapping could be obtainable and it is very sensitive to the relative phase and amplitudes of the applied fields. When the relative phase is tuned to 0 or π, the maximal atomic coherence is present and coherent population trapping occurs. While for the choice of π/2, the atomic coherence becomes weak. Meanwhile, for the fixed relative phase π/2, the value of coherence would decrease with the increase of Rabi frequency of the external field coupled with two lower levels. The responsible physical mechanism is quantum interference induced by the control fields, which is indicated in the dressed-state representation. The microwave coherent phenomenon is present in our scheme, which will have potential applications in optical communication and nonlinear optics in solid-state devices.

Probabilistic Teleportation of an Arbitrary Two-Particle State and Its Quantum Circuits

Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice＇s Bell state measurement results, Bob performs a collective unitary transformation on his inherent particles without introducing the auxiliary qubit. The original state can be probabilistically teleported. Meanwhile, quantum circuits for realization of successful teleportation are also presented.

Quantum circuits for realizing deterministic and exact teleportation via two partially entangled pairs of particles

Deterministic and exact teleportation can be achieved via two partially entangled pairs of particles [Gu Y J 2006 Opt. Comm. 259 385]. The key point of the protocol is a generalized measurement described by a positive operator- valued measure, which can be realized by performing a unitary operation in the extended space and a conventional Von Neumann orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the teleportation. Our method for constructing quantum circuits differs from the usual methods based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.

Realization of Quantum Circuits in Fock Space

In this letter, by using the method we offered in our paper [L. Ma and Y.D. Zhang, Commun. Theor. Phys.(Beijing, China) 36 (2001) 119], some extended quantum logic gates, such as quantum counter, quantum adder, are studied and their expressions are given. It may be useful for us to study the more complicated quantum logic circuits deeply.

An Extended Approach for Generating Unitary Matrices for Quantum Circuits

In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offered.Based on this,we propose an algorithm for computing the circuit unitary matrices in detail.Then,for quantum logic circuits composed of quantum logic gates,a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement.Finally,we apply the proposed algorithm to different reversible benchmark circuits based on NCT library(including NOT gate,Controlled-NOT gate,Toffoli gate)and generalized Toffoli(GT)library and provide our experimental results.

Direct measurement for general quantum states using parametric quantum circuits

In the field of quantum information,the acquisition of information for unknown quantum states is very important.When we only need to obtain specific elements of a state density matrix,the traditional quantum state tomography will become very complicated,because it requires a global quantum state reconstruction.Direct measurement of the quantum state allows us to obtain arbitrary specific matrix elements of the quantum state without state reconstruction,so direct measurement schemes have obtained extensive attention.Recently,some direct measurement schemes based on weak values have been proposed,but extra auxiliary states in these schemes are necessary and it will increase the complexity of the practical experiment.Meanwhile,the post-selection process in the scheme will reduce the utilization of resources.In order to avoid these disadvantages,a direct measurement scheme without auxiliary states is proposed in this paper.In this scheme,we achieve the direct measurement of quantum states by using quantum circuits,then we extend it to the measurement of general multi-particle states and complete the error analysis.Finally,when we take into account the dephasing of the quantum states,we modify the circuits and the modified circuits still work for the dephasing case.

Quantum circuit-based proxy blind signatures:A novel approach and experimental evaluation on the IBM quantum cloud platform

This paper presents a novel approach to proxy blind signatures in the realm of quantum circuits,aiming to enhance security while safeguarding sensitive information.The main objective of this research is to introduce a quantum proxy blind signature(QPBS)protocol that utilizes quantum logical gates and quantum measurement techniques.The QPBS protocol is constructed by the initial phase,proximal blinding message phase,remote authorization and signature phase,remote validation,and de-blinding phase.This innovative design ensures a secure mechanism for signing documents without revealing the content to the proxy signer,providing practical security authentication in a quantum environment under the assumption that the CNOT gates are securely implemented.Unlike existing approaches,our proposed QPBS protocol eliminates the need for quantum entanglement preparation,thus simplifying the implementation process.To assess the effectiveness and robustness of the QPBS protocol,we conduct comprehensive simulation studies in both ideal and noisy quantum environments on the IBM quantum cloud platform.The results demonstrate the superior performance of the QPBS algorithm,highlighting its resilience against repudiation and forgeability,which are key security concerns in the realm of proxy blind signatures.Furthermore,we have established authentic security thresholds(82.102%)in the presence of real noise,thereby emphasizing the practicality of our proposed solution.

Analysis of learnability of a novel hybrid quantum-classical convolutional neural network in image classification

We design a new hybrid quantum-classical convolutional neural network(HQCCNN)model based on parameter quantum circuits.In this model,we use parameterized quantum circuits(PQCs)to redesign the convolutional layer in classical convolutional neural networks,forming a new quantum convolutional layer to achieve unitary transformation of quantum states,enabling the model to more accurately extract hidden information from images.At the same time,we combine the classical fully connected layer with PQCs to form a new hybrid quantum-classical fully connected layer to further improve the accuracy of classification.Finally,we use the MNIST dataset to test the potential of the HQCCNN.The results indicate that the HQCCNN has good performance in solving classification problems.In binary classification tasks,the classification accuracy of numbers 5 and 7 is as high as 99.71%.In multivariate classification,the accuracy rate also reaches 98.51%.Finally,we compare the performance of the HQCCNN with other models and find that the HQCCNN has better classification performance and convergence speed.

A new method of constructing adversarial examplesfor quantum variational circuits

A quantum variational circuit is a quantum machine learning model similar to a neural network.A crafted adversarial example can lead to incorrect results for the model.Using adversarial examples to train the model will greatly improve its robustness.The existing method is to use automatic differentials or finite difference to obtain a gradient and use it to construct adversarial examples.This paper proposes an innovative method for constructing adversarial examples of quantum variational circuits.In this method,the gradient can be obtained by measuring the expected value of a quantum bit respectively in a series quantum circuit.This method can be used to construct the adversarial examples for a quantum variational circuit classifier.The implementation results prove the effectiveness of the proposed method.Compared with the existing method,our method requires fewer resources and is more efficient.

Integer multiple quantum image scaling based on NEQR and bicubic interpolation

As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been studied.In this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral multiple.Firstly,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules.Then,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic modules.Finally,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these pixels.Through simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.

Proposal for sequential Stern-Gerlach experiment with programmable quantum processors

The historical significance of the Stern–Gerlach(SG)experiment lies in its provision of the initial evidence for space quantization.Over time,its sequential form has evolved into an elegant paradigm that effectively illustrates the fundamental principles of quantum theory.To date,the practical implementation of the sequential SG experiment has not been fully achieved.In this study,we demonstrate the capability of programmable quantum processors to simulate the sequential SG experiment.The specific parametric shallow quantum circuits,which are suitable for the limitations of current noisy quantum hardware,are given to replicate the functionality of SG devices with the ability to perform measurements in different directions.Surprisingly,it has been demonstrated that Wigner’s SG interferometer can be readily implemented in our sequential quantum circuit.With the utilization of the identical circuits,it is also feasible to implement Wheeler’s delayed-choice experiment.We propose the utilization of cross-shaped programmable quantum processors to showcase sequential experiments,and the simulation results demonstrate a strong alignment with theoretical predictions.With the rapid advancement of cloud-based quantum computing,such as BAQIS Quafu,it is our belief that the proposed solution is well-suited for deployment on the cloud,allowing for public accessibility.Our findings not only expand the potential applications of quantum computers,but also contribute to a deeper comprehension of the fundamental principles underlying quantum theory.

Remote entangling gate between a quantum dot spin and a transmon qubit mediated by microwave photons

Spin qubits and superconducting qubits are promising candidates for realizing solid-state quantum information processors.Designing a hybrid architecture that combines the advantages of different qubits on the same chip is a highly desirable but challenging goal.Here we propose a hybrid architecture that utilizes a high-impedance SQUID array resonator as a quantum bus,thereby coherently coupling different solid-state qubits.We employ a resonant exchange spin qubit hosted in a triple quantum dot and a superconducting transmon qubit.Since this hybrid system is highly tunable,it can operate in a dispersive regime,where the interaction between the different qubits is mediated by virtual photons.By utilizing such interactions,entangling gate operations between different qubits can be realized in a short time of 30 ns with a fidelity of up to 96.5%under realistic parameter conditions.Further utilizing this interaction,remote entangled state between different qubits can be prepared and is robust to perturbations of various parameters.These results pave the way for exploring efficient fault-tolerant quantum computation on hybrid quantum architecture platforms.

Bosonic quantum error correction codes in superconducting quantum circuits

Quantum information is vulnerable to environmental noise and experimental imperfections,hindering the reli-ability of practical quantum information processors.Therefore,quantum error correction(QEC)that can pro-tect quantum information against noise is vital for universal and scalable quantum computation.Among many different experimental platforms,superconducting quantum circuits and bosonic encodings in superconducting microwave modes are appealing for their unprecedented potential in QEC.During the last few years,bosonic QEC is demonstrated to reach the break-even point,i.e.the lifetime of a logical qubit is enhanced to exceed that of any individual components composing the experimental system.Beyond that,universal gate sets and fault-tolerant operations on the bosonic codes are also realized,pushing quantum information processing towards the QEC era.In this article,we review the recent progress of the bosonic codes,including the Gottesman-Kitaev-Preskill codes,cat codes,and binomial codes,and discuss the opportunities of bosonic codes in various quantum applications,ranging from fault-tolerant quantum computation to quantum metrology.We also summarize the challenges associated with the bosonic codes and provide an outlook for the potential research directions in the long terms.

Symbolic Reasoning About Quantum Circuits in Coq

A quantum circuit is a computational unit that transforms an input quantum state to an output state.A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it.However,when the number of qubits increases,the matrix dimension grows exponentially and the computation becomes intractable.In this paper,we propose a symbolic approach to reasoning about quantum circuits.It is based on a small set of laws involving some basic manipulations on vectors and matrices.This symbolic reasoning scales better than the explicit one and is well suited to be automated in Coq,as demonstrated with some typical examples.

Circuit quantum electrodynamics with a quadruple quantum dot

In this theoretical work,we describe a mechanism for the coupling between a plane structure consisting of four quantum dots and a resonator.We systematically study the dependence of the quadruple coupling strength and the qubit decoherence rate and point out the optimized operating position of the hybrid system.According to the transmission given by the input-output theory,the signatures in the resonator spectrum are predicted.Furthermore,based on the parameters already achieved in previous works,we prove that the device described in this paper can achieve the strong coupling limit,i.e.,this approach can be used for system extension under the existing technical conditions.Our results show an effective and promotable approach to couple quantum dot structures in plane with the resonator and propose a meaningful extension method.

Anomalous non-Hermitian dynamical phenomenon on the quantum circuit

The anomalous non-Hermitian dynamical phenomenon with the non-Hermitian skin effect(NHSE)attracts wide attention due to its novel physics and promising applications.Here,we propose a new type of non-unitary discrete-time quantum walk system demonstrating the NHSE and anomalous non-Hermitian dynamical phenomena,including the dynamical chiral phenomenon,the funneling phenomenon on the domain wall,and the anomalous reflection on the phase impurity.Furthermore,we design the quantum circuit experiments of these quantum walk systems and numerically simulate them with quantum noises to verify the robustness of the non-Hermitian dynamical phenomenon on the noisy intermediate-scale quantum(NISQ)devices.Our work paves the way for implementing the non-Hermitian dynamical phenomenon on the quantum circuit.

A backdoor attack against quantum neural networks with limited information

Backdoor attacks are emerging security threats to deep neural networks.In these attacks,adversaries manipulate the network by constructing training samples embedded with backdoor triggers.The backdoored model performs as expected on clean test samples but consistently misclassifies samples containing the backdoor trigger as a specific target label.While quantum neural networks(QNNs)have shown promise in surpassing their classical counterparts in certain machine learning tasks,they are also susceptible to backdoor attacks.However,current attacks on QNNs are constrained by the adversary's understanding of the model structure and specific encoding methods.Given the diversity of encoding methods and model structures in QNNs,the effectiveness of such backdoor attacks remains uncertain.In this paper,we propose an algorithm that leverages dataset-based optimization to initiate backdoor attacks.A malicious adversary can embed backdoor triggers into a QNN model by poisoning only a small portion of the data.The victim QNN maintains high accuracy on clean test samples without the trigger but outputs the target label set by the adversary when predicting samples with the trigger.Furthermore,our proposed attack cannot be easily resisted by existing backdoor detection methods.

Variational quantum semi-supervised classifier based on label propagation

Label propagation is an essential semi-supervised learning method based on graphs,which has a broad spectrum of applications in pattern recognition and data mining.This paper proposes a quantum semi-supervised classifier based on label propagation.Considering the difficulty of graph construction,we develop a variational quantum label propagation(VQLP)method.In this method,a locally parameterized quantum circuit is created to reduce the parameters required in the optimization.Furthermore,we design a quantum semi-supervised binary classifier based on hybrid Bell and Z bases measurement,which has a shallower circuit depth and is more suitable for implementation on near-term quantum devices.We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set,and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier.This work opens a new path to quantum machine learning based on graphs.

One Hot Encoding Synthesis of Quantum Automata from Flowcharts

We present a new approach to the synthesis of quantum automata. In previous research, reversible quantum automata were designed from tabular specifications or state graphs, and minimum length codes, which lead to circuits with Toffoli gates with high numbers of inputs and thus to high quantum costs. This paper is the first to present a method to synthesize Sequential Quantum Circuits directly from flowcharts. In this paper, we directly map flowcharts to reversible/quantum circuits, using only inverters, 2*2 Feynman gates and 3*3 Toffoli gates, and thus reducing quantum costs. Our method has been confirmed by experiments on several benchmarks of practical flowcharts.