An improved circuit for Shor’s factoring algorithm using 2n+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2n+2$$\end{document} qubitsXiuli, Song; Liangsen, Wen
doi: 10.1007/s11128-023-04159-ypmid: N/A
Due to the existence of decoherence, researchers are limited in controlling large-scale qubits, which also prevents the application of Shor’s factoring algorithm in the case of large-scale qubits for the time being. To reduce the number of qubits required when using Shor’s factoring algorithm, by using borrowed ancilla qubits and reducing the number of gates in the constant addition circuit, a new quantum circuit for Shor’s factoring algorithm is proposed. The designed circuit works on 2n+2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2n+2$$\end{document} qubits, in practice is about 35% and 40% less than the best circuit of Takahashi et al. (Quantum Inf Comput 5(6):440–448, 2005) and Haner et al. (Quantum Inf Comput 17(7 &8):673–684, 2017) in terms of depth and size, respectively. Also, the designed circuit is completely general, and it does not depend on any property of the composite number to be factorized. Finally, we use Python with Qiskit to implement and simulate our circuit.
Imaginaring and deimaginaring power of quantum channels and the trade-off between imaginarity and entanglementZhang, Jieyu; Luo, Yu; Li, Yongming
doi: 10.1007/s11128-023-04131-wpmid: N/A
The resource theory of imaginarity provides a valuable framework for understanding the role of complex numbers. Quantum channels play a vital role in extraction and transmission of information, and they can both destroy and create imaginarity in quantum states. In this article, we introduce the concepts of imaginaring and deimaginaring power of quantum channels to describe quantum channels’ ability to create and destroy imaginarity. Furthermore, the imaginaring and deimaginaring power for several typical single-qubit channels based on l1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$l_{1}$$\end{document} norm, robustness and relative entropy of imaginarity were computed. In addition, we define the non-imaginarity-generating channel as the completely positive trace-preserving map which does not generate quantum imaginarity from an real state. Several properties of non-imaginarity-generating channels are investigated. Finally, we explore the trade-off relationship between imaginarity and entanglement. The relationship between the deimaginaring power of quantum channels based on relative entropy of the imaginarity and entanglement is studied. Additionally, we explore the creation of imaginarity in a bipartite state. We demonstrate that it is dependent on both the mixedness of initial system and the minimum amount of entanglement that can be created. Our work further studies imaginarity, which will contribute to the development of quantum mechanics and quantum techniques.
A multi-classification classifier based on variational quantum computationZhou, Jie; Li, Dongfen; Tan, Yuqiao; Yang, Xiaolong; Zheng, Yundan; Liu, Xiaofang
doi: 10.1007/s11128-023-04151-6pmid: N/A
The interaction between machine learning and quantum physics has given rise to an emerging frontier of quantum machine learning research. In this line, quantum classifiers have received significant attention recently as a quantum device designed to solve the classification problem in machine learning. In this paper, we propose a new variational quantum multi-class classifier that uses log2N\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$log_{2}N $$\end{document} qubits to represent N labels, converts the labels into different quantum states, and optimizes the circuit parameters by the fidelity between the true label state and the output state. Our method effectively reduces the width of the circuit and lowers the number of auxiliary particles needed from N to log2N\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$log_{2}N$$\end{document}. We conducted simulation experiments on several datasets. On the MNIST handwritten digits dataset, we achieved 99.8% accuracy for 4 classifications and 97% for 8 classifications. On the CIFAR-10 dataset, we obtained 85.3% accuracy for 8 classifications. Finally, on the CIFAR-100 dataset, we reached 76% accuracy for 16 classifications.
An orderly quantum multi-signature based on orthogonal product states for the multi-party transaction blockchainLiu, Ang; Chen, Xiu-bo; Wang, Zhuo; Chen, Ying; Qin, Xiaohong; Feng, Huamin
doi: 10.1007/s11128-023-04169-wpmid: N/A
This paper proposes an orderly identity-based quantum multi-signature scheme exploring the concept of locally indistinguishable orthogonal product states. In the developed scheme, the classic message is converted into a quantum bit string with indistinguishable orthogonal product states that cannot be precisely distinguished by local operations and classical communication (LOCC). The private key generator (PKG) generates keys by the signer’s ID and shares them with the signers, which are used in sequence permutation. Moreover, the verifier Bob generates keys shared with the signers, and the latter sign the message with both keys and their ID. Given that a signature verifier can verify the signature with ID, the proposed scheme has the advantages of the classic identity-based signature scheme. Additionally, it avoids the PKG decoding message from the signature, ensuring the security of non-reputation and unforgeability. Moreover, our method does not require long-term quantum memory, making it more secure and efficient.
Optimizing measurements sequences for quantum state verificationLiang, Weichao; Ticozzi, Francesco; Vallone, Giuseppe
doi: 10.1007/s11128-023-04167-ypmid: N/A
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate; namely, it produces states close to a target one within a prescribed threshold. While most of the result in the literature considers the case in which the measurement operators can be arbitrarily chosen depending on the target state, obtaining favorable (Heisenberg) scaling, we focus on the case in which the measurements can be only chosen from a given set. We show that, in this case, the order of measurements is critical for quickly assessing accuracy. We propose and compare different strategies to compute optimal or suboptimal measurement sequences either relying solely on a priori information, i.e., the target state for state preparation, or actively adapting the sequence to the previously obtained measurements. Numerical simulations show that the proposed algorithms reduce significantly the number of measurements needed for verification and indicate an advantage for the adaptive protocol especially assessing faulty preparations.
Simulation of the quantum Bertrand–Edgeworth gameGrau-Climent, Juan; Garcia-Perez, Luis; Losada, Juan Carlos; Alonso-Sanz, Ramon
doi: 10.1007/s11128-023-04163-2pmid: N/A
In the Bertrand–Edgeworth duopoly game, two players compete in price to capture the market demand of a uniform product. The game is studied from a general perspective, so that players with different production costs and capacity constraints as well as the two more important rules dealing with unsatisfied demand (proportional and efficient) are taken into consideration. A quantization scheme is applied to the game with the aim of improving the results compared to the classic game. The quantum Bertrand–Edgeworth duopoly game is studied in this work via spatial numerical simulation, supporting the results analytically when it is possible. In this context, it is found that high entanglement induces a Pareto optimal solution ruled by the lower capacity of the players. The way in which the players’ entanglement acts in the game is examined through simulation, paying special attention to the critical value of entanglement from which the Pareto optimal solution emerges.
Hybrid bidirectional quantum communication protocol of two single-qubit states under noisy channels with memoryMandal, Manoj Kumar; Choudhury, Binayak S.; Samanta, Soumen
doi: 10.1007/s11128-023-04165-0pmid: N/A
In this paper, we discuss a protocol for remote preparation and transfer of a known and an unknown state between two parties, respectively. It is a bidirectional hybrid protocol consisting of teleportation from one end and remote state preparation from the other end. Firstly, we describe a protocol for the above purpose using a five-qubit pure entangled state as a quantum channel. After that, we consider the effect of correlated Pauli noise on the protocol. Particularly, we consider bit-flip noise, bit-phase-flip noise, phase-damping noise, depolarizing noise and two-Pauli noise, all of which are with memory. We present an analysis of the fidelity with variations of certain involved parameters. Our findings qualitatively agree with the finding of several existing works that fidelity can be improved if the correlation parameter can be properly chosen. Also, we construct a quantum circuit for the preparation of our quantum resource and execute the circuit on IBM qasm simulator.
Quantum data-syndrome codes: Subsystem and impure code constructionsNemec, Andrew
doi: 10.1007/s11128-023-04166-zpmid: N/A
Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome errors, in which a set of linearly dependent stabilizer measurements are performed to increase redundancy. Motivated by wanting to reduce the total number of measurements performed, we introduce QDS subsystem codes, and show that they can outperform similar QDS stabilizer codes derived from them. We also give a construction of single-error-correcting QDS stabilizer codes from impure stabilizer codes and show that any such code must satisfy a variant of the quantum Hamming bound for QDS codes. Finally, we use this bound to prove a new bound that applies to impure, but not pure, stabilizer codes that may be of independent interest.