Quantum Information Processing

López Gutiérrez, Irene; Dietrich, Felix; Mendl, Christian B.

doi: 10.1007/s11128-023-04008-ypmid: N/A

Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known initial states together with time-delayed measurements for reconstructing the unitary map and corresponding Hamiltonian of the time dynamics. The overarching mathematical framework and feasibility guarantee of our method is provided by the Takens embedding theorem. We explain in detail how the reconstruction of a single-qubit Hamiltonian works in this setting and provide numerical methods and experiments for general few-qubit and lattice systems with local interactions. In particular, the method allows to find the Hamiltonian of a two qubit system by observing only one of the qubits.

Pellow-Jarman, Aidan; Sinayskiy, Ilya; Pillay, Anban; Petruccione, Francesco

doi: 10.1007/s11128-023-04020-2pmid: N/A

Finding solutions to systems of linear equations is a common problem in many areas of science and engineering, with much potential for a speed up on quantum devices. While the Harrow–Hassidim–Lloyd (HHL) quantum algorithm yields up to an exponential speed up over classical algorithms in some cases, it requires a fault-tolerant quantum computer, which is unlikely to be available in the near-term. Thus, attention has turned to the investigation of quantum algorithms for noisy intermediate-scale quantum (NISQ) devices where several near-term approaches to solving systems of linear equations have been proposed. This paper focuses on the Variational Quantum Linear Solvers (VQLS), and other closely related methods and adaptions. Several contributions are made in this paper, which include: the first application of the Evolutionary Ansatz to the VQLS (EAVQLS), the first implementation of the Logical Ansatz VQLS (LAVQLS), based on the Classical Combination of Quantum States (CQS) method, a proof of principle demonstration of the CQS method on real quantum hardware and a method for the implementation of the Adiabatic Ansatz on the VQLS (AAVQLS). These approaches are implemented and contrasted. The CQS method is run with moderate success on a real quantum device. The EAVQLS and AAVQLS show promise as possible improvements to the standard VQLS algorithm once refined.

Chen, Geng; Wang, Yuqi; Jian, Liya; Zhou, Yi; Liu, Shiming

doi: 10.1007/s11128-023-04000-6pmid: N/A

In the current era of big data, the privacy of user behavior is as important as the privacy of their data. In this paper, we propose a single ternary quantum homomorphic encryption (QHE) protocol based on qubit rotation, which has high security and flexibility. The user utilizes the classical angle as the key for QHE, and encryption and decryption do not need to be implemented in a specific order. Based on this flexible QHE protocol, we further propose a quantum privacy query (QPQ) protocol. Our protocol uses homologous encryption to send query requests and obtain results after processing with an oracle machine—which exists independently of the database—in one round of communication. Our protocol has advantages in terms of its feasibility and efficiency. In addition to this, our protocol offers new ideas for implementing QPQ.

Kim, Hyeonhak; Hong, Seokhie

doi: 10.1007/s11128-023-03991-6pmid: N/A

In the previous research on solving the elliptic curve discrete logarithm problem, quantum resources were concretely estimated. In Banegas et al. (IACR Trans Cryptogr Hardw Embed Syst 2021(1):451–472, 2020. https://doi.org/10.46586/tches.v2021.i1.451-472), the quantum algorithm was optimized for binary elliptic curves, with the main optimization target being the number of the logical qubits. The division algorithm was primarily optimized in Banegas et al. (2020) since every ancillary qubit is used in the division algorithm. In this paper, we propose a new quantum division algorithm on the binary field that uses fewer qubits. Specifically, for elements in a field of 2n\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2^n$$\end{document}, our algorithm saves n-3⌊logn⌋-2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n - 3\lfloor \log {n} \rfloor - 2$$\end{document} qubits instead of using n2-64n⌊log(n)⌋+O(n)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n^2 - 64n\lfloor \log (n) \rfloor + O(n)$$\end{document} more Toffoli gates, which leads to a more space-efficient quantum algorithm for binary elliptic curves. For the small size n of 16, 127, 163, 233, 283 and 571, both the number of qubits and the number of Toffoli gates are actually reduced. When the size n is 571, the reduction in ancillary qubits amounts to approximately 23% compared to the previous algorithm.

Chen, Lin; Yuan, Yifan; Yan, Jiahao; Liang, Mengfan

doi: 10.1007/s11128-023-04014-0pmid: N/A

We investigate the decrease and recovery of quantum security in terms of the non-distinguishability of UPBs. For the decrease, we show that any system merge of an existing four-qubit UPB of size ten is no longer a UPB. For the recovery, we append a suitable 4×2×2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$4\times 2\times 2$$\end{document} product state to the four-qubit UPB, and it turns out to be a family of 4×2×2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$4\times 2\times 2$$\end{document} UPBs of size eleven. We further show that the merge of some two systems in the four-qubit UPB results still in an indistinguishable set of product states and show a more robust quantum security against the intruder. To apply the quantum security for more multipartite systems, we construct a family of seven-qubit UPB of size 13. Our result presents the latest progress on the construction of multiqubit UPBs.

Lai, Hong; Pieprzyk, Josef; Pan, Lei; Li, Ya

doi: 10.1007/s11128-023-03990-7pmid: N/A

Quantum key distribution (QKD) protocols based on entangled states published so far do not fully exploit the potential of coefficients (i.e., the probability amplitude) of entangled states in the generation of cryptographic keys. In contrast, a matrix product state (MPS), which is a type of the well-defined tensor network states based on entanglement for quantum many-body systems, provides a complete description of the entire state entanglement. Unlike the von Neumann entropy, which describes the “quantity” of entanglements, MPS describes a specific entanglement relationship among states. In this paper, we explore an application of MPS for QKD protocols. We expect that the MPS representation allows us to design resource-saving QKD protocols for a smaller number of transmitted entangled photons than in the traditional QKD protocols which do not use MPS, because a qubit is a costly quantum resource. We show how to design a two-party (i.e., Alice and Bob) QKD protocol based on a three-photon entangled state that can be completely represented by three-photon MPS. In our protocol, Alice transforms the second entangled photons of three-photon MPS to Bob. A special structure of three-photon MPS allows not only to increase efficiency of our protocol but also to share keys amongst subsets of MPS. Our protocol illustrates the new advantages of applying three-photon MPS for QKD protocols. They go well beyond efficiency gain by halving the number of entangled photons used in QKD protocols.

Li, Lei; Wang, Qing-Wen; Shen, Shu-Qian; Li, Ming

doi: 10.1007/s11128-023-03995-2pmid: N/A

Mutual information of quantum channel is a natural extension of a basic concept in quantum information theory that of measuring the correlation of a composite quantum state. We first propose the mutual information of quantum channel based on max-relative entropy in multiple ways. We find that these quantities obey the data processing inequality under the action of superchannel. The super-additivity of mutual max-information of quantum channel is studied. Then, we investigate the corresponding smooth versions of mutual max-information of quantum channel, which also obey the data processing inequality under superchannel. We derive consistent lower and upper bounds for different one-shot testing channel,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$^{,}$$\end{document}s mutual max-information in terms of the mutual information of output state through such channel. Furthermore, these bounds allow us to provide an alternative approach to prove the asymptotic equipartition property (AEP) for quantum channel,\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$^{,}$$\end{document}s smooth mutual max-information. Finally, by using this AEP, we obtain a channel version of the quantum Stein’s lemma when discriminating between a large number of independent arbitrary channels and some special replacer channels.

Adnane, Brahim; Moqine, Younes; Houça, Rachid; Belouad, Abdelhadi; Choubabi, El Bouâzzaoui

doi: 10.1007/s11128-023-03974-7pmid: N/A

This paper investigates quantum entanglement in a two-qubit Heisenberg XYZ system with Kaplan–Shekhtman–Entin–Wohlman–Aharony and Dzyaloshinskii–Moriya couplings along the x-axis. By the concept of concurrence, the effects of these two types of interactions on thermal entanglement are studied in detail for both antiferromagnetic and ferromagnetic cases. By setting the strengths coupling of the spin, we quickly recover the Ising and XXX Heisenberg models. Additionally, we find that the influence of Kaplan–Shekhtman–Entin–Wohlman–Aharony and Dzyaloshinskii–Moriya couplings can enhance entanglement and influence the critical temperature beyond the entanglement vanishes.

Kim, Chol-Min; Kim, Nam-Chol; Ko, Myong-Chol; Ryom, Ju-Song; Choe, Hyok-Chol

doi: 10.1007/s11128-023-03976-5pmid: N/A

We proposed a new scheme of multichannel quantum routing for single plasmons (SPs) using the cross-type plasmonic waveguides (PWs) that couples to four two-level InGaAs quantum dots (QDs). In our proposed system, each of two PWs in cross type can be infinite silver nanowire. We theoretically studied the routing properties of the proposed system for the incident SPs by using the real-space formalism. Our results show that in such a coupled system, the routing of incident SPs can be achieved depending on several physical parameters, such as the detuning of the transition frequencies of QDs from the frequency of propagating SPs, the coupling strengths of the QDs to PWs and the separation distance between the QDs. It is shown that the transmission of SPs can be switched on or off by adjusting the separation distance between the QDs, which could be exploited to probe the spacing between the QDs. It is also shown that the transfer rate of SPs can be switchable and redirected by appropriately adjusting the QDs’ separation distance and coupling strengths, which is a prerequisite for quantum routers. Our multichannel scheme for the routing of the SPs could be utilized for making quantum devices realizable, such as quantum routers, quantum filters, directional couplers and quantum switches.

Zhang, Yaozong; Liu, Ying; Hou, Xiaotong; Gao, Jian

doi: 10.1007/s11128-023-04013-1pmid: N/A

Operator quantum error-correcting codes (OQECCs), also known as subsystem codes, can effectively protect quantum information from interference by encoding quantum information in the tensor factor of the subspace of the physical state space. Let R=Fq2+vFq2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R=\mathbb {F}_{q^2}+v\mathbb {F}_{q^2}$$\end{document} with v2=v\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$v^2=v$$\end{document} and q be an odd prime power. In this paper, by designing some flexible defining sets of the Gray images of Hermitian dual-containing constacyclic codes of length n=q2-12s\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n=\frac{q^2-1}{2s}$$\end{document} over R, where s=hℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$s=h\ell $$\end{document} is a divisor of q+1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$q+1$$\end{document}, h≥3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$h\ge 3$$\end{document} is an odd prime and ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document} is a positive integer, we construct two new infinite families of maximum distance separable (MDS) OQECCs with parameters: q2-1s,q2-1s-2d+2-r,r,dq\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left[ \left[ \frac{q^2-1}{s},\frac{q^2-1}{s}-2d+2-r,r,d\right] \right] _q$$\end{document}, where 3≤d≤q-12\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$3\le d\le \frac{q-1}{2}$$\end{document} and 0≤r<q2-1s-2d+2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0\le r<\frac{q^2-1}{s}-2d+2$$\end{document} for ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document} even;q2-1s,q2-1s-2d+2-r,r,dq\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left[ \left[ \frac{q^2-1}{s},\frac{q^2-1}{s}-2d+2-r,r,d\right] \right] _q$$\end{document}, where 3≤d≤(q+1)(s+1)2s-1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$3\le d\le \frac{(q+1)(s+1)}{2s}-1$$\end{document} and 0≤r<q2-1s-2d+2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0\le r<\frac{q^2-1}{s}-2d+2$$\end{document} for ℓ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell $$\end{document} odd. Notably, the parameters of these MDS OQECCs are new and not covered by well-known MDS OQECCs constructed from previous literature.