Pub Date : 2025-02-21DOI: 10.1109/TQE.2025.3544839
Claudio Sanavio;Enea Mauri;Sauro Succi
We assess the convergence of the Carleman linearization of advection–diffusion–reaction (ADR) equations with a logistic nonlinearity. It is shown that five Carleman iterates provide a satisfactory approximation of the original ADR across a broad range of parameters and strength of nonlinearity. To assess the feasibility of a quantum algorithm based on this linearization, we analyze the projection of the Carleman ADR matrix onto the tensor Pauli basis. It is found that the Carleman ADR matrix requires an exponential number of Pauli gates as a function of the number of qubits. This prevents the practical implementation of the Carleman approach to the quantum simulation of ADR problems on current hardware. We propose to address this limitation by resorting to block-encoding techniques for sparse matrix employing oracles. Such quantum ADR oracles are presented in explicit form and shown to turn the exponential complexity into a polynomial one. However, due to the low probability of successfully implementing the nonunitary Carleman operator, further research is needed to implement the multitimestep version of the present circuit.
{"title":"Explicit Quantum Circuit for Simulating the Advection–Diffusion–Reaction Dynamics","authors":"Claudio Sanavio;Enea Mauri;Sauro Succi","doi":"10.1109/TQE.2025.3544839","DOIUrl":"https://doi.org/10.1109/TQE.2025.3544839","url":null,"abstract":"We assess the convergence of the Carleman linearization of advection–diffusion–reaction (ADR) equations with a logistic nonlinearity. It is shown that five Carleman iterates provide a satisfactory approximation of the original ADR across a broad range of parameters and strength of nonlinearity. To assess the feasibility of a quantum algorithm based on this linearization, we analyze the projection of the Carleman ADR matrix onto the tensor Pauli basis. It is found that the Carleman ADR matrix requires an exponential number of Pauli gates as a function of the number of qubits. This prevents the practical implementation of the Carleman approach to the quantum simulation of ADR problems on current hardware. We propose to address this limitation by resorting to block-encoding techniques for sparse matrix employing oracles. Such quantum ADR oracles are presented in explicit form and shown to turn the exponential complexity into a polynomial one. However, due to the low probability of successfully implementing the nonunitary Carleman operator, further research is needed to implement the multitimestep version of the present circuit.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10899872","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-17DOI: 10.1109/TQE.2025.3542484
Marc Jofre
The combination of quantum and telecommunication networks enables to revolutionize the way information is used, offering unparalleled capabilities and making it an ideal choice for many critical applications. In this sense, quantum protocols generally have a unique requirement to have strict time synchronization in order to operate, which generally consume quantum resources of part of the exchanged qubits. Accordingly, work demonstrates and characterizes a temporal alignment mechanism for quantum networks based on frequency testing, allowing to preserve the quantum state of qubits. The time synchronization correction achieved is within 100 ns working at 5 MHz with temporal and relative frequency offsets commonly acquired in quantum links using conventional hardware clocks with temporal stability in the range of $10^{-8}$ and 200-ns jitter.
{"title":"Qubit Rate Modulation-Based Time Synchronization Mechanism for Multinode Quantum Networks","authors":"Marc Jofre","doi":"10.1109/TQE.2025.3542484","DOIUrl":"https://doi.org/10.1109/TQE.2025.3542484","url":null,"abstract":"The combination of quantum and telecommunication networks enables to revolutionize the way information is used, offering unparalleled capabilities and making it an ideal choice for many critical applications. In this sense, quantum protocols generally have a unique requirement to have strict time synchronization in order to operate, which generally consume quantum resources of part of the exchanged qubits. Accordingly, work demonstrates and characterizes a temporal alignment mechanism for quantum networks based on frequency testing, allowing to preserve the quantum state of qubits. The time synchronization correction achieved is within 100 ns working at 5 MHz with temporal and relative frequency offsets commonly acquired in quantum links using conventional hardware clocks with temporal stability in the range of <inline-formula> <tex-math>$10^{-8}$</tex-math></inline-formula> and 200-ns jitter.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-10"},"PeriodicalIF":0.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10891179","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In silicon quantum computers, a single electron is trapped in a microstructure called a quantum dot, and its spin is used as a qubit. For large-scale integration of qubits, we previously proposed an approach of sharing a control gate in the row or column of a 2-D quantum dot array. In our array, the shuttling of electrons is a useful technique to operate the target qubit independently and avoid crosstalk. However, since the shuttling is also conducted using shared control gates, the movement of qubits is complexly constrained. We, therefore, propose a formal model based on state transition systems to describe those constraints and operation procedures on the array. We also present an approach to generate operation procedures under the constraints. Utilizing this approach, we present a concrete method for our 16 × 8 quantum dot array. By implementing the proposed method as a quantum compiler, we confirmed that it is possible to generate operation procedures in a practical amount of time for arbitrary quantum circuits. We also demonstrated that crosstalk can be avoided by shuttling and that the fidelity in that case is higher than when crosstalk is not avoided.
{"title":"Generating Shuttling Procedures for Constrained Silicon Quantum Dot Array","authors":"Naoto Sato;Tomonori Sekiguchi;Takeru Utsugi;Hiroyuki Mizuno","doi":"10.1109/TQE.2025.3542462","DOIUrl":"https://doi.org/10.1109/TQE.2025.3542462","url":null,"abstract":"In silicon quantum computers, a single electron is trapped in a microstructure called a quantum dot, and its spin is used as a qubit. For large-scale integration of qubits, we previously proposed an approach of sharing a control gate in the row or column of a 2-D quantum dot array. In our array, the shuttling of electrons is a useful technique to operate the target qubit independently and avoid crosstalk. However, since the shuttling is also conducted using shared control gates, the movement of qubits is complexly constrained. We, therefore, propose a formal model based on state transition systems to describe those constraints and operation procedures on the array. We also present an approach to generate operation procedures under the constraints. Utilizing this approach, we present a concrete method for our 16 × 8 quantum dot array. By implementing the proposed method as a quantum compiler, we confirmed that it is possible to generate operation procedures in a practical amount of time for arbitrary quantum circuits. We also demonstrated that crosstalk can be avoided by shuttling and that the fidelity in that case is higher than when crosstalk is not avoided.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-38"},"PeriodicalIF":0.0,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10890998","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-13DOI: 10.1109/TQE.2025.3541882
Diego Alvarez-Estevez
Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of quantum kernel estimation and quantum kernel training (QKT) in connection with two quantum feature mappings, namely, ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad hoc datasets. This study aims to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically support vector machines and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. The experimental data call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.
{"title":"Benchmarking Quantum Machine Learning Kernel Training for Classification Tasks","authors":"Diego Alvarez-Estevez","doi":"10.1109/TQE.2025.3541882","DOIUrl":"https://doi.org/10.1109/TQE.2025.3541882","url":null,"abstract":"Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of quantum kernel estimation and quantum kernel training (QKT) in connection with two quantum feature mappings, namely, ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad hoc datasets. This study aims to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically support vector machines and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. The experimental data call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10884820","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-11DOI: 10.1109/TQE.2025.3541123
Amar Abane;Michael Cubeddu;Van Sy Mai;Abdella Battou
Entanglement routing in near-term quantum networks consists of choosing the optimal sequence of short-range entanglements to combine through swapping operations to establish end-to-end entanglement between two distant nodes. Similar to traditional routing technologies, a quantum routing protocol uses network information to choose the best paths to satisfy a set of end-to-end entanglement requests. However, in addition to network state information, a quantum routing protocol must also take into account the requested entanglement fidelity, the probabilistic nature of swapping operations, and the short lifetime of entangled states. In this work, we formulate a practical entanglement routing problem and analyze and categorize the main approaches to address it, drawing comparisons to, and inspiration from, classical network routing strategies where applicable. We classify and discuss the studied quantum routing schemes into reactive, proactive, and hybrid routing.
{"title":"Entanglement Routing in Quantum Networks: A Comprehensive Survey","authors":"Amar Abane;Michael Cubeddu;Van Sy Mai;Abdella Battou","doi":"10.1109/TQE.2025.3541123","DOIUrl":"https://doi.org/10.1109/TQE.2025.3541123","url":null,"abstract":"Entanglement routing in near-term quantum networks consists of choosing the optimal sequence of short-range entanglements to combine through swapping operations to establish end-to-end entanglement between two distant nodes. Similar to traditional routing technologies, a quantum routing protocol uses network information to choose the best paths to satisfy a set of end-to-end entanglement requests. However, in addition to network state information, a quantum routing protocol must also take into account the requested entanglement fidelity, the probabilistic nature of swapping operations, and the short lifetime of entangled states. In this work, we formulate a practical entanglement routing problem and analyze and categorize the main approaches to address it, drawing comparisons to, and inspiration from, classical network routing strategies where applicable. We classify and discuss the studied quantum routing schemes into reactive, proactive, and hybrid routing.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-39"},"PeriodicalIF":0.0,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10882978","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143570564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-05DOI: 10.1109/TQE.2025.3538934
Mark A. Webster;Dan E. Browne
Quantum error correction and the use of quantum error correction codes are likely to be essential for the realization of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes that are tailored for a particular error model may have much better performance. In this work, we present a novel evolutionary algorithm that searches for an optimal stabilizer code for a given error model, number of physical qubits, and number of encoded qubits. We demonstrate an efficient representation of stabilizer codes as binary strings, which allows for random generation of valid stabilizer codes as well as mutation and crossing of codes. Our algorithm finds stabilizer codes whose distance closely matches the best-known-distance codes of Grassl (2007) for $n leq 20$ physical qubits. We perform a search for optimal distance Calderbank–Steane–Shor codes and compare their distance to the best known codes. Finally, we show that the algorithm can be used to optimize stabilizer codes for biased error models, demonstrating a significant improvement in the undetectable error rate for $[[12,1]]_{2}$ codes versus the best-known-distance code with the same parameters. As part of this work, we also introduce an evolutionary algorithm QDistEvol for finding the distance of quantum error correction codes.
{"title":"Engineering Quantum Error Correction Codes Using Evolutionary Algorithms","authors":"Mark A. Webster;Dan E. Browne","doi":"10.1109/TQE.2025.3538934","DOIUrl":"https://doi.org/10.1109/TQE.2025.3538934","url":null,"abstract":"Quantum error correction and the use of quantum error correction codes are likely to be essential for the realization of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes that are tailored for a particular error model may have much better performance. In this work, we present a novel evolutionary algorithm that searches for an optimal stabilizer code for a given error model, number of physical qubits, and number of encoded qubits. We demonstrate an efficient representation of stabilizer codes as binary strings, which allows for random generation of valid stabilizer codes as well as mutation and crossing of codes. Our algorithm finds stabilizer codes whose distance closely matches the best-known-distance codes of Grassl (2007) for <inline-formula><tex-math>$n leq 20$</tex-math></inline-formula> physical qubits. We perform a search for optimal distance Calderbank–Steane–Shor codes and compare their distance to the best known codes. Finally, we show that the algorithm can be used to optimize stabilizer codes for biased error models, demonstrating a significant improvement in the undetectable error rate for <inline-formula><tex-math>$[[12,1]]_{2}$</tex-math></inline-formula> codes versus the best-known-distance code with the same parameters. As part of this work, we also introduce an evolutionary algorithm QDistEvol for finding the distance of quantum error correction codes.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-14"},"PeriodicalIF":0.0,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10874169","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-29DOI: 10.1109/TQE.2025.3535823
Alessio Di Santo;Walter Tiberti;Dajana Cassioli
Quantum secret sharing (QSS) is a cryptographic protocol that leverages quantum mechanics to distribute a secret among multiple parties. With respect to the classical counterpart, in QSS, the secret is encoded into quantum states and shared by a dealer such that only an authorized subsets of participants, i.e., the players, can reconstruct it. Several state-of-the-art studies aim to transpose classical secret sharing into the quantum realm, while maintaining their reliance on traditional network topologies (e.g., star, ring, and fully connected), and require that all the $n$ players calculate the secret. These studies exploit the Greenberger–Horne–Zeilinger state, which is a type of maximally entangled quantum state involving three or more qubits. However, none of these works account for redundancy, enhanced security/privacy features, or authentication mechanisms able to fingerprint players. To address these gaps, in this article, we introduce a new concept of QSS, which leans on a generic distributed quantum network, based on a threshold scheme, where all the players collaborate also to the routing of quantum information among them. The dealer, by exploiting a custom flexible weighting system, takes advantage of a newly defined quantum Dijkstra algorithm to select the most suitable subset of $t$ players, out of the entire set on $n$ players, to involve in the computation. To fingerprint and authenticate users, CRYSTAL-Kyber primitives are adopted, while also protecting each player’s privacy by hiding their identities. We show the effectiveness and performance of the proposed protocol by testing it against the main classical and quantum attacks, thereby improving the state-of-the-art security measures.
{"title":"Security and Fairness in Multiparty Quantum Secret Sharing Protocol","authors":"Alessio Di Santo;Walter Tiberti;Dajana Cassioli","doi":"10.1109/TQE.2025.3535823","DOIUrl":"https://doi.org/10.1109/TQE.2025.3535823","url":null,"abstract":"Quantum secret sharing (QSS) is a cryptographic protocol that leverages quantum mechanics to distribute a secret among multiple parties. With respect to the classical counterpart, in QSS, the secret is encoded into quantum states and shared by a dealer such that only an authorized subsets of participants, i.e., the players, can reconstruct it. Several state-of-the-art studies aim to transpose classical secret sharing into the quantum realm, while maintaining their reliance on traditional network topologies (e.g., star, ring, and fully connected), and require that all the <inline-formula><tex-math>$n$</tex-math></inline-formula> players calculate the secret. These studies exploit the Greenberger–Horne–Zeilinger state, which is a type of maximally entangled quantum state involving three or more qubits. However, none of these works account for redundancy, enhanced security/privacy features, or authentication mechanisms able to fingerprint players. To address these gaps, in this article, we introduce a new concept of QSS, which leans on a generic distributed quantum network, based on a threshold scheme, where all the players collaborate also to the routing of quantum information among them. The dealer, by exploiting a custom flexible weighting system, takes advantage of a newly defined quantum Dijkstra algorithm to select the most suitable subset of <inline-formula><tex-math>$t$</tex-math></inline-formula> players, out of the entire set on <inline-formula><tex-math>$n$</tex-math></inline-formula> players, to involve in the computation. To fingerprint and authenticate users, CRYSTAL-Kyber primitives are adopted, while also protecting each player’s privacy by hiding their identities. We show the effectiveness and performance of the proposed protocol by testing it against the main classical and quantum attacks, thereby improving the state-of-the-art security measures.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-18"},"PeriodicalIF":0.0,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10857623","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-28DOI: 10.1109/TQE.2025.3535319
{"title":"2024 Index IEEE Transactions on Quantum Engineering Vol. 5","authors":"","doi":"10.1109/TQE.2025.3535319","DOIUrl":"https://doi.org/10.1109/TQE.2025.3535319","url":null,"abstract":"","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"5 ","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10856694","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-20DOI: 10.1109/TQE.2025.3532017
Niclas Schillo;Andreas Sturm
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over classical computers, quantum algorithms for the solution of DEs have received a lot of attention. Particularly interesting are algorithms that offer advantages in the current noisy intermediate-scale quantum (NISQ) era, characterized by small and error-prone systems. We consider a framework of variational quantum algorithms, quantum circuit learning (QCL), in conjunction with derivation methods, in particular the parameter shift rule, to solve DEs. As these algorithms were specifically designed for NISQ computers, we analyze their applicability on NISQ devices by implementing QCL on an IBM quantum computer. Our analysis of QCL without the parameter shift rule shows that we can successfully learn different functions with three-qubit circuits. However, the hardware errors accumulate with increasing number of qubits, and thus, only a fraction of the qubits available on the current quantum systems can be effectively used. We further show that it is possible to determine derivatives of the learned functions using the parameter shift rule on the IBM hardware. The parameter shift rule results in higher errors, which limits its execution to low-order derivatives. Despite these limitations, we solve a first-order DE on the IBM quantum computer. We further explore the advantages of using multiple qubits in QCL by learning different functions simultaneously and demonstrate the solution of a coupled DE on a simulator.
{"title":"Variational Quantum Algorithms for Differential Equations on a Noisy Quantum Computer","authors":"Niclas Schillo;Andreas Sturm","doi":"10.1109/TQE.2025.3532017","DOIUrl":"https://doi.org/10.1109/TQE.2025.3532017","url":null,"abstract":"The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over classical computers, quantum algorithms for the solution of DEs have received a lot of attention. Particularly interesting are algorithms that offer advantages in the current noisy intermediate-scale quantum (NISQ) era, characterized by small and error-prone systems. We consider a framework of variational quantum algorithms, quantum circuit learning (QCL), in conjunction with derivation methods, in particular the parameter shift rule, to solve DEs. As these algorithms were specifically designed for NISQ computers, we analyze their applicability on NISQ devices by implementing QCL on an IBM quantum computer. Our analysis of QCL without the parameter shift rule shows that we can successfully learn different functions with three-qubit circuits. However, the hardware errors accumulate with increasing number of qubits, and thus, only a fraction of the qubits available on the current quantum systems can be effectively used. We further show that it is possible to determine derivatives of the learned functions using the parameter shift rule on the IBM hardware. The parameter shift rule results in higher errors, which limits its execution to low-order derivatives. Despite these limitations, we solve a first-order DE on the IBM quantum computer. We further explore the advantages of using multiple qubits in QCL by learning different functions simultaneously and demonstrate the solution of a coupled DE on a simulator.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-16"},"PeriodicalIF":0.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10848114","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-17DOI: 10.1109/TQE.2025.3530939
Ryutaroh Matsumoto
In some quantum secret sharing schemes, it is known that some shares can be distributed to participants before a secret is given to the dealer. However, it is unclear whether some shares can be distributed before a secret is given in the ramp quantum secret sharing schemes with the highest coding rate. This article proposes procedures to distribute some shares before a secret is given in those schemes. The new procedures enhance the applicability of the secret sharing schemes to wider scenarios as some participants can be unavailable when the dealer obtains the quantum secret. Then, it is proved that our new encoding procedures retain the correspondences between quantum secrets and quantum shares in the original schemes, which ensures that the highest coding rates of the original schemes are also retained.
{"title":"Advance Sharing Procedures for the Ramp Quantum Secret Sharing Schemes With the Highest Coding Rate","authors":"Ryutaroh Matsumoto","doi":"10.1109/TQE.2025.3530939","DOIUrl":"https://doi.org/10.1109/TQE.2025.3530939","url":null,"abstract":"In some quantum secret sharing schemes, it is known that some shares can be distributed to participants before a secret is given to the dealer. However, it is unclear whether some shares can be distributed before a secret is given in the ramp quantum secret sharing schemes with the highest coding rate. This article proposes procedures to distribute some shares before a secret is given in those schemes. The new procedures enhance the applicability of the secret sharing schemes to wider scenarios as some participants can be unavailable when the dealer obtains the quantum secret. Then, it is proved that our new encoding procedures retain the correspondences between quantum secrets and quantum shares in the original schemes, which ensures that the highest coding rates of the original schemes are also retained.","PeriodicalId":100644,"journal":{"name":"IEEE Transactions on Quantum Engineering","volume":"6 ","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10844313","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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