Correction to: Advancements in superconducting quantum computing

The interface between superconducting Josephson junction and semiconductor position-based qubit implemented in coupled semiconductor q-dots is described such that it can be the base for electrostatic interface between superconducting and semiconductor quantum computer. Modification of Andreev Bound State in Josephson junction by the presence of semiconductor qubit in its proximity and electrostatic interaction with superconducting qubit is spotted by the minimalist tight-binding model. The obtained analytical results allow in creating interface between semiconductor quantum computer and superconducting quantum computer. They open the perspective of construction of QISKIT like software that will describe both types of quantum computers as well as their interface. Key words: electrostatic entanglement, interface between semiconductor and superconducting quantum computer, tight-binding BdGe equations, analytical solutions, topological states of matter, hybrid quantum computer

Abstract: The rapid advancement of quantum computing is largely driven by innovations in quantum chip architectures, with superconducting and topological qubits emerging as the most promising candidates for scalable and fault-tolerant quantum processors. Superconducting qubits, built using Josephson junctions, have demonstrated significant progress in coherence time, gate fidelity, and quantum error correction, making them the backbone of leading quantum processors such as IBM’s Eagle and Google’s Sycamore. Meanwhile, topological qubits, based on Majorana zero modes (MZMs) and non-Abelian anyons, offer intrinsic error resistance, reducing the computational overhead required for fault-tolerant quantum operations. This chapter explores the fundamental principles, fabrication techniques, and scalability challenges associated with these next-generation quantum chips, highlighting key advancements in hybrid quantum architectures, quantum error mitigation, and cryogenic quantum-classical interfacing. Additionally, it examines the geopolitical and ethical considerations of quantum supremacy, along with the transformative impact of next-gen quantum chips on AI, cryptography, materials science, and optimization problems. As research accelerates, the path toward scalable, fault-tolerant quantum computing is becoming clearer, paving the way for a future where quantum processors outperform classical supercomputers in solving the world’s most complex challenges. Keywords: Quantum chips, superconducting qubits, topological qubits, Josephson junctions, Majorana zero modes, quantum error correction, hybrid quantum architectures, fault-tolerant quantum computing, cryogenic electronics, quantum-classical interfacing, scalable quantum processors, AI-driven quantum computing, quantum supremacy, post-quantum cryptography, nanofabrication, quantum hardware innovation

Analytical solutions for a tight-binding model are presented for a position-based qubit and N interacting qubits realized by quasi-one-dimensional network of coupled quantum dots expressed by connected or disconnected graphs of any topology in 2 and 3 dimensions where one electron is presented at each separated graphs. Electron(s) quantum dynamic state is described under various electromagnetic circumstances with an omission spin degree-of-freedom. The action of Hadamard and phase rotating gate is given by analytical formulas derived and formulated for any case of physical field evolution preserving the occupancy of two-energy level system. The procedure for heating up and cooling down of the quantum state placed in position based qubit is described. The interaction of position-based qubit with electromagnetic cavity is described. In particular non-local communication between position based qubits is given. It opens the perspective of implementation of quantum internet among electrostatic CMOS quantum computers (quantum chips). The interface between superconducting Josephson junction and semiconductor position-based qubit implemented in coupled semiconductor q-dots is described such that it can be the base for electrostatic interface between superconducting and semiconductor quantum computer. Modification of Andreev Bound State in Josephson junction by the presence of semiconductor qubit in its proximity and electrostatic interaction with superconducting qubit is spotted by the minimalistic tight-binding model. The obtained results allow in creating interface between semiconductor quantum computer and superconducting quantum computer. They open the perspective of construction of QISKIT like software that will describe both types of quantum computers as well as their interface.

We propose an efficient scheme for transferring quantum states and generating\nentangled states between two qubits of different nature. The hybrid system\nconsists a single nitrogen vacancy (NV) center and a superconducting (SC)\nqubit, which couple to an optical cavity and a microwave resonator,\nrespectively. Meanwhile, the optical cavity and the microwave resonator are\ncoupled via the electro-optic effect. By adjusting the relative parameters, we\ncan achieve high fidelity quantum state transfer as well as highly entangled\nstates between the NV center and the SC qubit. This protocol is within the\nreach of currently available techniques, and may provide interesting\napplications in quantum communication and computation with single NV centers\nand SC qubits.\n

Abstract: Quantum computing is on the brink of transforming computation, cryptography, artificial intelligence, and materials science, with quantum computing chips at the core of this revolution. "Quantum Computing Chips: Advances in Superconducting and Topological Qubits" provides an in-depth exploration of the latest advancements in quantum hardware, focusing on superconducting and topological qubits, two of the most promising approaches for scalable, fault-tolerant quantum computing. The book examines the fundamental principles of quantum computing, qubit architectures, and fabrication techniques, highlighting how Josephson junctions, transmon qubits, and Majorana fermions contribute to quantum logic operations. It delves into quantum chip integration, error correction strategies, hybrid quantum-classical computing, and emerging quantum networking technologies, offering insights into how industry leaders such as Google, IBM, and Microsoft are advancing quantum processor development. The book also explores the commercialization, industrial impact, and policy challenges of quantum computing chips, discussing applications in cryptography, AI acceleration, quantum simulation, and financial modeling. Through technical analysis, case studies, and expert insights, this book serves as a comprehensive resource for scientists, engineers, researchers, and technology leaders navigating the rapidly evolving quantum computing landscape. Keywords: Quantum computing, superconducting qubits, topological qubits, Josephson junctions, transmon qubits, Majorana fermions, non-Abelian anyons, quantum error correction, quantum chip fabrication, cryogenic quantum systems, hybrid quantum-classical computing, quantum networking, quantum supremacy, quantum cryptography, quantum AI acceleration, quantum materials science, fault-tolerant quantum computing, scalable quantum processors, quantum circuit design, quantum gate fidelity, quantum simulation, IBM quantum computing, Google quantum computing, Microsoft quantum computing, quantum industry, quantum economy, quantum policy, quantum innovation.

Ten years ago the first superconducting qubit was demonstrated experimentally [1]. By now quantum computing with superconducting qubits has become a subject of intensive experimental and theoretical research in dozens of groups around the world. The idea of this Special Issue of the journal is to show the status of experimental research in this area after the first decade of work. Most of the best experimental groups working with superconducting qubits (with a few regrettable exceptions) are represented in this Special Issue. We hope that it gives a useful snapshot in time, demonstrating the main experimental achievements and directions of research in superconducting quantum computing. There are many possible physical realizations of qubits [2,3]. Among the candidate systems, the obvious advantages of quantum computing with Josephson junctions are the efficient control of a quantum circuit with voltage/current/microwave pulses and use of a well-developed technology suitable for large scale integration. The fast experimental progress in experiments with superconducting qubits in the last decade confirms the importance of these advantages. Superconducting qubits come in a variety of types, which are often separated into three categories: charge, flux, and phase qubits (though not all groups use this terminology). Single Cooper pair charge of an island carries the quantum information in the charge qubit (e.g., [1,4–16]), while the superconducting phase is the relevant degree of freedom for flux and phase qubits, which differ by the logic state encoding: two quantum levels in different wells of a potential profile are used in the flux qubit (e.g., [17–32]), and two levels in the same well are used in the phase qubit (e.g., [33–42]).

We propose an efficient scheme for generating entangled states between a single nitrogen-vacancy (NV) centre in diamond and a superconducting qubit in a hybrid set-up. In this device, the NV centre and the superconducting qubit couple to a nanomechanical resonator and a superconducting coplanar waveguide cavity, respectively, while the microwave cavity and the mechanical resonator are parametrically coupled with a tunable coupling strength. We show that, highly entangled states between the NV centre and the superconducting qubit can be achieved, by means of the Jaynes–Cummings interactions in the NV-resonator and qubit-cavity subsystems which transfer the entanglement between the vibration phonons and the cavity photons to the NV centre and the superconducting qubit. This work may provide interesting applications in quantum computation and communication with single NV spins and superconducting qubits.

Superconducting quantum computing has emerged as a leading platform in the pursuit of practical quantum computers, driven by rapid advances from industry, academia, and government initiatives. This review examines the state of superconducting quantum technology, with emphasis on qubit design, processor architecture, scalability, and supporting quantum software. We compare the hardware strategies and performance milestones of key players—including IBM Quantum, Google Quantum AI, Rigetti Computing, Intel Quantum, QuTech, and Oxford Quantum Circuits—highlighting innovations in qubit coherence, control, and system integration. Landmark demonstrations such as quantum supremacy experiments are discussed alongside progress toward real-world applications in the noisy intermediate-scale quantum (NISQ) era. Beyond hardware, attention is given to the broader software and service ecosystem, including quantum programming frameworks, operating environments, and cloud-accessible platforms such as Amazon Braket, Azure Quantum, and OriginQ Cloud, which enable remote access and algorithm development. Persistent challenges in superconducting quantum computing—such as error correction, system stability, and large-scale integration—are assessed in light of emerging approaches aimed at fault-tolerant quantum computing. As the field moves from the NISQ era toward fault-tolerant quantum computing, we capture the defining hardware achievements and characteristics of current superconducting processors, while examining the ongoing efforts and challenges in overcoming NISQ-era limitations. These developments offer critical insights into the path toward scalable quantum systems and their transformative impact on future technologies, while also underscoring the strategic and societal considerations that require balancing innovation with responsible oversight and thoughtful governance.

Superconducting circuits are one of the leading architectures in quantum computing. To undertake quantum computing one must be able to perform quantum gates; however, two-qubit gates are still limited in fidelity and gate time. The cross-resonance gate is a two-qubit gate that uses direct microwave drives and has seen much success in its implementation; but, there are theoretical indications that it has not yet reached the coherence limited fidelity value and its gate time is still relatively long compared with other quantum gate methods. Quantum optimal control theory is a powerful tool in the design of controls for quantum operations and has shown the capability to improve gate fidelities and reduce gate times. Robust quantum optimal control methodologies have further built on this to develop high fidelity quantum gates that are robust to uncertainties and noise in the system. In this thesis we use robust quantum optimal control theory to achieve these goals for the cross-resonance gate in a variety of superconducting qubit architectures. First, we investigate two superconducting qubits embedded in a common 3D microwave cavity in which the control drive is implemented via the common cavity mode of the cavity. We determine pulse shapes that implement the cross-resonance gate that are robust to uncertainty in the qubit transition frequencies for both a strictly two-level superconducting qubit and a three-level qubit. Second, we look at the cross-resonance gate with direct drives on each qubit, finding the minimal time to perform the cross-resonance gate with pulses that are robust to uncertainty in a measured system parameter for three cases: two three-level qubits with no drive crosstalk, two three-level qubits with some drive crosstalk, and two two-level qubits. Lastly, we report on simulations undertaken towards implementing a robust, high fidelity cross-resonance gate in a novel superconducting quantum device known as the coaxmon.

Over the past two decades significant advances have been made in the research of superconducting quantum computing and quantum simulation, in particular of the device design and fabrication that leads to ever-increasing superconducting qubit coherence times and scales. With Google’s announcement of the realization of “quantum supremacy”, superconducting quantum computing has attracted even more attention. Superconducting qubits are macroscopic objects with quantum properties such as quantized energy levels and quantum-state superposition and entanglement. Their quantum states can be precisely manipulated by tuning the magnetic flux, charge, and phase difference of the Josephson junctions with nonlinear inductance through electromagnetic pulse signals, thereby implementing the quantum information processing. They have advantages in many aspects and are expected to become the central part of universal quantum computing. Superconducting qubits and auxiliary devices prepared with niobium or other hard metals like tantalum as bottom layers of large-area components have unique properties and potentials for further development. In this paper the research work in this area is briefly reviewed, starting from the design and working principle of a variety of superconducting qubits, to the detailed procedures of substrate selection and pretreatment, film growth, pattern transfer, etching, and Josephson junction fabrication, and finally the practical superconducting qubit and their auxiliary device fabrications with niobium base layers are also presented. We aim to provide a clear overview for the fabrication process of these superconducting devices as well as an outlook for further device improvement and optimization in order to help establish a perspective for future progress.

Superconducting qubits are leading candidates in the race to build a quantum computer capable of realizing computations beyond the reach of modern supercomputers. The superconducting qubit modality has been used to demonstrate prototype algorithms in the noisy intermediate-scale quantum (NISQ) technology era, in which non-error-corrected qubits are used to implement quantum simulations and quantum algorithms. With the recent demonstrations of multiple high-fidelity, two-qubit gates as well as operations on logical qubits in extensible superconducting qubit systems, this modality also holds promise for the longer-term goal of building larger-scale error-corrected quantum computers. In this brief review, we discuss several of the recent experimental advances in qubit hardware, gate implementations, readout capabilities, early NISQ algorithm implementations, and quantum error correction using superconducting qubits. Although continued work on many aspects of this technology is certainly necessary, the pace of both conceptual and technical progress in recent years has been impressive, and here we hope to convey the excitement stemming from this progress.

Demonstration of quantum entanglement, a key resource in quantum computation arising from a nonclassical correlation of states, requires complete measurement of all states in varying bases. By using simultaneous measurement and state tomography, we demonstrated entanglement between two solid-state qubits. Single qubit operations and capacitive coupling between two super-conducting phase qubits were used to generate a Bell-type state. Full two-qubit tomography yielded a density matrix showing an entangled state with fidelity up to 87%. Our results demonstrate a high degree of unitary control of the system, indicating that larger implementations are within reach.

Monolithic integration of control electronics with superconducting qubits will facilitate scalability of a superconducting quantum computer by reducing the room temperature electronics necessary for performing quantum state manipulation. We report the experimental results of the monolithic integration of an on-chip radiation source with a persistent-current (PC) qubit and dc SQUID measurement device. The devices were fabricated at MIT Lincoln Laboratory in a Nb/Al/AlOx/Nb trilayer process. The two PC qubit states were detected by measuring the switching current of an underdamped dc SQUID magnetometer inductively coupled to the qubit. The radiation source comprised an overdamped dc SQUID operating in the voltage state and inductively coupled to the qubit and measurement SQUID through a low-Q RLC filter. The oscillator was designed to have tunable amplitude and frequency to satisfy the requirements for coherent quantum manipulation of a superconducting PC qubit. We will discuss the measurements in the millikelvin regime and the effects of the oscillator noise on the state of the qubit.

The hybrid quantum system composed of superconductor and cold atoms is expected to achieve fast quantum gates, long-life quantum storage and long-distance transmission through optical fibers, making it one of the most promising hybrid quantum systems to realize optical interconnection between two superconducting quantum computers. In this paper, we comprehensively review the recent research advancements in the optical interconnection of two superconducting quantum computers, based on the superconductor and cold atoms hybrid quantum system, specifically the review covers the coherent coupling between superconducting chips and cold atoms, the coherent microwave-to-optics conversion, and the long-range microwave interconnection between superconducting qubits and quantum converters. The system is expected to provide a physical and technical foundation for practical optical-fiber interconnection of two superconducting quantum computers, and have broad applications in distributed superconducting quantum computation and hybrid quantum networks.

Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [googlemachine,gambetta2015building], and several-hundred-qubit machines are around the corner. Machines of this scale have the capacity to demonstrate quantum supremacy, the tipping point where QC is faster than the fastest classical alternative for a particular problem. Because error correction techniques will be central to QC and will be the most expensive component of quantum computation, choosing the lowest-overhead error correction scheme is critical to overall QC success. This paper evaluates two established quantum error correction codes---planar and double-defect surface codes---using a set of compilation, scheduling and network simulation tools. In considering scalable methods for optimizing both codes, we do so in the context of a full microarchitectural and compiler analysis. Contrary to previous predictions, we find that the simpler planar codes are sometimes more favorable for implementation on superconducting quantum computers, especially under conditions of high communication congestion.