Efficient scheme for initializing a quantum register with an arbitrary superposed state

This chapter discusses quantum information science (QIS), quantum key distribution (QKD), and quantum teleportation. The new field of QIS encompasses several overlapping subdisciplines: quantum computing, quantum key distribution (also known as quantum cryptography), and quantum metrology (the measurement of small parameters and weak forces with ultra-high precision). In QIS, bits of information are encoded in quantum states, which themselves can be in superposition states and/or entanglement states. Generically, the 0 and 1 quantum bits are represented as qubits (quantum bits). QKD, or quantum cryptography, is a completely secure method of secret communication, and will remain so even if a quantum computer becomes available. Quantum teleportation is one of the more exotic features to have emerged from the field of QIS. It refers to the ability to transfer an unknown quantum state from one location to another, possibly very distant, location by using quantum entanglement.

Quantum teleportation is one of the most basic quantum protocols, which transfers an unknown quantum state from one location to another through local operation and classical communication by using shared quantum entanglement without physical transfer of the information carrier. And it has been widely used in various quantum information protocols such as entanglement swapping, quantum repeaters, quantum gate teleportation, quantum computation based on measurement, and quantum teleportation networks, which have important application value in quantum computation and quantum information. Quantum teleportation is a naturally bipartite process, in which an unknown quantum state can only be transmitted from one node to another. With the further development of quantum information research, it is necessary to transfer quantum states or quantum information among more and more nodes. Multipartite quantum protocols are expected to form fundamental components for larger-scale quantum communication and computation. A bipartite quantum teleportation should be extended to a multipartite protocol known as a quantum teleportation network. In this paper, a multifunctional quantum teleportation network is proposed theoretically. We first propose a special method of constructing four-partite quantum resources in continuous variables (CVs), and based on this, construct two different types of CV quantum teleportation networks. One type of network contains just one quantum teleportation process consisting of a sender, a receiver and two controllers. In this type of network, the unknown quantum state can be recovered at any other node according to the requirement after the measurement in the input node, which enriches the transfer direction and transfer mode of the unknown quantum state. And meanwhile, the two controllers can control the transfer of a quantum state from the sender to the receiver by restricting the sender and receiver’s access to their information, which makes the quantum teleportation network controllable. The other type of network has two quantum teleportation processes, each containing only a sender, a receiver and no controllers, which increases the number of quantum states that can be transmitted. Then we analyze the dependence of the fidelity of each quantum teleportation network on different physical parameters, and compare the characteristics, advantages and disadvantages among different types of quantum teleportation networks. The scheme for constructing a multifunctional quantum teleportation network in this paper shows some advantages, such as the greater number of quantum nodes, diversity of types, simple operation procedure. And all these advantages provide a broader application prospect for establishing larger and more complex quantum information networks in the future and quicken the pace of the application of quantum information.

Quantum information theory has provided the formal framework for describing how information is stored, transmitted, and transformed in physical quantum systems [Renes, 2022; Tomamichel, 2015; Wilde, 2013]. Its entropic formulations underpin our understanding of quantum computation, communication, and cryptography. Yet this theory traditionally treats all quantum operations as freely available, ignoring computational restrictions. In practice, however, any manipulation of quantum information must be performed by devices of bounded complexity and runtime. Capturing such realistic constraints requires extending quantum information theory to include computational efficiency as a fundamental component. This work takes a first step toward building a computational version of quantum information theory, one that treats efficiency as part of the theory itself. The goal is to understand how the behavior of quantum information changes when the parties involved can only perform computationally efficient operations. This approach bridges the abstract, ideal setting of quantum information theory with the practical limitations of real quantum devices, offering a means to study information processing under realistic resource constraints. At the center of this work are two new quantities: the quantum computational min-entropy and the quantum computational max-entropy. These entropies extend standard quantum entropies by explicitly limiting the computational power of the observer or adversary. The quantum computational min-entropy captures how unpredictable a quantum system A remains to an observer holding system B, when that observer is restricted to quantum circuits of bounded size. Formally, for a bipartite state ρ_{AB}, we define {H^c}^s_{min}(A|B)_{ρ} ≔ -log d_A max_{ℰ^s_{B→A'}} F((𝕀_A ⊗ ℰ^s)(ρ_{AB}),|Φ_{AA'}⟩⟨Φ_{AA'}|) , where the maximization is over quantum channels that can be implemented by circuits of size at most s, and F denotes fidelity with a maximally entangled state. In the classical setting, the min-entropy can be expressed through the maximal probability of correctly guessing a random variable given some side-information. In the fully quantum setting, this idea extends to uncertainty about quantum information [König et al., 2009], quantifying how well one system can be inferred from another using local quantum operations. Our definition generalizes this operational viewpoint by restricting the computational power of the observer to efficient quantum circuits. This definition extends the operational meaning of the information-theoretic quantum min-entropy [König et al., 2009] by incorporating computational constraints, and it provides the fully quantum counterpart of the classical unpredictability entropy [Hsiao et al., 2007]. We establish fundamental properties for the computational min-entropy, including monotonicity in the circuit size and smoothing parameters, efficient data-processing inequalities, and fully quantum leakage and purification chain rules, which were left as open questions in earlier definitions of quantum computational entropies [Yi-Hsiu Chen et al., 2017; Munson et al., 2025]. For classical–quantum states, it coincides with the previously defined quantum computational unpredictability entropy [Noam Avidan and Rotem Arnon, 2025], showing that the new definition correctly generalizes known results. We also introduce the quantum computational max-entropy through a duality relation [Tomamichel et al., 2010] with the min-entropy using a fixed purification. Finally, we prove unconditional separations between the computational and information-theoretic entropies, demonstrating that computational restrictions can fundamentally alter entropic behavior even for simple states. These results establish the fundamental mathematical framework for studying quantum information within realistic computational constraints. By integrating efficiency directly into entropic quantities, they open the door to a fully developed computational quantum information theory that parallels its information-theoretic counterpart. Such a framework provides the foundation for analyzing cryptographic security against computationally bounded quantum adversaries [Noam Avidan and Rotem Arnon, 2025] and the limits of efficient quantum state manipulation. More broadly, it suggests that many core notions in quantum information theory may have refined computational analogues yet to be explored.

Quantum error correction is a set of methods to protect quantum information—that is, quantum states—from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Most work on quantum error correction has focused on systems of quantum bits, or qubits, which are two-level quantum systems. These can be physically realized by the states of a spin-1/2 particle, the polarization of a single photon, two distinguished levels of a trapped atom or ion, the current states of a microscopic superconducting loop, or many other physical systems. The most widely used codes are the stabilizer codes, which are closely related to classical linear codes. The code space is the joint +1 eigenspace of a set of commuting Pauli operators on n qubits, called stabilizer generators; the error syndrome is determined by measuring these operators, which allows errors to be diagnosed and corrected. A stabilizer code is characterized by three parameters [[n,k,d]], where n is the number of physical qubits, k is the number of encoded logical qubits, and d is the minimum distance of the code (the smallest number of simultaneous qubit errors that can transform one valid codeword into another). Every useful code has n>k; this physical redundancy is necessary to detect and correct errors without disturbing the logical state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design. Other approaches to error mitigation in quantum systems include decoherence-free subspaces, noiseless subsystems, and dynamical decoupling.

Quantum mechanics is the most ground-breaking and fascinating theoretical concept developed in physics during the past century. Much of our present understanding of the microscopic world and its extension into the macroscopic world, including modern technical applications, is based upon quantum mechanics. We have experienced a remarkable development of information and communication technology during the past two decades, to a large extent depending upon successful fabrication of smaller and smaller components and circuits. However, we are finally approaching the physical limits of component miniaturization as we enter a microscopic world ruled by quantum mechanics.

Quantum computing is a multidisciplinary field at the intersectionof quantum physics, computer science, and mathematics, aiming to har-ness quantum mechanical phenomena for computational advantage. Thisarticle provides a comprehensive review of both the foundational princi-ples and advanced theoretical models of quantum computing. We beginwith the basic framework of quantum computation, introducing the con-cept of qubits as two-level quantum systems, the linear algebra of Hilbertspaces, Dirac’s bra–ket notation, and the postulates of quantum mechan-ics (state superposition, unitary evolution, and projective measurement).We then discuss quantum logic gates and circuits, highlighting how clas-sical reversible computation principles extend to universal quantum gatesets. Next, we survey key quantum algorithms (from Shor’s factoring toGrover’s searching and beyond) and the complexity-theoretic implicationsof quantum computers, contrasting the class BQP with classical complex-ity classes. We cover the theoretical foundations of quantum error cor-rection and fault tolerance, explaining how quantum information can beprotected from decoherence using redundancy and how fault-tolerant pro-tocols can, in principle, allow scalable quantum computation despite noisyhardware. We then explore advanced models and paradigms of quantumcomputation, including measurement-based quantum computing (one-wayquantum computing), topological quantum computation with anyons, adi-abatic quantum computing and quantum annealing, continuous-variablequantum computing, and related approaches. We also provide an overviewof quantum information theory as it relates to computation, discussingentanglement, quantum entropy, and information-theoretic limits like theHolevo bound. Finally, we review the leading physical implementations(quantum hardware models) of quantum computers—trapped ions, super-conducting circuits, photonic systems, solid-state spin qubits, and oth-ers—outlining the challenges and achievements of each approach.

Quantum computers will make it possible to solve problems faster and more effectively than conventional computers currently can. Commercial quantum computers might be available in the next several years. Performing quantum operations on quantum registers is crucial to the building blocks of a quantum computing system. When these events occur in a system, they result in something fundamentally different from what you expect from a computer system. Using quantum physics, it is feasible that some computer jobs may be done more rapidly than they would be if the tasks were conducted using conventional Boolean logic and classical computers. This work discussed the recent developments and in-depth state of the art literature in Quantum Computing (QC) and related areas. This work primarily focuses on core concepts of Quantum computing such as Quantum mechanics, quantum gates, and quantum circuits, which serve as pillars for Quantum Computing and Quantum Information. Further, the QC-based concepts are implemented using a case study. The case study explores quantum computing techniques to address a real-life financial problem QAOA on IBM's Quantum Computer using Qiskit.

Developing quantum systems which are robust against noise are of prime importance to the realisation of quantum technologies. Without fault tolerance, we will never be able to preserve delicate quantum states for macroscopic time scales, a necessary requirement in the construction of scalable quantum computer. Topologically ordered models offer very beautiful mechanisms for preserving quantum states. In such models, quantum information is encoded globally over a degenerate topological Hilbert space which offers a natural robustness against local environmental noise. Remarkably, topological order is present in certain realistic condensed-matter systems. This provides a platform for accessing topological order in a laboratory. Moreover, considering condensed-matter systems enables us to combine topological features with other physical effects to enhance their behaviour. In this Thesis we study the physics of topologically ordered lattice models with defects. We seek practical applications of lattice defects for the realisation of a fault-tolerant quantum computer. The first result we present shows that anyonic data of point-like lattice defects, called twists, can be found by measuring the entanglement of the ground state of the host system. The data we learn relates to the capacity of a twist defect to perform quantum computational tasks. The second result in this Thesis concerns the dynamics of the qudit toric code model with line-like defects coupled to a thermal bath. We show we can entropically inspire fragile glassy dynamics in the system. Such dynamics qualitatively improve the coherence times of quantum information encoded in the ground state of the lattice. A novel way of achieving fault-tolerant quantum computation is by producing and manipulating twist defects of topologically ordered systems. In many ways, this paradigm of topological quantum computation is analogous to quantum computation using anyons. The first area of study in this Thesis extends the analogy between anyons and twists. Specifically, we show that the anyonic data of twists in Kitaev’s toric code model can be extracted

In quantum computation and quantum information processing, the manipulation and engineering of quantum systems to suit certain purposes are an ongoing task. One such example is quantum state transfer (QST), an essential requirement for both quantum communication and large-scale quantum computation. Here we engineer a chain of four superconducting qubits with tunable couplers to realize the perfect state transfer (PST) protocol originally proposed in quantum spin networks and successfully demonstrate the efficient transfer of an arbitrary single-qubit state from one end of the chain to the other, achieving a high fidelity of 0.986 in just 25 ns. This demonstrated QST is readily to extend to larger chain and multi-node configurations, thus serving as a desirable tool for scalable quantum information processing.

In a recent remarkable experiment [Sci. Adv. 2, e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate was demonstrated by using linear optics. Here we propose a simple experimental scheme by utilizing the dispersive interaction in superconducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits. The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles. In particular, it is shown that this Fredkin gate can be realized using a single-step operation and more importantly, each target qudit can be in an arbitrary state with arbitrary degrees of freedom. Furthermore, we show that this experimental scheme has many potential applications in quantum computation and quantum information processing such as generating arbitrary entangled states (discrete-variable states or continuous-variable states) of the two memories, measuring the fidelity and the entanglement between the two memories. With state-of-the-art circuit QED technology, the numerical simulation is performed to demonstrate that two-memory NOON states, entangled coherent states, and entangled cat states can be efficiently synthesized.

Traditional electronic and communication devices operate by processing binary information encoded as bits. Such digital devices have led to the most advanced technologies that we encounter in our everyday lives and they influence virtually every aspect of our society. Nonetheless, there exists a much richer way to encode and process information. By encoding information in quantum mechanical states as qubits, phenomena such as coherence and entanglement can be harnessed to execute tasks that are intractable to digital devices. Under this paradigm, it should be possible to realize quantum computers, quantum communication networks and quantum sensors that outperform their classical counterparts. The electronic spin states of color-center defects in the semiconductor silicon carbide have recently emerged as promising qubit candidates. They have long-lived quantum coherence up to room temperature, they can be controlled with mature magnetic resonance techniques, and they have a built-in optical interface operating near the telecommunication bands. In this thesis I will present two of our contributions to this field. The first is the electric-field control of electron spin qubits. This development lays foundation for quantum electronics that operate via electrical gating, much like traditional electronics. The second is the universal control and entanglement of electron and nuclear spin qubits in an ensemble under ambient conditions. This development lays foundation for quantum devices that have a built-in redundancy and can operate in real-world conditions. Both developments represent important steps towards practical quantum devices in an electronic grade material.

Classic computing can take credit for technology ranging from mobile phones to supercomputers. But in recent years, a budding counterpart to these conventional devices has emerged: quantum computers. Whereas classic computing sometimes fails to solve complex calculations, such as factoring hundred-digit numbers, quantum computing holds the potential to easily tackle such problems. The field of quantum computing has attracted researchers, such as National Academy of Sciences member Christopher Monroe. An experimental atomic physicist at the University of Maryland and fellow of the Joint Quantum Institute and the Joint Center for Quantum Information and Computer Science in Maryland, Monroe uses lasers to exploit atomic particles to study complex computational problems. Monroe spoke to PNAS about how quantum computing might evolve. Christopher Monroe. > PNAS:Can you describe some of the basic mechanics of quantum computing? > Monroe:It all comes down to the superposition principle, in which a quantum system can exist in multiple states at the same time. Consider the fundamental unit of information: the bit. A bit is binary information that can be a 0 or a 1. A quantum bit, or qubit, can be in a superposition of both 0 and 1 as long as it’s isolated and unobserved. A single qubit is pretty trivial, but when you put many qubits together, there become exponentially many possibilities. > > Let’s consider 300 qubits. That’s an interesting number because the number of possible configurations, 2300, is more than the number of particles in the universe. You could never simulate what happens with 300 qubits on a classical machine; there’s not enough stuff in the universe to do it. The magic with quantum is the power of exponential growth: every time you add a qubit, you double the number of configurations. > > But to control these qubits and exploit this massive storage, we …

This chapter presents state-of-the-art and future perspectives of quantum computing and communication. Timeline of relevant findings in quantum informatics, such as quantum algorithms, quantum cryptography protocols, and quantum computing models, is summarized. Mathematics of information representation with quantum states is presented. The quantum circuit and adiabatic models of quantum computation are outlined. The functionality, limitations, and security of the quantum key distribution (QKD) protocol is presented. Current implementations of quantum computers and principles of quantum programming are shortly described.

Microwave photons trapped in a superconducting cavity constitute an ideal system to realize some of the thought experiments imagined by the founding fathers of quantum physics. The interaction of these trapped photons with Rydberg atoms crossing the cavity illustrates fundamental aspects of measurement theory. The experiments performed with this "photon box" at Ecole Normale Supérieure (ENS) belong to the domain of quantum optics called "Cavity Quantum Electrodynamics". We have realized the non-destructive counting of photons, the recording of field quantum jumps, the preparation and reconstruction of "Schrödinger cat" states of radiation and the study of their decoherence, which provides a striking illustration of the transition from the quantum to the classical world. These experiments have also led to the demonstration of basic steps in quantum information processing, including the deterministic entanglement of atoms and the realization of quantum gates using atoms and photons as quantum bits. This lecture starts by an introduction stressing the connection between the ENS photon box and the ion trap experiments of David Wineland, whose accompanying lecture recalls his own contribution to the field of single particle control. I give then a personal account of the early days of Cavity Quantum Electrodynamics before describing the main experiments performed at ENS during the last twenty years and concluding by a discussion comparing our work to other researches dealing with the control of single quantum particles.

Quantum information science is one of the frontier areas of science and technology. It is also an interdisciplinary area of research where scientists from physics, mathematics, and computer science can contribute alike. One of the main goals is how well one can process information using laws of quantum theory. Quantum information theory aims to process information that is not amenable with classical devices. At the same time this also provides new insights into the nature of the quantum world. Quantum information processing includes quantum computation, quantum communication, quantum cryptography and various information processing tasks. Not only does this provide a fundamental arena to investigate quantum phenomena but also gives new technological benefits like quantum teleportation, remote state preparation and secure communications. In India there is a growing interest in this emerging field. In view of this we had organized an International Program on Quantum Information (IPQI-2010) at the Institute of Physics, Bhubaneswar during January 4–January 30, 2010. In this programme, there were experts from all over the world and topics of focus were on various issues related to quantum information science and general quantum theory, characterization and quantification of entanglement, quantum channels and quantum operations, role of entanglement in quantum algorithms and quantum computation, developing new quantum algorithms, understanding of capacities of quantum channels, and new communication tasks in the multiparty case.