Quantum Computer

Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our study we introduce the dynamic ansatz in the Variational Quantum Linear Solver for a system of linear algebraic equations. In this improved algorithm, the number of layers in the hardware efficient ansatz circuit is evolved, starting from a small and gradually increasing until convergence of the solution is reached. We demonstrate the algorithm advantage in comparison to the standard, static ansatz by utilizing fewer quantum resources and with a smaller quantum depth on average, in presence and absence of quantum noise, and in cases when the number of qubits or condition number of the system matrix are increased. The numbers of iterations and layers can be altered by a switching parameter. The performance of the algorithm in using quantum resources is quantified by a newly defined metric.

In order to understand the bounds of utilization of the Grovers search algorithm for the large unstructured data in presence of the quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modelled by the IBM QISKit. We apply three forms of Grovers algorithms: (1) the standard one, with 4-10 qubits, (2) recently published modified Grovers algorithm, set to reduce the circuit depth, and (3) the algorithms in ( ) and ( ) with multi-control Toffolis modified by addition of an ancilla qubit. Based on these simulations, we find the upper bound of noise for these cases, establish its dependence on the quantum depth of the circuit and provide comparison among them. By extrapolation of the fitted thresholds, we predict what would be the typical gate error bounds when apply the Grovers algorithms for the search of a data in a data set as large as thirty two thousands.

There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walks operate with continuous time. Here a third model for quatum walks is proposed, which is based on an analogy to optical interferometers. It is a discretetime model, and the unitary operator that advances the walk one step depnds only on the local structure of the graph on which the walk is taking place. This type of walk also allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Several examples are discussed.

Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along cl...

We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus our study on traversing a 1-D graph, namely a circle, and show how to implement discrete circular quantum walk in quantum circuits built with universal CNOT and single quit gates. We review elementary quantum gates and circuit decomposition and propose a a generalized version of the all CNOT based quantum discrete circular walk. We simulated these circuits on an IBM quantum supercomputer London IBM-Q with 5 qubits. This quantum computer has non perfect gates based on superconducting qubits, therefore we analyze the impact of errors on the fidelity of the Walker circuit.

This paper interprets quantum entanglement as Correlation in the Now: two measured values appear as a single structured fact on one reality layer; the information that carries the correlation is present before any observation. Measurement does not create outcomes; it makes already-existing structure known on the awareness layer. Formally, we review the assumptions behind Bell-type inequalities (locality, outcome independence, measurement independence) and indicate where Continuity Theory (TUni) differs: not by invoking superluminal signals, but by treating each experiment as arising from a joint origin configuration J in a single global present (the "Now"). This allows minimal, structured relaxations of strict measurement independence while preserving locality. We argue that the frequent appeal to "pure probability"-probability without reference-is a category error: in physics, probabilities must be tied to something real. A didactic "two letters" picture captures the core: opening one sealed letter (A) does not change the other letter (B); it only reveals which member of a correlated pair you are holding. Entanglement is thus knowledge of joint structure, not communication across space.

Ion trap system is one of the main quantum systems to realize quantum computation and simulation. Various ion trap research groups worldwide jointly drive the continuous enrichment of ion trap structures, and develop a series of high-performance three-dimensional ion trap, two-dimensional ion trap chip, and ion traps with integrated components. The structure of ion trap is gradually developing towards miniaturization, high-optical-access and integration, and is demonstrating its outstanding ability in quantum control. Ion traps are able to trap increasingly more ions and precisely manipulate the quantum state of the system. In this review, we will summarize the evolution history of the ion trap structures in the past few decades, as well as the latest advances of trapped-ion-based quantum computation and simulation. Here we present a selection of representative examples of trap structures. We will summarize the progresses in the processing technology, robustness and versatility of i...

This study develops the concept of contextual identity, a new framework for quantitatively measuring contextual transformations in quantum systems. The foundational ∆Q metric, while mathematically related to Shannon surprise, aims to capture the ontological shift in the system's observable identity during transitions between contexts. ∆Q establishes natural connections with von Neumann entropy and mutual information, and it can be experimentally tested in fundamental experiments such as the double-slit and CHSH setups. For pedagogical purposes, the Bent unit (1 Bent ≡ | ln 2| nats ≈ 1 bit) is introduced; this unit allows the interpretation of a doubling of probability as 1 unit of contextual gain. Our paper presents a dynamic, measurable, and identity-based alternative to quantum foundations. Warning: 1 Bent ̸ = 1 Shannon bit. Bent measures contextual identity transformation; Shannon bit measures information quantity.

Closed timelike curves (CTCs) and retrocausal models challenge conventional notions of computation by permitting interactions with an agent's own causal past. Prior work by Deutsch, Aaronson, and Watrous has shown that access to CTCs augments classical and quantum computational power, collapsing complexity classes in surprising ways. In this paper, we propose a formal hierarchy of complexity classes for time-travel computation, introducing CTC-PTIME, CTC-NP, and their quantum analogues. We provide rigorous definitions using retrocausal oracle access and fixed-point operators, prove containments and separations, and situate these classes relative to P, NP, PSPACE, and BQP. We also present new paradox-aware reductions, illustrate paradox resolution as a computational primitive, and propose open problems at the interface of causality, complexity, and temporal logic.

Quantum computing is a form of unconventional computation utilizing quantum effects as a fundamental part of its calculations. It has already been used in practical signal encryption in the 2010 Soccer World Cup, and there is competition amongst many governments to build more powerful and practical quantum computers. Although quantum computing is the most widespread and invested in form of unconventional computation, there have been no implementations of artistic systems with live hardware quantum computers. Furthermore there is a vast gap between public understanding of classical digital computing and of quantum computing. Q-Muse is a quantum computer music system design for a specific performance. The Entangled Orchestra is a performance for Orchestra, Electronics and Live Internet-Connected Photonic Quantum Computer. There are many types of quantum computation hardware implementations including Nuclear Magnetic Resonance, Trapped Ions, and Optical Computing. Q-Muse incorporates t...

The Classical-Quantum Hybrid Architecture for Topological Exploit Detection (CQH-TED) establishes a theoretical and architectural framework for synthesizing robust defenses against Neural Privilege Escalation Exploits (NPEEs). Operating within the UCA-VM, the system partition its workload: Classical Units handle continuous learning and control (O(poly(N))), while a dedicated Quantum Processing Unit (QPU) manages the combinatorial pattern search (O(2N/2)). The core of the tracking algorithm, the Combinatorial-Associative Pattern Tracking Algorithm (C-A PTA), maps input sequences to a Topological Invariant (DR), enabling a Supervised Classifier (Γ) to learn the structural boundary between safe operation and exploitation. The paper further details the Universal Exploit Synthesis (Ssynth) for game-playing AIs and defines a multi-criteria prioritization function (S) for targets, identifying the structurally vulnerable "bottom of the iceberg" beneath a simple surface (e.g., a website's game interface).

The Classical-Quantum Hybrid Architecture for Topological Exploit Detection (CQH-TED) establishes a theoretical and architectural framework for synthesizing robust defenses against Neural Privilege Escalation Exploits (NPEEs). Operating within the UCA-VM (Unexploitable Control Architecture for Vulnerability Modeling), the system partitions its workload: Classical Units handle continuous learning and control (O(poly(N))), while a dedicated Quantum Processing Unit (QPU) manages the combinatorial pattern search (O(2N/2)). The core of the tracking algorithm, the C-A PTA, maps input sequences to a Topological Invariant (DR), enabling a Supervised Classifier (Γ) to learn the structural boundary between safe operation and exploitation. The paper further details the Universal Exploit Synthesis (Ssynth) for game-playing AIs and defines a multi-criteria prioritization function (S) for targets, identifying the structurally vulnerable "bottom of the iceberg" beneath a simple surface (e.g., a website's game interface).

The Classical-Quantum Hybrid Architecture for Topological Exploit Detection (CQH-TED) establishes a theoretical and architectural framework for synthesizing robust defenses against Neural Privilege Escalation Exploits (NPEEs). Operating within the UCA-VM (Unexploitable Control Architecture for Vulnerability Modeling), the system partitions its workload: Classical Units handle continuous learning and control (O(poly(N))), while a Quantum Processing Unit (QPU) manages the combinatorial pattern search (O(2N/2)). The core of the tracking algorithm is the C-A PTA, which maps input sequences to a Topological Invariant (DR), enabling a Supervised Classifier (Γ) to learn the structural boundary between safe operation and exploitation.

We introduce the concept of robot behaviors -deterministic, probabilistic and entangled. In contrast to classical circuits, quantum circuit can realize all three of these behaviors. When applied to a robot, a quantum circuit controller realizes what we call quantum robot behaviors. . Occam Razor principle is satisfied by finding circuits of reduced complexity. Thus we extended the logic synthesis approach to Inductive Machine Learning for the case of learning quantum circuits from behavioral examples. BEHAVIORS FROM EXAMPLES.

Fault-tolerant quantum computation promises to solve outstanding problems in quantum chemistry within the next decade. Realizing this promise requires scalable tools that allow users to translate descriptions of electronic structure problems to optimized quantum gate sequences executed on physical hardware, without requiring specialized quantum computing knowledge. To this end, we present a quantum chemistry library, under the open-source MIT license, that implements and enables straightforward use of state-of-art quantum simulation algorithms. The library is implemented in Q#, a language designed to express quantum algorithms at scale, and interfaces with NWChem, a leading electronic structure package. We define a standardized schema for this interface, Broombridge, that describes second-quantized Hamiltonians, along with metadata required for effective quantum simulation, such as trial wavefunction ansatzes. This schema is generated for arbitrary molecules by NWChem, conveniently accessible, for instance, through Docker containers and a recently developed web interface EMSL Arrows. We illustrate use of the library with various examples, including ground-and excited-state calculations for LiH, H 10 , and C 20 with an active-space simplification, and automatically obtain resource estimates for classically intractable examples. I. Introduction II. Review A. Quantum computing and programming B. Quantum chemistry C. Quantum simulation III. The Broombridge schema for representing electronic structure problems A. Broombridge v0.1 specifications B. Generating Broombridge with NWChem IV. Simulating quantum chemistry with the Microsoft Quantum Development Kit A. Constructing qubit Hamiltonians from chemistry Hamiltonians B. Synthesizing quantum simulation circuits C. Estimating eigenvalues V. Example applications A. Lithium hydride ground-and excited-state energies B. Empirical Trotter error estimation of stretched H 10 chains C. Quantum computing predictions and resource estimations for C 20 isomerizations VI. Conclusions

Quantum nonlocality is one of the most striking features of quantum mechanics: correlations between distant systems that defy any classical explanation based on local hidden variables. Since Bell's theorem [Bell1964] it has been known that such correlations must violate specific inequalities, and decades of increasingly precise experiments have confirmed this prediction. Landmark loophole-free tests [Hensen2015, Giustina2015, Shalm2015] demonstrate beyond reasonable doubt that local realism cannot account for the observed phenomena. Alternative classical explanations-such as hidden communication, superdeterminism, or retrocausality-remain speculative and lack empirical support. Recognizing nonlocality as an irreducible property of nature reshapes our understanding of causality, information, and the conceptual foundations of emerging quantum technologies [Brunner2014, Ekert1991].

A quantum lattice algorithm (QLA) is developed for the solution of Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation. For x-dependent and y-dependent inhomogeneities, the corresponding QLA requries 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the collisional entanglement of two qubits. However, z-dependent inhomogeneities require a QLA with 16 qubits/lattice site since the Pauli spin matrix $\sigma_z$ is diagonal. QLA simulations are performed for the time evolution of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. There is excellent agreement between all three representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions...

To achieve high resolution simulations of MHD turbulence, one must have highly parallelized algorithms that scale to hundreds of thousands of cores. Direct lattice Boltzmann algorithms are such explicit schemes - but they are typically restricted in the achievable Reynolds numbers due to numerical instabilities. Here we examine entropic generalizations of LB by introducing a scalar distribution for the magnetic field With the magnetic field arising as a first moment we can enforce positive definiteness on the magnetic scalar distribution and hence an entropic representation. This will permit simulations to be performed at arbitrary high magnetic Reynolds number - limited only by the number of cores available. Results will be presented for the Orszag-Tang vortex. Moreover large eddy simulation (LES) closures can be incorporated into LB without destroying the parallelization of the algorithm as macroscopic gradients are local moments in the LB representation. LB does not loose its par...

Because of its simplicity, nearly perfect parallelization and vectorization on supercomputer platforms, lattice Boltzmann (LB) methods hold great promise for simulations of nonlinear physics. Indeed, our MHD-LB code has the best sustained performance/PE of any code on ...

We propose a review of recent developments on entanglement and non-classical effects in collective two-atom systems and present a uniform physical picture of the many predicted phenomena. The collective effects have brought into sharp focus some of the most basic features of quantum theory, such as nonclassical states of light and entangled states of multiatom systems. The entangled states are linear superpositions of the internal states of the system which cannot be separated into product states of the individual atoms. This property is recognized as entirely quantum-mechanical effect and have played a crucial role in many discussions of the nature of quantum measurements and, in particular, in the developments of quantum communications. Much of the fundamental interest in entangled states is connected with its practical application ranging from quantum computation, information processing, cryptography, and interferometry to atomic spectroscopy.

We discuss a model of a cavity filled with a passive nonlinear 'Kerr' medium and periodically kicked by a series of ultra-short laser pulses. We perform numerical calculations to find the variance of the field quadrature to determine the squeezing properties of the cavity field. We show that degree of the squeezing depends on the parameters describing external, pulsed excitation.

This thesis presents synthesis of the reversible comparator. The proposed circuits are designed using only parity preserving Fredkin and Feynman double gates. Thus, these circuits inherently turn into fault tolerant circuits. In addition, a lower bound on the number of constant inputs and garbage outputs for the reversible fault tolerant comparator has been proposed. It has been evidenced that the proposed circuit is constructed with these optimal garbage outputs and constant inputs. Moreover, a design algorithm for the generalized fault tolerant comparator has been presented. The comparative results show that the proposed design performs much better and has significantly better scalability than the existing approaches.

Notwithstanding interest and excitement building around quantum computing in the last decades, a concise statement saying where this computing can truly help is still missing. As it is shown in the present paper, equal cost of computation for truth and falsity of experimental quantum propositions (required in order to infer a conclusion from a premise) cannot be achieved with classical computing. On the other hand, this equality might be realized with quantum parallel computing provided that the efficiency of such computing can be greater than 1.

We present a comprehensive experimental study comprising 544 independent quantum experiments with 2,654,208 measurements on IBM Brisbane superconducting quantum processor, demonstrating unprecedented quantum coherence levels through parametric resonance stabilization. Our systematic investigation across 64 parameter configurations reveals peak coherence of 99.74% with robust performance (¿93%) throughout the entire parameter space. Scaling analysis from 1-5 qubit systems shows 100% state generation success, achieving all 32 theoretical states in 5-qubit configurations. Time evolution studies demonstrate coherence preservation exceeding 96% through circuits of 392 gate depth. Statistical validation across 20 independent runs confirms exceptional reproducibility with mean coherence of 98.24% ± 1.50% (95% CI: [97.52%, 98.96%]). These results establish parametric resonance as a transformative approach for quantum coherence enhancement, enabling practical quantum algorithms on near-term devices without hardware modifications.

We present the first experimental validation of infinite quantum coherence through the Quantum Harmonic Resonance Framework (QHRF) on IBM Quantum superconducting processors. Through comprehensive parameter optimization and scaling analysis across 2-5 qubit systems, we demonstrate sustained coherence levels exceeding 99% on noisy intermediate-scale quantum (NISQ) devices. Our results show optimal performance at frequency f = 0.100 and breathing amplitude b = 0.200, achieving 34.2% enhancement in state concentration over baseline. The infinite coherence protocol maintains 99.40% coherence in 3-qubit systems despite circuit depths exceeding 120 gates. Statistical validation across 10 independent runs confirms reproducibility with coefficient of variation below 0.2%. These findings validate QHRF's theoretical predictions and establish a new paradigm for coherence preservation in quantum computing.

This article reviews chosen topics related to the development of Information Quantum Technologies in the major areas of measurements, communications, and computing. These fields start to build their ecosystems which in the future will probably coalesce into a homogeneous quantum information layer consisting of such interconnected components as quantum internet, full size quantum computers with efficient error corrections and ultrasensitive quantum metrology nodes stationary and mobile. Today, however, the skepticism expressing many doubts about the realizability of this optimistic view fights with a cheap optimism pouring out of some popular press releases. Where is the truth? Financing of the IQT by key players in research, development and markets substantially strengthens the optimistic side. Keeping the bright side with some reservations, we concentrate on showing the FAST pace of IQT developments in such areas as biological sciences, quantum evolutionary computations, quantum internet and some of its components.

This paper presents a new recursive formulation for Walsh-Hadamard Transform (WHT) that allows the generation of higher order (longer size) multidimensional (m-d) WHT architectures from m 2 lower order (shorter sizes) WHT architectures. The objective of our work is to derive a unified framework and a design methodology that allows direct mapping of the proposed algorithms into modular VLSI architectures. Our methodology is based on manipulating tensor product forms so that they can be mapped directly into modular parallel architectures. The resulting WHT circuits have very simple modular structure and regular topology.

We say that a topological [Formula: see text]-manifold [Formula: see text] is a cubical [Formula: see text]-manifold if it is contained in the [Formula: see text]-skeleton of the canonical cubulation [Formula: see text] of [Formula: see text] ([Formula: see text]). In this paper, we prove that any closed, oriented cubical [Formula: see text]-manifold has a transverse field of 2-planes in the sense of Whitehead and therefore it is smoothable by a small ambient isotopy.

In this paper, we prove that two cubic knots K1, K2 are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the Reidemeister moves for classical tame knots. We use this fact to describe a cubic knot in a discrete way, as a cyclic permutation of contiguous vertices of the ℤ3-lattice (with some restrictions); moreover, we describe a regular diagram of a cubic knot in terms of such cyclic permutations.

As a crossover frontier of physics and mechanics, quantum computing is showing its great potential in computational mechanics. However, quantum hardware noise remains a critical barrier to achieving accurate simulation results due to the limitation of the current hardware. In this paper, we integrate error-mitigated quantum computing in data-driven computational homogenization, where the zero-noise extrapolation (ZNE) technique is employed to improve the reliability of quantum computing. Specifically, ZNE is utilized to mitigate the quantum hardware noise in two quantum algorithms for distance calculation, namely a Swap-based algorithm and an H-based algorithm, thereby improving the overall accuracy of data-driven computational homogenization. Multiscale simulations of a 2D composite L-shaped beam and a 3D composite cylindrical shell are conducted with the quantum computer simulator Qiskit, and the results validate the effectiveness of the proposed method. We believe this work presents a promising step towards using quantum computing in computational mechanics.

As a crossover frontier of physics and mechanics, quantum computing is showing its great potential in computational mechanics. However, quantum hardware noise remains a critical barrier to achieving accurate simulation results due to the limitation of the current hardware. In this paper, we integrate error-mitigated quantum computing in data-driven computational homogenization, where the zero-noise extrapolation (ZNE) technique is employed to improve the reliability of quantum computing. Specifically, ZNE is utilized to mitigate the quantum hardware noise in two quantum algorithms for distance calculation, namely a Swap-based algorithm and an H-based algorithm, thereby improving the overall accuracy of data-driven computational homogenization. Multiscale simulations of a 2D composite L-shaped beam and a 3D composite cylindrical shell are conducted with the quantum computer simulator Qiskit, and the results validate the effectiveness of the proposed method. We believe this work presents a promising step towards using quantum computing in computational mechanics.

Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we present a new quantum algorithm to show that entanglement could help to gain advantage over classical algorithm and even the quantum algorithm without entanglement. Furthermore, we implement experiments to demonstrate our proposed algorithm using superconducting qubits. Our results show the viability of the algorithm and suggest that entanglement is essential in getting quantum speedup for certain problems in quantum computing, which provide a reliable and clear guidance for developing useful quantum algorithms in future.

The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques more suited to contemporary practical problems . Among those, especially the NP hard problems provide an apt platform to demonstrate supremacy of quantum over classical technologies in terms of resources and time. TSP is one such NP hard problem in combinatorial optimization which takes exponential time order for solving by brute force method. Here we propose a quantum algorithm to solve the travelling salesman problem using phase estimation technique. We approach the problem by encoding the given distances between the cities as phases. We construct unitary operators whose eigenvectors are the computational basis states and eigenvalues are various combinations of these phases. Then we apply phase estimation algorithm to certain eigenstates which give us all the total distances possible for all the routes. After obtaining the distances we can search through this information using the quantum search algorithm for finding the minimum [10] to find the least possible distance as well the route taken. This provides us a quadratic speedup over the classical brute force method for a large number of cities. In this paper, we illustrate an example of the travelling salesman problem by taking four cities and present the results by simulating the codes in the IBM's quantum simulator. Travelling Salesman Problem (TSP) is a classic optimization problem in the field of computer science. It belongs to an intriguing class of 'hard' optimization problems called NP hard . The problem involves a salesman who has to travel N cities, visiting each city once and reaching ultimately at the same city where he started. This cycle of visiting each city once, where each city represents a unique vertex in a graph, and returning to the starting city is known as a Hamiltonian cycle . Each city is connected to other cities with a specific cost associated to each connection. The cost gives an idea of * These authors contributed equally to this work.

Quantum secret sharing is a way to share secret messages amongst a number of clients in a group with unconditional security. For the first time, Hillery et al. [Phys. Rev. A 59, 1829 (1999)] proposed the quantum version of classical secret sharing protocol using GHZ states. Here, we implement this quantum secret sharing protocol in IBM 5-qubit quantum processor 'ibmqx4' and compare the experimentally obtained results with the theoretically predicted ones. The results are analyzed through quantum state tomography technique and the fidelity of these states were calculated for different number of executions made in the device. It is concluded that the experimental results match with the theoretical values with a high fidelity.

Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we present a new quantum algorithm to show that entanglement could help to gain advantage over classical algorithm and even the quantum algorithm without entanglement. Furthermore, we implement experiments to demonstrate our proposed algorithm using superconducting qubits. Our results show the viability of the algorithm and suggest that entanglement is essential in getting quantum speedup for certain problems in quantum computing, which provide a reliable and clear guidance for developing useful quantum algorithms in future.

Concurrence introduced by Hill and Wootters [Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive for entangled states and vanishes for all separable states. We present an extension of entanglement measure to general pure continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara and Panigrahi [Quantum Inf. Process. 16, 118 (2017)] for pure discrete variable systems in arbitrary dimensions and extending the concept to mixed continuous variable states. A family of faithful entanglement measures is constructed that admit necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Phys. Rev. Lett. 78, 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair-coherent states and non-Gaussian continuous variable Bell states, matches with known results. We also quantify entanglement of phase randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.

Presence of entangled states is explicitly shown in Topological insulator (TI) Bi2T e3. The surface and bulk state are found to have the different structures of entanglement. The surface states live as maximally entangled states in the four-dimensional subspace of total Hilbert space (spin, orbital, space). However, bulk states are entangled in the whole Hilbert space. Bulk states are found to be entangled maximally by controlled injection of electrons with momentum only along the zdirection. Scheme to detect entanglement in a 2-D model using measurement, confirming natural implementation of universal Hadamard with Controlled-NOT gates is explicated. I.

We study the nature of entanglement in presence of Deutschian closed timelike curves (D-CTCs) and we observe that qubits traveling along a D-CTC allow unambiguous discrimination of Bell states with Local Operations and Classical Communications (LOCC), that is otherwise known to be impossible. A consequence of this leads us to discover that localized D-CTCs can create entanglement between two parties, using just local operations and classical communication. This contradicts the fundamental definition of entanglement.

A one way partial quantum bit commitment protocol is developed, using states with built-in classical correlation, completely independent of entanglement. It involves concealing information in a set of mutually non-orthogonal states and revealing it through measurements on a set of product states that are mutually orthogonal. Given 2 N choices to commit from, the protocol encodes each choice in a N +1 qubit state, from 2 N non-orthogonal states. A previously agreed upon N qubit state corresponding to each choice, when coupled with the N + 1 qubit state, yields an element belonging to a set of orthogonal product states, which can be deterministically distinguished. The protocol is demonstrated by implementing it for a 'coin-toss' game. A procedure to enhance security of the protocol is explicated, increasing the number of qubits required. Thus a modification is suggested to reduce this required number.

Discriminating between orthogonal quantum systems without destroying their entanglement is of interest to quantum computation and communication. In this paper, we explicate the schemes for the non-destructive discrimination (NDD) of 16 orthogonal four qubit cluster states and 32 orthogonal five qubit cluster states respectively. This technique will find its applications in various branches of quantum information theory.

A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. Quantum search algorithm can be described as the rotation of state vectors in a Hilbert space. The state vectors uniformly rotate by iterative sequences until they hit the target position. To optimize the algorithm, it is necessary to have the precise knowledge about some parameters like the number of target positions and total number of states. Here, we demonstrate the implementation of optimal fixedpoint quantum search algorithm in IBMQ simulator developed by IBM corporation. We perform the search algorithm for one-iteration for two, three, four and five qubit systems and confirm the accuracy of our results through histogram.

Quantum scrambling measured by out-of-time-ordered correlator (OTOC) has an important role in understanding the physics of black holes and evaluating quantum chaos. It is known that Rydberg atom has been a general interest due to its extremely favourable properties for building a quantum simulator. Fast and efficient quantum simulators can be developed by studying quantum scrambling in related systems. Here we present a general quantum circuit to theoretically implement an interferometric protocol which is a technique proposed to measure OTOC functions. We apply this circuit to measure OTOC and hence the quantum scrambling in a simulation of a 1-D Ising spin model for Rydberg atom. We apply this method to both initial product and entangled states to compare the scrambling of quantum information in both cases. Finally we discuss other constructions where this technique can

Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle through different types of potential barriers by performing digital quantum simulations using IBM quantum computers. We consider two and three-qubit systems to visualize the tunneling process and illustrate its unique quantum nature. We observe the tunneling and oscillations of the particles in a step-well, double-well, and multi-well potentials through our experimental results. One may extend the proposed quantum circuits and simulation techniques used here for observing the tunneling phenomena for multi-particle systems in different potentials.

The strategic Go game, known for the tedious mathematical complexities, has been used as a theme in many fiction, movies, and books. Here, we introduce the Go game and provide a new version of quantum Go in which the boxes are initially in a superposition of quantum states |0 and |1 and the players have two kinds of moves (classical and quantum) to mark each box. The mark on each box depends on the state to which the qubit collapses after the measurement. All other rules remain the same, except for here, we capture only one stone and not chains. Due to the enormous power and exponential speed-up of quantum computers as compared to classical computers, we may think of quantum computing as the future. So, here we provide a tangible introduction to superposition, collapse, and entanglement via our version of quantum Go. Finally, we compare the classical complexity with the quantum complexity involved in playing the Go game.

Quantum error detection has always been a fundamental challenge in a fault-tolerant quantum computer. Hence, it is of immense importance to detect and deal with arbitrary errors to efficiently perform quantum computation. Several error detection codes have been proposed and realized for lower number of qubit systems. Here we present an error detection code for a (2n + 1)-qubit entangled state using two syndrome qubits and simulate it on IBM's 16-qubit quantum computer for a 13-qubit entangled system. The code is able to detect an arbitrary quantum error in any one of the first 2n qubits of the (2n+1)-qubit entangled state and detects any bit-flip error on the last qubit of the (2n + 1)-qubit entangled state via measurements on a pair of ancillary error syndrome qubits. The protocol presented here paves the way for designing error detection codes for the general higher number of entangled qubit