Constant-depth circuits for dynamic simulations of materials on quantum computers

The transverse field Ising and XY models (the simplest quantum spin models) provide the organising principle for the rich variety of interconnected subjects which are covered in this book. From a generic introduction to in-depth discussions of the subtleties of the transverse field Ising and related models, it includes the essentials of quantum dynamics and quantum information. A wide range of relevant topics has also been provided: quantum phase transitions, various measures of quantum information, the effects of disorder and frustration, quenching dynamics and the Kibble–Zurek scaling relation, the Kitaev model, topological phases of quantum systems, and bosonisation. In addition, it also discusses the experimental studies of transverse field models (including the first experimental realisation of quantum annealing) and the recent realisation of the transverse field Ising model using tunable Josephson junctions. Further, it points to the obstacles still remaining to develop a successful quantum computer.

Background. Quantum computing is a technology that has great potential to revolutionize various scientific disciplines with its extraordinary computing capabilities. Multiple fields, such as cryptography, optimization, and complex simulation, have begun to explore quantum computing applications. However, a deep understanding of how these technologies can be used effectively in cross-disciplinary informatics still needs to be improved. Purpose. This research aims to develop a theoretical framework that explains the role of quantum computing in advancing interdisciplinary informatics. The main focus is to identify potential applications and challenges faced in applying this technology in various fields and evaluate its impact on the development of science and technology. Method. This research uses a qualitative approach, a literature review, and theoretical analysis methods. Data were collected from various academic sources, including journals, books, and conferences relevant to quantum computing and interdisciplinary informatics. Analysis was conducted to identify patterns, themes, and relationships between quantum computing and cross-disciplinary applications. Results. The research results show that quantum computing has the potential to solve complex computational problems in various fields, including cryptography, optimization, and physical simulation. Quantum computing can provide more efficient and faster solutions than classical computing. However, the research also identified several significant challenges, such as the need for quantum-specific algorithms and sophisticated technological infrastructure. Conclusion. Quantum computing is essential in advancing interdisciplinary informatics by providing superior computing capabilities. The theoretical framework developed in this research can be used to further study and develop quantum computing applications in various fields. The identified challenges require special attention to ensure effective and efficient implementation of this technology.

Background. Quantum computing is a technology that has great potential to revolutionize various scientific disciplines with its extraordinary computing capabilities. Multiple fields, such as cryptography, optimization, and complex simulation, have begun to explore quantum computing applications. However, a deep understanding of how these technologies can be used effectively in cross-disciplinary informatics still needs to be improved. Purpose. This research aims to develop a theoretical framework that explains the role of quantum computing in advancing interdisciplinary informatics. The main focus is to identify potential applications and challenges faced in applying this technology in various fields and evaluate its impact on the development of science and technology. Method. This research uses a qualitative approach, a literature review, and theoretical analysis methods. Data were collected from various academic sources, including journals, books, and conferences relevant to quantum computing and interdisciplinary informatics. Analysis was conducted to identify patterns, themes, and relationships between quantum computing and cross-disciplinary applications. Results. The research results show that quantum computing has the potential to solve complex computational problems in various fields, including cryptography, optimization, and physical simulation. Quantum computing can provide more efficient and faster solutions than classical computing. However, the research also identified several significant challenges, such as the need for quantum-specific algorithms and sophisticated technological infrastructure. Conclusion. Quantum computing is essential in advancing interdisciplinary informatics by providing superior computing capabilities. The theoretical framework developed in this research can be used to further study and develop quantum computing applications in various fields. The identified challenges require special attention to ensure effective and efficient implementation of this technology.

Efficiently estimating energy expectation values of quantum lattice systems on quantum computers is a crucial subroutine for various quantum algorithms, which can lead to significant overhead due to the high measurement shot numbers required. We introduce a measurement strategy tailored to quantum lattice systems and (noisy) energy eigenstates. It is based on a geometric partitioning of the Hamiltonian into local patches and performing the measurements in the eigenbases of those patches. The resulting energy estimator has a smaller variance than the ones of Pauli grouping schemes, which leads to a reduction of the total number of shots. We provide rigorous guarantees for this variance improvement for energy eigenstates, also in the presence of depolarizing noise. As one can choose the subsystem size, one can ensure that measurement circuits remain within implementable depths. In numerical experiments, we demonstrate the shot count reduction for various 2D lattice models, including the transverse field XY and Ising models, as well as the Fermi-Hubbard model. We find sampling improvements of several orders of magnitude already for plaquettes of two by two qubits, where the required readout circuits remain very moderate in depth.

Large-scale quantum computers possess the capacity to effectively tackle practical problems that can be insurmountable for classical computers. The main challenge in building these quantum computers is to realize scalable modules for remote qubits and entanglement. By assembling small, specialized parts into a larger architecture, the modular approach mitigates complexity and uncertainty. Such a distributed architecture requires non-local quantum gate operations between remote qubits. An essential method for implementing such operations, known as quantum gate teleportation, requires only local operations, classical communication, and shared entanglement. Till today, the quantum gate teleportation using a photonic chip has remained elusive. Here, we experimentally demonstrate the quantum teleportation of an on-chip controlled-NOT (CNOT) gate, implemented via a silicon polarization directional coupler. Assisted with the scalable silicon chip platform, high-fidelity local quantum logic gates, linear optical components, post-selected entanglement, and coincidence measurements from photonic qubits, we first measure and characterize our teleported chip-scale CNOT gate with an average truth table fidelity of 93.1 ± 0.3%. Second, for different input polarization states, we obtain an average quantum state fidelity of 87.0 ± 2.2% with our teleported on-chip CNOT gate. Third, we use our non-local CNOT gate for remote entanglement creation of four Bell states, with an average quantum state fidelity of 86.2 ± 0.8%. Fourth, we fully characterize our teleported on-chip CNOT gate with a quantum process fidelity of 83.1 ± 2.0%, and an average non-local CNOT gate fidelity of 86.5 ± 2.2%. Our teleported photonic on-chip quantum logic gate could be extended both to multiple qubits and chip-scale modules towards fault-tolerant and large-scale distributed quantum computation.

We investigate how pulse-sequences and operation times of elementary quantum gates can be optimized for silicon-based donor electron spin quantum computer architecture, complementary to the original Kane's nuclear spin proposal. This gate-sequence-optimal or time-optimal quantum gate control in a quantum circuit is in addition to the more conventional concept of optimality in terms of the number of elementary gates needed in a quantum transformation. The optimal control method we use is the so-called gradient ascent pulse engineering (GRAPE) scheme. We focus on the high fidelity controlled-NOT (CNOT) gate and explicitly find the digitized control sequences by optimizing the effective, reduced donor electron spin Hamiltonian, with external controls over the hyperfine A and exchange J interactions. We first try different piecewise constant control steps and numerically calculate the fidelity (error) against the time needed to implement a CNOT gate with stopping criteria of error in the optimizer set to 〖10〗^(-9) in order to economize the simulation time. Here, the error is defined as 1-F, where F is fidelity. The error is less than 〖10〗^(-8) for times longer than 100ns, and it is found that 30 piecewise constant control steps for the CNOT gate operation will be sufficient to meet the required fidelity (error), and the performance would not be improved further with more steps. With operation time t=100ns and stopping criteria of error set to 〖10〗^(-16), we can find that the near time-optimal, high-fidelity CNOT gate control sequence has an error of 〖1.11×10〗^(-16). We then simulate the control sequences of the CNOT gate, obtained from reduced Hamiltonian simulations, with the full spin Hamiltonian. We find the error of about 〖10〗^(-6) which is below the error threshold required for fault-tolerant (〖10〗^(-4)) quantum computation. The CNOT gate operation time of 100ns is 3 times faster than the globally controlled electron spin scheme of 297ns. One of the great advantages of this near optimal-time high fidelity CNOT gate is that the exchange interaction is not required to be strong (the maximum value is J/h=20MHz compared to the typical value of 10.2GHz. This relaxes significantly the stringent distance constraint of two neighboring donor atoms of about 10nm as reported in the original Kane's proposal to be about 30nm which is within the reach of the current fabrication technology.

In recent years, Reversible Logic is becoming a prominent technology due to its power reduction capability in circuit designing, thus having applications in quantum computing. The reversible circuit is implemented using reversible quantum gates such as CNOT gate, Fredkin gate, Toffoli gate etc. Among the various combinational circuits, quantum multiplexer and de-multiplexer circuits are two of the most important circuits. In this paper, we have proposed generalized algorithms for the construction of Quantum multiplexers (QMUX) and demultiplexers (QDe-MUX) using universal Fredkin gate for any given number of select lines. Using these novel algorithms, any valid size of Quantum multiplexers (QMUX) and de-multiplexers (QDe-MUX) circuit can be generated.

We all have been using classical computers for a long time. Quantum computing uses the phenomena of quantum mechanics like superposition and entanglement. Quantum computations can help achieve for the breakthroughs we have been looking for in science, machine learning, financial planning, medicine, etc., where classical computers’ computing power is not enough. It was not long back when quantum computing's applications in our life were all just theoretical. However, to utilise the power of quantum computations for real‐life applications, several recent developments have been made. Keeping that in mind, this study aims to explore the existing and upcoming applications of quantum computing. In this study, they start with an introduction of quantum computing fundamentals, following which, they give a brief overview of various applications of quantum computing in several significant areas of computer science, such as cryptography, machine learning, deep learning, and quantum simulations. They also cover various real‐life scenarios such as risk analysis, logistics, and satellite communication.

A comprehensive investigation of the entanglement characteristics is carried out on tripartite spin-1/2 systems, examining prototypical tripartite states, the thermal Heisenberg model, and the transverse field Ising model. The entanglement is computed using the Rényi relative entropy. In the traditional Rényi relative entropy, the generalization parameter can take values only in the range due to the requirements of joint convexity of the measure. To use the Rényi relative entropy over a wider range of , we use the sandwiched form which is jointly convex in the regime . In prototypical tripartite states, we find that GHZ states are monogamous, but surprisingly so are W states. On the other hand, star states exhibit polygamy, due to the higher level of purity of the bipartite subsystems. For spin models, we study the dependence of entanglement on various parameters such as temperature, spin-spin interaction, and anisotropy, and identify regions where entanglement is the largest. The Rényi parameter scales the amount of entanglement in the system. The entanglement measure based on the traditional and the sandwiched Rényi relative entropies obey the Araki-Lieb-Thirring inequality. In the Heisenberg models, namely the XYZ, XXZ, and XY models, the system is always monogamous. However, in the transverse field Ising model, the state is initially polygamous and becomes monogamous with temperature and coupling.

The canonical decomposition for two-qubit operators has proven very useful for applications in quantum computing. This decomposition generates equivalence classes up to local quantum gates. We provide a variety of complete, explicit decompositions of given two-qubit operators in terms of single, double, and triple controlled-NOT (CNOT) gates. By analytically addressing the needed pre- and post-tensor product factors, we demonstrate that exact results are possible, even when a parameter is included. The examples given are of interest to superconducting qubit, spin-based, dipolar molecule, and other quantum information processing systems.

Quantum information processing has a wide range of uses, including the solution of complex algorithms, cryptography, dense coding, quantum computation, and quantum teleportation. Quantum entanglement, a phenomenon that is crucial to many different applications of quantum computation, is an essential resource for quantum computation, and the need for quantum circuits that generate entangled states is one of the ongoing needs for constructing quantum computers. In this study, we present a general approach to the design of quantum circuits that produce entangled states. The approach can be applied to the design of various entanglement circuits with any number of qubits (n-qubit systems), and it makes use of a set of CNOT and Hadamard gates, where the number of CNOT gates should always be (n-1) and each gate connects the two adjacent qubits. In this paper, a three-entangled teleportation scheme of a GHZ-like state (named after its inventor Greenberger-Horne-Zeilinger) through three particles as a quantum channel is presented. The probability of successful teleportation depends on the degree of entanglement of GHZ-like states. A 5-qubit quantum teleportation over a GHZ-like channel has also been used. And single-qubit gates are defined, which are Pauli gates. These gates are represented by arrays I, X, Y, and Z. The results in this paper are good and promising theoretical results in the field of quantum entanglement and quantum teleportation using the Mathematica program.

The field of quantum computing has grown fast in recent years, both in theoretical advancements and the practical construction of quantum computers. These computers were initially proposed, among other reasons, to efficiently simulate and comprehend the complexities of quantum physics. In this paper, we present a comprehensive scheme for the exact simulation of the 1-D XY model on a quantum computer. We successfully diagonalize the proposed Hamiltonian, enabling access to the complete energy spectrum. Furthermore, we propose a novel approach to design a quantum circuit to perform exact time evolution. Among all the possibilities this opens, we compute the ground and excited state energies for the symmetric XY model with spin chains of n=4n=4 and n=8n=8 spins. Further, we calculate the expected value of transverse magnetization for the ground state in the transverse Ising model. Both studies allow the observation of a quantum phase transition from an antiferromagnetic to a paramagnetic state. Additionally, we have simulated the time evolution of the state all spins up in the transverse Ising model. The scalability and high performance of our algorithm make it an ideal candidate for benchmarking purposes, while also laying the foundation for simulating other integrable models on quantum computers.

Numerical simulation of NQR/NMR: Applications in quantum computing

In general, reciprocity requires that signals travel in the same manner in both forward and reverse directions. It governs the behaviour of the majority of electronic circuits and components, imposing severe restrictions on how they operate. Components that violate reciprocity, such as gyrators, isolators and circulators, are, however, of use in many different electronic applications. Non-reciprocal electronic components have typically been implemented using ferrites, but such magnetic materials cannot be integrated in modern semiconductor fabrication processes and magnetic non-reciprocal components remain bulky and expensive. Creating non-reciprocal components without the use of magnetic materials has a long history, but has recently been reinvigorated due to advancements in semiconductor technology. Here we review the development of non-reciprocal devices and the development of non-magnetic non-reciprocal electronics, focusing on devices based on temporal modulation, which arguably exhibit the greatest potential. We consider approaches based on temporal modulation of permittivity and conductivity, as well as hybrid acoustic–electronic components, which have applications including high-power transmitters for communications, simultaneous transmit and receive radars, and full-duplex wireless radios. We also explore superconducting non-reciprocal components based on temporal modulation of permeability for potential applications in quantum computing and consider the key future challenges in the field. This Review Article examines the development of non-magnetic non-reciprocal electronics with a focus on devices based on temporal modulation, including approaches based on temporal modulation of permittivity and conductivity, as well as superconducting components for applications in quantum computing.

Exotic particles called Majorana fermions have potential applications in quantum computing, but their existence has yet to be definitively confirmed. Two groups have now glimpsed these particles. Exotic particles called Majorana fermions have potential applications in quantum computing, but their existence has yet to be definitively confirmed. Two groups have now glimpsed these particles.