Quantum Gates Research Articles

Analysis and Implementation of Quantum Gates (X, Z, Y, Hadamard CNOT and CCNOT) by using matrices for Quantum Computing

The constraints of present supercomputers in addressing exponentially intricate problems are apparent, as these jobs sometimes necessitate hundreds or even thousands of years due to the exponential increase in computational requirements. Quantum computing, which utilizes concepts from quantum physics and operates with qubits, offers a promising solution by significantly decreasing problem-solving durations to only seconds or minutes. Using IBM's quantum computing platform, this work investigates the construction and analysis of fundamental quantum gates, including X, Z, Y, Hadamard, CNOT, and CCNOT. This work presents a comprehensive analysis of these gates using matrix representations, demonstrating their operational mechanics and algebraic functions, and fundamental role of matrix theory in quantum gate operations and its contribution to the future development of quantum computing.

Predicting arbitrary state properties from single Hamiltonian quench dynamics

Analog quantum simulation is an essential routine for quantum computing and plays a crucial role in studying quantum many-body physics. Typically, the quantum evolution of an analog simulator is largely determined by its physical characteristics, lacking the precise control or versatility of quantum gates. This limitation poses challenges in extracting physical properties on analog quantum simulators, an essential step of quantum simulations. To address this issue, we introduce the protocol, which uses a single quench Hamiltonian for estimating arbitrary state properties, eliminating the need for ancillary systems and random unitaries. Additionally, we derive the sample complexity of this protocol and show that it performs comparably to the classical shadow protocol. The Hamiltonian shadow protocol does not require sophisticated control and can be applied to a wide range of analog quantum simulators. We demonstrate its utility through numerical demonstrations with Rydberg atom arrays under realistic parameter settings. The new protocol significantly broadens the application of randomized measurements for analog quantum simulators without precise control and ancillary systems. Published by the American Physical Society 2024

Silicon–based integrated orbital angular momentum parity sorter

Abstract A silicon–based integrated orbital angular momentum (OAM) parity sorter using two-dimensional multimode interference (2D MMI) waveguides is designed and numerically analyzed. An OAM parity sorter, which sorts OAM modes according to their parity (even or odd) is an elegant device in a broad range of OAM states processing applications including quantum gates, quantum key distribution, generation of high dimensional quantum gates, quantum information, and teleportation. The presented three–part integrated parity sorter is realized based on the self–imaging and field–splitting properties of MMI structures. Its total length is 11 444 µm. The proposed device works for OAM modes with |l| ⩽ 5. The performance of OAM sorting is investigated with the results confirming the high purity (up to 98.33% and 94.45% at even and odd ports, respectively) for the telecommunication wavelength λ 0 = 1550 nm.

Analysis of the Principles of Quantum Computing and State-of-the-Art Applications

Abstract. Contemporarily, quantum computing has emerged as a promising field, offering potential breakthroughs in various computational tasks that are currently limited by classical computing. With this in mind, this study delves into the principles of quantum computing, exploring the fundamental concept of quantum entanglement and its implications for computation. After outlining the historical development and research significance of quantum computing, this research presents an overview of the latest advancements in the field. The paper then focuses on the principles of quantum computation, including the use of qubits and quantum gates, illustrated with relevant mathematical formulations and diagrams. Furthermore, this study discusses the state-of-the-art applications of quantum computing, showcasing recent achievements and results obtained from these cutting-edge technologies. A comparative analysis with traditional algorithms highlights the advantages and potential gains offered by quantum computing. Finally, the current limitations of quantum computing are discussed and the insights into future research directions and prospects are proposed for this exciting field.

Implementation of controlled unitary gates and its application in a remote-controlled quantum gate

Recently, remote-controlled quantum information processing has been proposed for its applications in secure quantum processing protocols and distributed quantum networks. For remote-controlled quantum gates, the experimental realization of controlled unitary (CU) gates between any quantum gates is an essential task. Here, we propose and experimentally demonstrate a scheme for implementing CU gates between any pair of unitary gates using the polarization and time-bin degrees of freedom of single photons. Then, we experimentally implement remote-controlled single-qubit unitary gates by controlling either the state preparation or measurement of the control qubit with high process fidelities. We believe the proposed remote-controlled quantum gate model can pave the way for secure and efficient quantum information processing.

Magnetic Molecules as Building Blocks for Quantum Technologies

AbstractSince the initial observation of quantum effects, scientists have worked diligently to understand and harness their potential. Thanks to many pioneers, a level where quantum effects can be exploited is reached. Numerous cutting‐edge technologies, such as quantum sensing and quantum computing, are proposed. A common trait in all technologies is the need to manipulate and read out their states; therefore, the quantum characteristics of the building blocks must adhere to strict guidelines. Magnetic Molecules (MMs) are promising candidates. They can be obtained indistinguishably, and the control over their structural and electronic properties, makes them appealing to act as quantum bits or “qubits”. MMs can be connected to other units while preserving their coherence properties, enabling the implementation of quantum gates. Furthermore, the low‐lying energy levels can be exploited as qudits, which can exist in more than 2 states simultaneously (d > 2), allowing them to hold more information efficiently. The larger electronic/nuclear space in qudits can decrease the number of physical units and enhance computational efficiency, reducing error and making them promise for complex problem‐solving. In this perspective article, the physical characteristics of MMs and key achievements that position them as promising candidates for quantum technologies, are described.

Native multi-qubit gates in transmon qubits via synchronous driving

Quantum computation holds the promise of solving computational problems which are believed to be classically intractable. However, in practice, quantum devices are still limited by their relatively short coherence times and imperfect circuit-hardware mapping. In this work, we present the parallelization of pre-calibrated pulses at the hardware level as an easy-to-implement strategy to optimize quantum gates. Focusing on RZX\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_{ZX}$$\\end{document} gates, we demonstrate that such parallelization leads to improved fidelity and gate time reduction, when compared to serial concatenation. As measured by Cycle Benchmarking and Process Tomography, we reduce gate errors by half. We show that this strategy can be applied to other gates like the CNOT and CZ, and it may benefit tasks such as Hamiltonian simulation problems, amplitude amplification, and error-correction codes.

Electrodynamics-based quantum gate optimization with born scattering

In this paper, we propose employing electron scattering to realize unitary quantum gates that are controlled by three qubits. Using Feynman’s rules, we find an expression for the transition amplitude for scattering from an external electromagnetic source. In this context, the scattering amplitude is modeled as a unitary gate whose state can be regulated. The optimal value of the vector potential needed to implement the gate is obtained by minimizing the difference between the designed gate and the target gate, with the total energy consumed as a constraint. The design algorithm is obtained by discretizing the resulting integral equations into vector equations. This design algorithm can be applied in various fields such as quantum computing, communication, and sensing. It offers a promising approach for developing efficient and accurate gates for quantum information processing. Furthermore, this approach can also be extended to design gates for multi-qubit systems, which are essential for large-scale quantum computing. The use of this algorithm can significantly contribute to the development of practical quantum technologies.

Realization of a hybrid multi-qubit quantum phase gate in circuit QED

We propose to implement a hybrid multi-qubit quantum phase gate based on a setup comprising multiple microwave cavities coupled to a common superconducting transmon qutrit in the circuit quantum electrodynamics. The function of this hybrid quantum phase gate is that a phase related to the total number of cavities in non-vacuum state will be introduced when the transmon qubit is in an excited state. Furthermore, we propose an application, quantum voting machine, with this hybrid quantum gate. This scheme is scalable and simple to operate, requiring just a single step and necessitating only the reading of quantum states of one target qubit. While for quantum voting machine, it ensures the verifiability of the voting results through the measurement of the phase information of the target qubit. Additionally, the anonymity of the voters is ensured as the voting outcome is solely tied to the total number of affirmative votes. Numerical simulations indicate the feasibility of this hybrid quantum gate and quantum voting machine within the current quantum technology.

Reducing the effect of noise on quantum gate design by linear filtering

Reducing the effect of noise on quantum gate design by linear filtering

Qubit analog with polariton superfluid in an annular trap.

We report on the experimental realization and characterization of a qubit analog with semiconductor exciton-polaritons. In our system, a polaritonic condensate is confined by a spatially patterned pump laser in an annular trap that supports energy-degenerate vortex states of the polariton superfluid. Using temporal interference measurements, we observe coherent oscillations between a pair of counter-circulating vortex states coupled by elastic scattering of polaritons off the laser-imprinted potential. The qubit basis states correspond to the symmetric and antisymmetric superpositions of the two vortex states. By engineering the potential, we tune the coupling and coherent oscillations between the two circulating current states, control the energies of the qubit basis states, and initialize the qubit in the desired state. The dynamics of the system is accurately reproduced by our theoretical two-state model, and we discuss potential avenues to implement quantum gates and algorithms with polaritonic qubits analogous to quantum computation with standard qubits.

Continuously tunable single-photon level nonlinearity with Rydberg state wave-function engineering

Extending optical nonlinearity into the extremely weak light regime is at the heart of quantum optics, since it enables the efficient generation of photonic entanglement and implementation of photonic quantum logic gate. Here, we demonstrate the capability for continuously tunable single-photon level nonlinearity, enabled by precise control of Rydberg interaction over two orders of magnitude, through the use of microwave-assisted wave-function engineering. To characterize this nonlinearity, light storage and retrieval protocol utilizing Rydberg electromagnetically induced transparency is employed, and the quantum statistics of the retrieved photons are analyzed. As a first application, we demonstrate our protocol can speed up the preparation of single photons in low-lying Rydberg states by a factor of up to∼40. Our work holds the potential to accelerate quantum operations and to improve the circuit depth and connectivity in Rydberg systems, representing a crucial step towards scalable quantum information processing with Rydberg atoms.

Quantum teleportation based on the elegant joint measurement

As a generalization of the well-known Bell state measurement (BSM), the elegant joint measurement (EJM) is a kind of novel two-qubit joint measurement, parameterized by a subtle phase factor θ∈[0,π/2]. We investigate here the quantum teleportation based on the EJM that conceptually goes beyond BSM. It is a probabilistic teleportation caused by nonunitary quantum evolution except for the special case of the BSM with θ=π/2. We show in detail the feasible quantum circuits to realize the present scenario, where a few unitary operations and a nonunitary quantum gate are being utilized. This work suggests that it is feasible to extend the customary (BSM-based) teleportation scenarios to the EJM-based ones, and different from the BSM being single input it may provide a continuously variable input setting or even multiple measurement settings for the sender of the quantum state.

Harmonic flow-field representations of quantum bits and gates

We describe a general procedure for mapping arbitrary n-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multiqubit states find natural field representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor's algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and nonstandard computation. Published by the American Physical Society 2024

Experimental quantum teleportation of a Toffoli gate across three spatially distributed parties in a photonic quantum network

Quantum computers may offer significant computational advantages over classical counterparts, revolutionizing the technology landscape in the near future. When networked together, the advantage of quantum computing may be further amplified, and there may emerge innovative applications. Among various active explorations on distributed quantum computing, multiqubit quantum gates between distant networked quantum computers are of particular interest because they offer operational advantages of efficiency and fidelity. Here we report the first experimental demonstration of quantum teleportation for a Toffoli gate, which is a commonly used multiqubit quantum gate, across three spatially distributed parties within a photonic quantum network. Employing the Hofmann method, we estimate the fidelity of the teleported Toffoli gate to be at least 0.706 ± 0.131. This successful demonstration of the quantum teleportation of a Toffoli gate constitutes a critical step toward the ultimate realization of distributed quantum computation.

CONTENTS OF TRAINING IN CONSTRUCTING CONTROLLED QUANTUM GATES

The article makes a selection and subsequent structuring of the content of training in the construction of controlled quantum gates using twelve decompositions of single-qubit quantum gates (Z-Y, Z-X, X-Y, Y-Z, X-Z, Y-X; Z-Y-X, Z-X-Y, X-Y-Z, X-Z-Y, Y-X-Z, Y-Z-X) used in the process of teaching the section “Quantum Computing and Programming in the QCL Language” of the training course “Applied Programming in High-Level Languages” to students of the Institute of Information Technology and Technological Education (3rd year, Herzen State Pedagogical University of Russia).

Quantum annealing for nearest neighbour compliance problem

Quantum Computing has emerged as a promising alternative, utilising quantum mechanics for faster computations. This paper explores the nearest neighbour compliance (NNC) Problem in Gate-based Quantum Computers, where quantum gates are constrained to operate on physically adjacent qubits. The NNC problem aims to optimise the insertion of SWAP-gates to ensure compliance with these constraints while minimising their count. This work introduces Quantum Annealing to tackle the NNC problem, proposing two Quadratic Unconstrained Optimisation Problem formulations. The formulations are tested on a contemporary Quantum Annealer, and their performance is compared with previous methods. It shows that the prospect of using Quantum Annealing is promising, however, the current state of the hardware makes that finding the embedding is the limiting factor.

BHT-QAOA: The Generalization of Quantum Approximate Optimization Algorithm to Solve Arbitrary Boolean Problems as Hamiltonians.

A new methodology is introduced to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). This methodology is termed the "Boolean-Hamiltonians Transform for QAOA" (BHT-QAOA). Because a great deal of research and studies are mainly focused on solving combinatorial optimization problems using QAOA, the BHT-QAOA adds an additional capability to QAOA to find all optimized approximated solutions for Boolean problems, by transforming such problems from Boolean oracles (in different structures) into Phase oracles, and then into the Hamiltonians of QAOA. From such a transformation, we noticed that the total utilized numbers of qubits and quantum gates are dramatically minimized for the generated Hamiltonians of QAOA. In this article, arbitrary Boolean problems are examined by successfully solving them with our BHT-QAOA, using different structures based on various logic synthesis methods, an IBM quantum computer, and a classical optimization minimizer. Accordingly, the BHT-QAOA will provide broad opportunities to solve many classical Boolean-based problems as Hamiltonians, for the practical engineering applications of several algorithms, digital synthesizers, robotics, and machine learning, just to name a few, in the hybrid classical-quantum domain.

Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms

Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms

Nonlocal photonic quantum gates over 7.0 km

Quantum networks provide a prospective paradigm to connect separated quantum nodes, which relies on the distribution of long-distance entanglement and active feedforward control of qubits between remote nodes. Such approaches can be utilized to construct nonlocal quantum gates, forming building blocks for distributed quantum computing and other novel quantum applications. However, these gates have only been realized within single nodes or between nodes separated by a few tens of meters, limiting the ability to harness computing resources in large-scale quantum networks. Here, we demonstrate nonlocal photonic quantum gates between two nodes spatially separated by 7.0 km using stationary qubits based on multiplexed quantum memories, flying qubits at telecom wavelengths, and active feedforward control based on field-deployed fibers. Furthermore, we illustrate quantum parallelism by implementing the Deutsch-Jozsa algorithm and the quantum phase estimation algorithm between the two remote nodes. These results represent a proof-of-principle demonstration of quantum gates over metropolitan-scale distances and lay the foundation for the construction of large-scale distributed quantum networks relying on existing fiber channels.