Quantum Gates Research Articles

Gate-set evaluation metrics for closed-loop optimal control on nitrogen-vacancy center ensembles in diamond

A recurring challenge in quantum science and technology is the precise control of their underlying dynamics that lead to the desired quantum operations, often described by a set of quantum gates. These gates can be subject to application-specific errors, leading to a dependence of their controls on the chosen circuit, the quality measure and the gate-set itself. A natural solution would be to apply quantum optimal control in an application-oriented fashion. In turn, this requires the definition of a meaningful measure of the contextual gate-set performance. Therefore, we explore and compare the applicability of quantum process tomography, linear inversion gate-set tomography, randomized linear gate-set tomography, and randomized benchmarking as measures for closed-loop quantum optimal control experiments, using a macroscopic ensemble of nitrogen-vacancy centers in diamond as a test-bed. Our work demonstrates the relative trade-offs between those measures and how to significantly enhance the gate-set performance, leading to an improvement across all investigated methods.

Finding Zero Correlation Linear Hulls Using Quantum Bernstein-vazirani Algorithm

Abstract Facing the threat of quantum computing to cryptography schemes, it is urgent to study the applications of quantum algorithms to cryptanalysis and evaluate the security of cryptographic schemes in a quantum computing environment. To do this, it is necessary to analyze the ability of cryptanalysis methods, such as integral and linear attacks, when combined with quantum algorithms. In this article, we investigate the properties of block ciphers with SPN structure and their security against a quantum adversary and apply the Bernstein-Vazirani algorithm to zero correlation linear attacks. Based on the relation between linear approximates of SPN ciphers and the dual cipher’s linear structures, we proposed a quantum algorithm that can find linear hulls with zero correlation of SPN ciphers. We show the validity of the proposed quantum algorithm and estimate the corresponding computational complexity. Implementing our quantum algorithm only costs polynomial qubits and quantum gates.

Exploiting automatic differentiation for quantum optimal control of driven dissipative two-level systems

In principle one can use Pontryagin's minimum principle to treat an optimal control problem and derive the gradient for the cost functional. However, for the driven spin-boson model studied here, the response of the system to the variation of the control is determined by the master equation and the equation of motion for the propagator of the coherent system dynamics. As a result, the application of Pontryagin's minimum principle is less straightforward. An alternative to this approach is the technique of automatic differentiation which in principle amounts to doing calculus on the fully discretized form of the optimal control problem. Automatic differentiation tools can be viewed as black boxes taking as input a program computing the cost functional and giving as output another program computing its gradient. First we derive for the polaron transformed Hamiltonian a Born-Markov master equation using the Bloch-Redfield formalism. By combining the latter with automatic differentiation we are able to implement Z-gate and coherent destruction of tunnelling with high fidelity. Optimization of a dissipative quantum gate poses a more complex numerical problem, since it should occur independent of the input state. To overcome this difficulty, we apply optimal control to the concept of resolvent of the master equation which is the generalisation of quantum unitary evolution operator in the case of dissipative dynamics.

Quantum Machine Learning: Bridging Quantum Computing and Artificial Intelligence

Abstract: This comprehensive article explores the burgeoning field of Quantum Machine Learning (QML), examining its foundational principles, key algorithms, and potential applications. We delve into the fundamentals of quantum computing, including qubits, quantum gates, and the challenges of quantum measurement and decoherence. The article provides an indepth analysis of Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN), comparing them with their classical counterparts and highlighting their unique advantages and limitations. We investigate the promising applications of QML in material science, cryptography, and optimization problems, showcasing its potential to revolutionize drug discovery, secure communication, and complex problem-solving. The review also addresses the significant challenges facing QML, including hardware constraints, error correction, algorithm development, and integration with classical systems. By synthesizing current research and identifying future directions, this article offers a comprehensive overview of QML's transformative potential in artificial intelligence and computational science, while acknowledging the hurdles that must be overcome to fully realize its capabilities.

Polarization and Orbital Angular Momentum Encoded Quantum Toffoli Gate Enabled by Diffractive Neural Networks.

Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive to performing complex quantum algorithms. Here, we propose and present an experimental demonstration of a quantum Toffoli gate fully exploiting the polarization and orbital angular momentum of a single photon. The Toffoli gate is implemented using the polarized diffractive neural networks scheme, achieving a mean truth table visibility of 97.27±0.20%. We characterize the gate's performance through quantum state tomography on 216 different input states and quantum process tomography, which yields a process fidelity of 94.05±0.02%. Our method offers a novel approach for realizing the Toffoli gate without requiring exponential optical elements while maintaining extensibility to the implementation of other three-qubit gates.

Alternative fast quantum logic gates using nonadiabatic Landau-Zener-Stückelberg-Majorana transitions

A conventional realization of quantum logic gates and control is based on resonant Rabi oscillations of the occupation probability of the system. This approach has certain limitations and complications, like counter-rotating terms. We study an alternative paradigm for implementing quantum logic gates based on Landau-Zener-Stückelberg-Majorana (LZSM) interferometry with nonresonant driving and the alternation of adiabatic evolution and nonadiabatic transitions. Compared to Rabi oscillations, the main differences are a nonresonant driving frequency and a small number of periods in the external driving. We explore the dynamics of a multilevel quantum system under LZSM drives and optimize the parameters for increasing the gate speed. We define the parameters of the external driving required for implementing a specific quantum logic gate using the adiabatic-impulse model. In particular, we demonstrate the implementations of single-qubit X, Y, Hadamard gates, and two-qubit i and gates using the LZSM transitions. The considered LZSM approach for implementing arbitrary quantum logic gates can be applied to a large variety of multilevel quantum systems and external driving. Published by the American Physical Society 2024

Active robustness against detuning error for Rydberg quantum gates

Active robustness against detuning error for Rydberg quantum gates

Heralded hyper-CNOT gates for two-photon systems assisted by quantum scattering in waveguides

Photonic hyper-parallel quantum gates play a critical role in high-capacity quantum communication and fast quantum computing. Here, based on photon scattering in one-dimensional (1D) waveguides, we present some heralded schemes for constructing four-qubit hyper-controlled-not (hyper-CNOT) gates in two-photon systems. The qubits are encoded on both the polarization and spatial-mode degrees of freedoms (DOFs) of the photons, which can simplify the quantum circuit and reduce the quantum resource consumption. In our schemes, the faulty scattering events between photons and emitters caused by system imperfections can be filtered out and discarded. That is, our protocols for hyper-CNOT gates work in a heralded way. Our calculations show that, with great progress in the emitter-waveguide systems, our photonic hyper-CNOT gates may be experimentally feasible.

Efficient Characterization of Qudit Logical Gates with Gate Set Tomography Using an Error-Free Virtual Z Gate Model.

Gate set tomography (GST) characterizes the process matrix of quantum logic gates, along with measurement and state preparation errors in quantum processors. GST typically requires extensive data collection and significant computational resources for model estimation. We propose a more efficient GST approach for qudits, utilizing the qudit Hadamard and virtual Z gates to construct fiducials while assuming virtual Z gates are error-free. Our method reduces the computational costs of estimating characterization results, making GST more practical at scale. We experimentally demonstrate the applicability of this approach on a superconducting transmon qutrit.

Astrophotonics: recent and future developments

Astrophotonics is a burgeoning field that lies at the interface of photonics and modern astronomical instrumentation. Here we provide a pedagogical review of basic photonic functions that enable modern instruments, and give an overview of recent and future applications. Traditionally, optical fibres have been used in innovative ways to vastly increase the multiplex advantage of an astronomical instrument, e.g. the ability to observe hundreds or thousands of stars simultaneously. But modern instruments are using many new photonic functions, some emerging from the telecom industry, and others specific to the demands of adaptive optics systems on modern telescopes. As telescopes continue to increase in size, we look to a future where instruments exploit the properties of individual photons. In particular, we envisage telescopes and interferometers that build on international developments in quantum networks, the so-called quantum internet. With the aid of entangled photons and quantum logic gates, the new infrastructures seek to preserve the photonic state and timing of individual photons over a coherent network.

Signal Crosstalk in a Flip-Chip Quantum Processor

Quantum processors require a signal-delivery architecture with high addressability (low crosstalk) to ensure high performance already at the scale of dozens of qubits. Signal crosstalk causes inadvertent driving of quantum gates, which will adversely affect quantum gate fidelities in scaled-up devices. Here, we demonstrate packaged flip-chip superconducting quantum processors with signal-crosstalk performance competitive with those reported in other platforms. For capacitively coupled qubit-drive lines, we find on-resonant crosstalk better than −27 dB (average −37 dB). For inductively coupled magnetic-flux-drive lines, we find less than 0.13% direct-current flux crosstalk (average 0.05%). These observed crosstalk levels are adequately small and indicate a decreasing trend with increasing distance, which is promising for further scaling up to larger numbers of qubits. We discuss the implications of our results for the design of a low-crosstalk on-chip signal-delivery architecture, including the influence of a shielding tunnel structure, potential sources of crosstalk, and estimation of crosstalk-induced qubit-gate error in scaled-up quantum processors. Published by the American Physical Society 2024

Implementation of controlled-not quantum gate by nonlinear coupled electro-nano-optomechanical oscillators

Implementation of controlled-not quantum gate by nonlinear coupled electro-nano-optomechanical oscillators

High‐Dimensional Photonic Quantum Computing with a Measurement‐Free Auxiliary System

AbstractEnhancing the capabilities of quantum computing relies heavily on harnessing the power of qudit‐based high‐dimensional quantum gates. In the study, single‐qudit 4D , , and gates tailored for a two‐photon system in polarization states are presented. Furthermore, a two‐qudit ‐dimensional controlled‐not (CNOT) gate designed for a four‐photon system is introduced. These high‐dimensional gates can offer versatile and straightforward optical implementations, ensuring them to fulfill in a deterministic way. To facilitate these processes, an auxiliary system in the form of a ‐type atom residing in a cavity is employed. Remarkably, the auxiliary system retains its original state after the operation process ends, so it is not required to measure and plays a pivotal role in promoting effective interactions among distinct photons in its extended coherence time. Importantly, the in‐depth analysis of the fidelities and efficiencies of these quantum gates showcase remarkable outcomes, affirming the superiority of the proposed protocols. Therefore, these high‐dimensional gates not only amplify quantum parallelism, but also bolster the speed of quantum computations, fortify resilience against errors, and foster scalability for executing intricate quantum operations.

Benchmarking of quantum fidelity kernels for Gaussian process regression

Abstract Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an unbiased benchmarking of quantum kernels, it is necessary to construct the most optimal functional form of the classical kernels and the most optimal quantum kernels for each given data set. We develop an algorithm that uses an analog of the Bayesian information criterion to optimize the sequence of quantum gates used to estimate quantum kernels for Gaussian process models. The algorithm increases the complexity of the quantum circuits incrementally, while improving the performance of the resulting kernels, and is shown to yield much higher model accuracy with fewer quantum gates than a fixed quantum circuit ansatz. We demonstrate that quantum kernels thus obtained can be used to build accurate models of global potential energy surfaces (PES) for polyatomic molecules. The average interpolation error of the six-dimensional PES obtained with a random distribution of 2000 energy points is 16 cm−1 for H3O+, 15 cm−1 for H2CO and 88 cm−1 for HNO2. We show that a compositional optimization of classical kernels for Gaussian process regression converges to the same errors. This indicates that quantum kernels can achieve the same, though not better, expressivity as classical kernels for regression problems.

Simulation of two-qubit quantum gate based on classical transverse spatial waveguide modes encoding

Simulation of two-qubit quantum gate based on classical transverse spatial waveguide modes encoding

Quantum Deep Learning: A Review

Quantum computing is described as a process by which a system calculates output. Quantum physics usually refers to the smallest discrete unit of any property; the basic unit of data in quantum is the qubit; this qubit unit is equivalent to the bit unit in classical neural networks. Quantum deep learning combines quantum computing with deep learning to reduce training time for neural networks, which has proven effective in solving some intractable problems on classical computers. Quantum deep learning has proven effective in solving some intractable problems on classical computers. A quantum network can benefit from quantum informationflow because it is a more efficient framework than classical systems. Each quantum deep learning consists of a quantum gate. In this review, we provide a comprehensive review of recent studies that include different quantum deep learning applications, including healthcare, handwriting, and many others. Also, methodologies, problems, main datasets, results, strengths, limitations, and challenges are included in this review.

Fidelity-dissipation relations in quantum gates

Accurate quantum computing relies on the precision of quantum gates. However, quantum gates in practice are generally affected by dissipative environments, which can significantly reduce their fidelity. In this paper, we elucidate the fundamental relations between the average fidelity of generic quantum gates and the dissipation that occurs during the computing processes. Considering scenarios in which a quantum gate is subject to Markovian environments, we rigorously derive fidelity-dissipation relations that hold for arbitrary operational times. Intriguingly, when the quantum gate undergoes thermal relaxation, the result can be used as a valuable tool for estimating dissipation through experimentally measurable fidelity, without requiring detailed knowledge of the dissipative structure. For the case of arbitrary environments, we uncover a trade-off relation between the average fidelity and energy dissipation, implying that these quantities cannot be large simultaneously. Our results unveil the computational limitations imposed by thermodynamics, shedding light on the profound connection between thermodynamics and quantum computing. Published by the American Physical Society 2024

Energetic cost as a consequence of parallel transporting speed limit

Time-optimal unitary operating quantum systems and energy-efficient quantum gates are vital in quantum engineering. Here, we establish the connection between the energetic cost and the quantum speed limit for parallel evolving of a quantum system. Our results show that the energetic cost is the consequence of parallel transporting speed limit, which opens up the critical role of parallel transport of the quantum state for the quantum technologies such as the quantum simulation, the quantum information processing. Our investigations present a route to construct the energetic-efficient quantum gate. In addition, our theoretical framework provides an alternative method for calculating quantum speed limit. Two typical relevant systems are employed to illustrate our results: the spin-1/2 particle in the rotating magnetic field and the entanglement swap gate.

X, Y, and Z Subgroups of the Unitary Group

The subgroups XU(2), YU(2), and ZU(2) of the unitary group U(2) allow to find twenty-four different decompositions of an arbitrary [Formula: see text] unitary matrix. Because the group YU(2) has not been considered before, 20 out of the 24 decompositions are new. Introducing this YU(2) group allows to highlight, within quantum circuit design, a symmetry similar to the threefold symmetry of the Pauli matrices of spin systems. Similar subgroups of the unitary group U([Formula: see text]) lead to various new decompositions of an arbitrary [Formula: see text] unitary matrix. Whereas for [Formula: see text] equal 2, this leads to the synthesis of single-qubit quantum gates, for [Formula: see text] equal a power of 2, this leads to new design methods for multiple-qubit circuits.

Fast super robust nonadiabatic geometric quantum computation

Nonadiabatic geometric quantum computation (NGQC) provides a method for implementing fast and robust quantum gates. To enhance the robustness of NGQC against control errors, many solutions have been proposed by previous researchers. However, these solutions often lead to longer operation times for quantum gates. To simultaneously enhance quantum gate robustness against control errors and reduce operation times to mitigate decoherence effects, we introduce fast super robust NGQC (FSR-NGQC). This approach achieves faster speeds when operating small-angle rotation gates. Through numerical calculations, we have demonstrated the performance of our scheme in a decoherence environment. The results show that our scheme achieves higher fidelity, thus enabling fast and robust geometric quantum computing.