Complex Gate Research Articles

Implementing the Grover algorithm in homomorphic encryption schemes

We apply quantum homomorphic encryption (QHE) schemes suitable for circuits with a polynomial number of T+T† gates to Grover's algorithm, performing a simulation in Qiskit of a Grover circuit that contains three qubits. The T+T†-gate complexity of Grover's algorithm is also analyzed in order to show that any Grover circuit can be evaluated homomorphically in an efficient manner. We discuss how to apply these QHE schemes to allow for the efficient homomorphic evaluation of any Grover circuit composed of n qubits using n−2 extra ancilla qubits. We also show how the homomorphic evaluation of the special case where there is only one marked item can be implemented using an algorithm that makes the decryption process more efficient compared with the standard Grover algorithm. Published by the American Physical Society 2024

Learning Quantum States and Unitaries of Bounded Gate Complexity

While quantum state tomography is notoriously hard, most states hold little interest to practically minded tomographers. Given that states and unitaries appearing in nature are of bounded gate complexity, it is natural to ask if efficient learning becomes possible. In this work, we prove that to learn a state generated by a quantum circuit with G two-qubit gates to a small trace distance, a sample complexity scaling linearly in G is necessary and sufficient. We also prove that the optimal query complexity to learn a unitary generated by G gates to a small average-case error scales linearly in G. While sample-efficient learning can be achieved, we show that under reasonable cryptographic conjectures, the computational complexity for learning states and unitaries of gate complexity G must scale exponentially in G. We illustrate how these results establish fundamental limitations on the expressivity of quantum machine-learning models and provide new perspectives on no-free-lunch theorems in unitary learning. Together, our results answer how the complexity of learning quantum states and unitaries relate to the complexity of creating these states and unitaries. Published by the American Physical Society 2024

Efficient Algorithms for All Port-Based Teleportation Protocols

Port-based teleportation (PBT) is a form of quantum teleportation in which no corrective unitary is required on the part of the receiver. Two primary regimes exist—deterministic PBT in which teleportation is always successful, but is imperfect, and probabilistic PBT, in which teleportation succeeds with probability less than one, but teleportation is perfect upon a success. Two further regimes exist within each of these, in which the resource state used for the teleportation is fixed to a maximally entangled state or free to be optimized. Recent works have resolved the long-standing problem of efficiently implementing port-based teleportation, tackling the two deterministic cases for qudits. Here, we provide algorithms in all four regimes for qubits. Emphasis is placed on the practicality of these algorithms, where we give polynomial improvements in the known gate complexity for PBT, as well as an exponential improvement in the required number of ancillas (albeit in separate protocols). Our approach to the implementation of the square-root measurement in PBT can be directly generalized to other highly symmetric state ensembles. For certain families of states, such a framework yields efficient algorithms in the case in which the Petz-recovery algorithm for the square-root measurement runs in exponential time. Published by the American Physical Society 2024

Sterolysin from a 1950s culture of Karlodinium veneficum (aka Gymnodinium veneficum Ballantine) forms lethal sterol dependent membrane pores

In 1957 Abbott and Ballantine described a highly toxic activity from a dinoflagellate isolated from the English Channel in 1949 by Mary Park. From a culture maintained at Plymouth Laboratory since 1950, we have been able to isolate two toxic molecules (abbotoxin and 59-E-Chloro-abbotoxin), determine the planar structures by analysis of HRMS and 1D and 2D NMR spectra, and found them to be karlotoxin (KmTx) congeners. Both toxins kill larval zebrafish with symptoms identical to those described by Abbot and Ballantine for gobies (Gobius virescens). Using surface plasma resonance the sterol binding specificity of karlotoxins is shown to require desmethyl sterols. Our results with black lipid membranes indicate that karlotoxin forms large-conductance channels in the lipid membrane, which are characterized by large ionic conductance, poor ionic selectivity, and a complex gating behavior that exhibits strong voltage dependence and multiple gating patterns. In addition, we show that KmTx 2 pore formation is a highly targeted mechanism involving sterol-specificity. This is the first report of the functional properties of the membrane pores formed by karlotoxins and is consistent with the initial observations of Abbott and Ballantine from 1957.

The Gate of Ki Ranggo Wirosentiko's Grave: Traces of Non-Islamic Cultural Acculturation in the Material Culture Heritage of the Palembang Sultanate

Palembang is known as one of the centers of the Palembang Sultanate. One of the most important cultural relics in Palembang is the Palembang Sultan Cemetery complex. Each of these cemetery complexes has a different architectural shape of the tomb, one of which is the tomb complex of Ki Ranggo Wirosntiko. A Striking distinction in this tomb is the shape of the tomb gate complex building that depicts influences in non-Islam culture. This article will explain the differences in shape in the building of the gate and the influence of non-Islamic culture on the shape of the tomb gate of Ki Ranggo Wirosentiko. The method used is the archeological method using a stylistic analysis of the observation of the ornaments found in the gates of this complex. The results of this study show that the building of the tomb gate of Ki Ranggo Wirosentiko shows acculturation with non-Islamic culture. The profile of the outer gate depicting Hindu influence is marked by the similarity with the stylistic elements in the Bentar temple and Paduraksa Temple, East Java. The resemblance is also visible on the profile of the foot and the mould of the gate resembling the profile found in the Paduraksa Temple. On the profile of the third gate, there is an inscription of the year 1142 H or 1730 M using Arabic letters. The local influence appears on the third gate's appearance, indicating the presence of mustak. Based on the profile of the building of the tomb gate Ki Ranggo Wirosentiko shows the influence of Hindu, Buddhist, Arab, and local cultures on the decorative range of the construction of the grave of the temple.

Efficient simulation of potential energy operators on quantum hardware: a study on sodium iodide (NaI)

This study introduces a conceptually novel polynomial encoding algorithm for simulating potential energy operators encoded in diagonal unitary forms in a quantum computing machine. The current trend in quantum computational chemistry is effective experimentation to achieve high-precision quantum computational advantage. However, high computational gate complexity and fidelity loss are some of the impediments to the realization of this advantage in a real quantum hardware. In this study, we address the challenges of building a diagonal Hamiltonian operator having exponential functional form, and its implementation in the context of the time evolution problem (Hamiltonian simulation and encoding). Potential energy operators when represented in the first quantization form is an example of such types of operators. Through systematic decomposition and construction, we demonstrate the efficacy of the proposed polynomial encoding method in reducing gate complexity from O(2n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(2^n)$$\\end{document} to O∑i=1rnCr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \\sum _{i=1}^{r} {} ^nC_r \\right)$$\\end{document} (for some r≪n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r\\ll n$$\\end{document}). This offers a solution with lower complexity in comparison to the conventional Hadamard basis encoding approach. The effectiveness of the proposed algorithm was validated with its implementation in the IBM quantum simulator and IBM quantum hardware. This study demonstrates the proposed approach by taking the example of the potential energy operator of the sodium iodide molecule (NaI) in the first quantization form. The numerical results demonstrate the potential applicability of the proposed method in quantum chemistry problems, while the analytical bound for error analysis and computational gate complexity discussed, throw light on issues regarding its implementation.

Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra

We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely algorithmic and no additional qubits are required for quantum data structures. Our algorithms start from a classical data structure in which the matrix of interest is specified in the Pauli basis. For N×N Hermitian matrices, the space cost is log(N)+1 qubits and, depending on the structure of the matrices, the gate complexity can be comparable to state-of-the-art methods that use quantum data structures of up to size O(N2), when considering equivalent end-to-end problems. Within our framework, we present a quantum linear system solver that allows one to sample properties of the solution vector, as well as algorithms for sampling properties of ground states and Gibbs states of Hamiltonians. As a concrete application, we combine these subroutines to present a scheme for calculating Green’s functions of quantum many-body systems. Published by the American Physical Society 2024

Dual-Junction Field-Effect Transistor with Ultralow Subthreshold Swing Approaching the Theoretical Limit.

Metal-oxide-semiconductor field-effect transistors as basic electronic devices of integrated circuits have been greatly developed and widely used in the past decades. However, as the thickness of the conducting channel decreases, the interface electronic scattering between the gate oxide layer and the channel significantly impacts the performance of the transistor. To address this issue, van der Waals heterojunction field-effect transistors (vdWJFETs) have been proposed using two-dimensional semiconductors, which utilize the built-in electric field at the sharp van der Waals interface to regulate the channel conductance without the need of a complex gate oxide layer. In this study, a novel dual-junction vdWJFET composed of a MoS2 channel and a Te nanosheet gate has been developed. This device achieves an ultralow subthreshold swing (SS) and an extremely low current hysteresis, greatly surpassing the single-junction vdWJFET. In the transistor, the SS decreases from 475.04 to 68.3 mV dec-1, nearly approaching the theoretical limit of 60 mV dec-1 at room temperature. The pinch-off voltage (Vp) decreases from -4.5 to -0.75 V, with a current hysteresis of ∼10 mV and a considerable field-effect mobility (μ) of 36.43 cm2 V-1 s-1. The novel dual-junction vdWJFET provides a new approach to realize a transistor with a theoretical ideal SS and a negligible current hysteresis toward low-power electronic applications.

An adaptive differential evolution algorithm with multi-strategy for solving complex optimization problem

In this paper, an adaptive differential evolution algorithm with multi-strategy, namely ESADE is proposed to solve the premature convergence and high time complexity for complex optimization problem. In the ESADE, the population is divided into several sub-populations after the fitness value of each individual is sorted. Then different mutation strategies are proposed for different populations to balance the global exploration and local optimization. Next, a new self-adaptive strategy is designed adjust parameters to avoid falling into local optimum while the convergence accuracy has reached its maximum value. And a complex airport gate allocation multi-objective optimization model with the maximum flight allocation rate, the maximum near gate allocation rate, and the maximum passenger rate at near gate is constructed, which is divided into several single-objective optimization model. Finally, the ESADE is applied solve airport gate allocation optimization model. The experiment results show that the proposed ESADE algorithm can effectively solve the complex airport gate allocation problem and achieve ideal airport gate allocation results by comparing with the current common heuristic optimization algorithms.

Circuit complexity of quantum access models for encoding classical data

How to efficiently encode classical data is a fundamental task in quantum computing. While many existing works treat classical data encoding as a black box in oracle-based quantum algorithms, their explicit constructions are crucial for the efficiency of practical algorithm implementations. Here, we unveil the mystery of the classical data encoding black box and study the Clifford + T complexity in constructing several typical quantum access models. For general matrices (even including sparse ones), we prove that sparse-access input models and block-encoding both require nearly linear circuit complexities relative to the matrix dimension. We also give construction protocols achieving near-optimal gate complexities. On the other hand, the construction becomes efficient with respect to the data qubit when the matrix is a linear combination of polynomial terms of efficiently implementable unitaries. As a typical example, we propose improved block-encoding when these unitaries are Pauli strings. Our protocols are built upon improved quantum state preparation and a select oracle for Pauli strings, which hold independent values. Our access model constructions provide considerable flexibility, allowing for tunable ancillary qubit numbers and offering corresponding space-time trade-offs.

Quantum Simulation of Bound State Scattering

The last few years have seen rapid development of applications of quantum computation to quantum field theory. The first algorithms for quantum simulation of scattering have been proposed in the context of scalar and fermionic theories, requiring thousands of logical qubits. These algorithms are not suitable to simulate scattering of incoming bound states, as the initial-state preparation relies typically on adiabatically transforming wavepackets of the free theory into wavepackets of the interacting theory. In this paper we present a strategy to excite wavepackets of the interacting theory directly from the vacuum of the interacting theory, allowing the preparation of states of composite particles. This is the first step towards digital quantum simulation of scattering of bound states. The approach is based on the Haag-Ruelle scattering theory, which provides a way to construct creation and annihilation operators of a theory in a full, nonperturbative framework. We provide a quantum algorithm requiring a number of ancillary qubits that is logarithmic in the size of the wavepackets, and with a success probability vanishing at most like a polynomial in the lattice parameters and the energy of the wavepacket. The gate complexity for a single iteration of the circuit is equivalent to that of a time evolution for a fixed time. Furthermore, we propose a complete protocol for scattering simulation using this algorithm. We study its efficiency and find improvements with respect to previous algorithms in the literature. Published by the American Physical Society 2024

Basic quantum subroutines: finding multiple marked elements and summing numbers

We show how to find all k marked elements in a list of size N using the optimal number O(Nk) of quantum queries and only a polylogarithmic overhead in the gate complexity, in the setting where one has a small quantum memory. Previous algorithms either incurred a factor k overhead in the gate complexity, or had an extra factor log⁡(k) in the query complexity.We then consider the problem of finding a multiplicative δ-approximation of s=∑i=1Nvi where v=(vi)∈[0,1]N, given quantum query access to a binary description of v. We give an algorithm that does so, with probability at least 1−ρ, using O(Nlog⁡(1/ρ)/δ) quantum queries (under mild assumptions on ρ). This quadratically improves the dependence on 1/δ and log⁡(1/ρ) compared to a straightforward application of amplitude estimation. To obtain the improved log⁡(1/ρ) dependence we use the first result.

Average-Case Speedup for Product Formulas

Quantum simulation is a promising application of future quantum computers. Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. For an accurate product formula approximation, the state-of-the-art gate complexity depends on the number of terms in the Hamiltonian and a local energy estimate. In this work, we give evidence that product formulas, in practice, may work much better than expected. We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states, while the existing estimate is for the worst states. For general k-local Hamiltonians and higher-order product formulas, we obtain gate count estimates for input states drawn from any orthogonal basis. The gate complexity significantly improves over the worst case for systems with large connectivity. Our typical-case results generalize to Hamiltonians with Fermionic terms, with input states drawn from a fixed-particle number subspace, and with Gaussian coefficients (e.g., the SYK models). Technically, we employ a family of simple but versatile inequalities from non-commutative martingales called uniform smoothness, which leads to Hypercontractivity, namely p-norm estimates for k-local operators. This delivers concentration bounds via Markov’s inequality. For optimality, we give analytic and numerical examples that simultaneously match our typical-case estimates and the existing worst-case estimates. Therefore, our improvement is due to asking a qualitatively different question, and our results open doors to the study of quantum algorithms in the average case.

An archaeomagnetic study of the Ishtar Gate, Babylon.

Data from the marriage of paleomagnetism and archaeology (archaeomagnetism) are the backbone of attempts to create geomagnetic field models for ancient times. Paleointensity experimental design has been the focus of intensive efforts and the requirements and shortcomings are increasingly well understood. Some archaeological materials have excellent age control from inscriptions, which can be tied to a given decade or even a specific year in some cases. In this study, we analyzed fired mud bricks used for the construction of the Ishtar Gate, the entrance complex to the ancient city of Babylon in Southern Mesopotamia. We were able to extract reliable intensity data from all three phases of the gate, the earliest of which includes bricks inscribed with the name of King Nebuchadnezzar II (605 to 562 BCE). These results (1) add high quality intensity data to a region relatively unexplored so far (Southern Mesopotamia), (2) contribute to a better understanding of paleosecular variation in this region, and the development of an archaeomagnetic dating reference for one of the key regions in the history of human civilizations; (3) demonstrate the potential of inscribed bricks (glazed and unglazed), a common material in ancient Mesopotamia, to archaeomagnetic studies; and (4) suggest that the gate complex was constructed some time after the Babylonian conquest of Jerusalem, and that there were no substantial chronological gaps in the construction of each consecutive phase. The best fit of our data (averaging 136±2.1 ZAm2) with those of the reference curve (the Levantine Archaeomagnetic Curve) is 569 BCE.

Parallel Quantum Algorithm for Hamiltonian Simulation

We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including various Hamiltonians of practical interest like local Hamiltonians and Pauli sums. Given the oracle access to the target sparse Hamiltonian, in both query and gate complexity, the running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence polylog⁡log⁡(1/ϵ) on the simulation precision ϵ. This presents an exponential improvement over the dependence polylog⁡(1/ϵ) of previous optimal sparse Hamiltonian simulation algorithm without parallelism. To obtain this result, we introduce a novel notion of parallel quantum walk, based on Childs' quantum walk. The target evolution unitary is approximated by a truncated Taylor series, which is obtained by combining these quantum walks in a parallel way. A lower bound Ω(log⁡log⁡(1/ϵ)) is established, showing that the ϵ-dependence of the gate depth achieved in this work cannot be significantly improved.Our algorithm is applied to simulating three physical models: the Heisenberg model, the Sachdev-Ye-Kitaev model and a quantum chemistry model in second quantization. By explicitly calculating the gate complexity for implementing the oracles, we show that on all these models, the total gate depth of our algorithm has a polylog⁡log⁡(1/ϵ) dependence in the parallel setting.

Analisis Mengenai Kependidikan pada MAS PAB 1 Sampali

MAS PAB 1 Sampali is located at Jalan Pasar Hitam No. 69 Sampali, Sampali Village, Percut SEI Tuan District, Sampali Sub-District, Deli Serdang Regency, North Sumatra Province. This private school is part of a complex or entrance gate with several other schools. Established and operating since 1988, MAS PAB 1 Sampali also has the best and most competent educators, administrative staff, and school administrators in their field. Learning support activities, such as extracurricular activities, student organizations, study communities, sports teams, and libraries, also help students learn to the fullest. In addition, the school also focuses on instilling noble character and developing students' talents in sports, arts, and other extracurricular activities such as student council, boy scouts, and flag raising troop. The facilities at MAS PAB 1 Sampali are also adequate, including special rooms for counseling for students who need it.

Reconfigurable Skyrmion-Based Logic Gates: Versatile Design and Full-Scale Implementation.

Herein, we investigate the behavior of skyrmions within a racetrack design incorporating voltage-controlled magnetic anisotropy (VCMA) gates. Our analysis encompassed multiple forces, including spin currents and anisotropy gradients induced by bias voltages. As a result, the efficient control of skyrmion dynamics was achieved across various VCMA gate configurations. Building upon these findings, we propose an efficient approach to reconfigurable skyrmion logic (RSL) in a thin antiferromagnetic (AFM) film through a versatile design. Our RSL harnesses the selective integration of VCMA, spin-polarized currents, and skyrmion-skyrmion (sky-sky) interactions to implement multiple logic gates, including AND, OR, XOR, NOT, NAND, XNOR, and NOR. The design brings a significant advantage with its simplified fabrication process, making the implementation of the RSL practical and accessible for various applications. Furthermore, the RSL enables seamless dynamic switching between logic gates, thereby enhancing its multifunctionality. Additionally, the strategic incorporation of sky-sky interactions and skyrmion-edge repulsion prominently facilitates the realization of complex gates, such as NAND, XNOR, and NOR gates, that typically require intricate design efforts. Hence, this streamlined integration of RSL, coupled with its adaptability to changing computational needs, underscores its potential as a practical solution for implementing high-functionality skyrmion-based logic gates.

Error-robust quantum signal processing using Rydberg atoms

Rydberg atom arrays have recently emerged as one of the most promising platforms for quantum simulation and quantum information processing. However, as is the case for other experimental platforms, the longer-term success of the Rydberg atom arrays in implementing quantum algorithms depends crucially on their robustness to gate-induced errors. Here we show that, for an idealized biased-error model based on Rydberg atom dynamics, the implementation of quantum signal processing (QSP) protocols can be made error robust, in the sense that the asymptotic scaling of the gate-induced error probability is slower than that of gate complexity. Moreover, our numerical results that use experimentally accessible parameters indicate that QSP iterates made out of more than 100 gates can be implemented with constant error probability. To showcase our approach, we provide a concrete blueprint to implement QSP-based near-optimal Hamiltonian simulation on the Rydberg atom platform. The proposed protocol substantially improves both the scaling and the overhead of gate-induced errors in comparison to those protocols that implement a fourth-order product formula. Published by the American Physical Society 2024

Quantum algorithm for lattice Boltzmann (QALB) simulation of incompressible fluids with a nonlinear collision term

We present a full quantum algorithm for the lattice Boltzmann method for simulating fluid flows, the only such algorithm to implement both the streaming and collision substeps as unitary operators using an efficient number of qubits. We use Hamiltonian simulation as the main route underlying the algorithm, and show that it uses qubits that scale logarithmically in the flow Reynolds number but gates that scale only polynomially. We motivate the discussion by a brief overview of existing attempts at simulating classical fluids on quantum computers and present a pedagogical discussion on assigning quantum operators to classical variables in both the streaming and the collision substeps, after highlighting the incompatibility of the latter with the implementations of the streaming step that exists in the literature. We use the Bhatnagar–Gross–Krook ansatz for the collision term, representing the relaxation toward an equilibrium distribution. For nonlinear collisions, we use Kowalski's framework that links the nonlinear dynamics of a system to the evolution of bosonic modes, assigning a Carleman linearization order to the truncation in the Fock space of the bosons. We present the qubit and gate complexities, in terms of the chosen accuracy and the Reynolds number. In the Appendix, we work out the details of implementing the operators of the truncated bosonic Fock space in terms of single-qubit gates as well as the error scaling for a general polynomial driving function.

Optical spectroscopic detection of Schottky barrier height at a two-dimensional transition-metal dichalcogenide/metal interface.

Atomically thin two-dimensional transition-metal dichalcogenides (2D-TMDs) have emerged as semiconductors for next-generation nanoelectronics. As 2D-TMD-based devices typically utilize metals as the contacts, it is crucial to understand the properties of the 2D-TMD/metal interface, including the characteristics of the Schottky barriers formed at the semiconductor-metal junction. Conventional methods for investigating the Schottky barrier height (SBH) at these interfaces predominantly rely on contact-based electrical measurements with complex gating structures. In this study, we introduce an all-optical approach for non-contact measurement of the SBH, utilizing high-quality WS2/Au heterostructures as a model system. Our approach employs a below-bandgap pump to excite hot carriers from the gold into WS2 with varying thicknesses. By monitoring the resultant carrier density changes within the WS2 layers with a broadband probe, we traced the dynamics and magnitude of charge transfer across the interface. A systematic sweep of the pump wavelength enables us to determine the SBH values and unveil an inverse relationship between the SBH and the thickness of the WS2 layers. First-principles calculations reveal the correlation between the probability of injection and the density of states near the conduction band minimum of WS2. The versatile optical methodology for probing TMD/metal interfaces can shed light on the intricate charge transfer characteristics within various 2D heterostructures, facilitating the development of more efficient and scalable nano-electronic and optoelectronic technologies.