Adiabatic Switching Research Articles

Nonequilibrium Dynamics of the Hubbard Dimer

Electron dynamics in a two‐sites Hubbard model is studied using the nonequilibrium Green's function approach. The study is motivated by the empirical observation that a full solution of the integro‐differential Kadanoff–Baym equation (KBE) is more stable and often accompanied by artificial damping [Marc Puig von Friesen, C. Verdozzi, and C.‐O. Almbladh (2009)] than its time‐linear reformulations relying on the generalized Kadanoff–Baym ansatz (GKBA). Additionally, for conserving theories, numerical simulations suggest that KBE produces natural occupations bounded by one and zero in agreement with the Pauli exclusion principle, whereas, in some regimes, GKBA‐based theories violate this principle. As the first step for understanding these issues, the electron dynamics arising in the adiabatic switching scenario is studied. Many‐body approximations are classified according to the channel of the Bethe–Salpeter equation in which electronic correlations are explicitly treated. They give rise to the so‐called second Born, T‐matrix, and GW approximations. In each of these cases, the model is reduced to a system of ordinary differential equations, which resemble equations of motion for a driven harmonic oscillator with time‐dependent frequencies. A more complete treatment of electronic correlations is achieved by combining different correlation channels, with parquet theory serving as a starting point.

Adiabatic quantum-flux-parametron boosters for long interconnection and large fanouts

Adiabatic quantum flux parametron (AQFP) is energy-efficient superconducting logic that operates with zero static energy consumption and extremely small dynamic energy consumption thanks to the adiabatic switching of the logic gates. One drawback in AQFP logic circuits is the wire length and fan-out limitations because of the low driving ability of the logic gates, which results in a large circuit area and significant latency. In the present study, we propose AQFP boosters with high driving ability. Two types of AQFP boosters are proposed: one is composed of a parallel connection of AQFP buffers, and the other uses multistage buffers driven by one excitation clock. We evaluated the maximum wire length of the proposed boosters by circuit simulations, including thermal noises, and found that the maximum wire length is 3.9 mm for fan-out one and 1 mm for fan-out four. We implemented the boosters and demonstrated their correct operations at low-speed tests. We also demonstrated a 5-to-31 decoder using the proposed boosters. It was shown that the circuit area, latency, and energy consumption were improved by about 30% compared to the design without the boosters.

An Adiabatic Quantum-Flux-Parametron 8-bit Ripple Carry Adder Using Delay-Line Clocking

Adiabatic quantum-flux-parametron (AQFP) logic is a superconductor logic family that can operate with low switching energy due to adiabatic switching. In a previous study, we proposed a low-latency clocking scheme called delay-line clocking, in which the latency for each logic operation is determined by the propagation delay of the excitation current. We demonstrated several AQFP logic gates with delay-line clocking and demonstrated a phase skipping operation, in which some of the AQFP buffers for phase synchronization are removed to reduce the junction count and energy dissipation. In the present study, we design and demonstrate an AQFP 8-bit ripple carry adder with delay-line clocking to show that delay-line clocking and the phase skipping operation are applicable to large-scale AQFP circuits. The latency of this adder is 960 ps, which is 40% of that for a conventional design. Moreover, due to the phase skipping operation, the junction count is reduced to approximately 70% of that for the conventional design. We find that this adder can operate at up to 4 GHz. The above results indicate that large-scale AQFP circuits can operate with low latency and low junction count by using delay-line clocking and a phase skipping operation.

Design and Implementation of Energy-Efficient Binary Neural Networks Using Adiabatic Quantum-Flux-Parametron Logic

Adiabatic quantum-flux-parametron (AQFP) logic is a promising technology for future energy-efficient, highperformance information processing systems. It has significantly low power dissipation thanks to the adiabatic switching of Josephson junctions. In this paper, we introduce an AQFPbased binary neural network (BNN) design methodology utilizing an in-memory computing scheme, analog accumulation, and a crossbar structure. The proposed design can effectively resolve the memory issue in superconducting digital circuits by significantly reducing memory usage in a non-Von Neumann fashion compared to conventional neural networks. As a proof-ofconcept, we designed and implemented an 8×8 AQFP BNN using the proposed design methodology targeted the AIST 10kA/cm2 4-layer niobium process. The Josephson junction count and energy dissipation of the proposed 8×8 BNN design are 2236 and 11.18 aJ, respectively.

A basis- and integral-free representation of time-dependent perturbation theory via the Omega matrix calculus

We obtain a basis- and integral-free representation of the n -term in time-dependent perturbation theory of the quantum time-evolution operator. The main technical tool to construct the aforementioned representation comprises the Omega matrix calculus; that is, an extension of MacMahon’s partition analysis to the realm of matrix calculus. In particular, we show that if we specialize our formulation to the time-independent and finite-dimensional case, we recover Putzer (1966) original formulation to compute the matrix exponential avoiding the Jordan canonical form. Furthermore, if we use an explicit basis for the time-independent part of the generator of evolution, then our work implies a representation of the perturbation expansion similar to an approach discussed in the recent work of Kalev and Hen (2021) using divided differences. Finally, we obtain closed form expressions which generalize and unify all the perturbation calculations considered in Kalev and Hen (2021) and advance some considerations regarding degeneracy associated with the unperturbed Hamiltonian in the context of adiabatic switching.

A low power design using FinFET based adiabatic switching principle: Application to 16-Bit arithmetic logic unit

This paper presents a novel 16-bit arithmetic logic unit (ALU) design by cascading simple 1-bit ALUs using metal–oxide-semiconductor field effect transistor (MOSFET) and FinFET technologies while incorporating adiabatic switching principle. Analyses are carried out at 32 nm Berkley predictive technology module (PTM). The paper has employed popular standard adiabatic logic families– such as quasi-static energy recovery logic (QSERL), two phase drive adiabatic dynamic complementary metal oxide semiconductor (CMOS) logic (2PADCL), adiabatic dynamic CMOS logic (ADCL), and two phase clocked adiabatic static CMOS logic (2PASCL). Single-phase adiabatic logic circuit is also introduced. Results show that the proposed technique has power savings of 67.14 %, 39.47 %, 34.65 %, 8.73 %, and 4.16 % for CMOS, QSERL, 2PADCL, ADCL, and 2PASCL respectively with MOSFET technology whereas, it saves 95.22 %, 21.34 %, 20.75 %, 15.66 %, and 8.69 % respectively for same literatures with FinFET technology.

Energy-Efficient circuits with improved diode free adiabatic logic design methodology

This paper demonstrates a detailed analysis of an unique improved diode-free adiabatic logic (IDFAL) circuit. The IDFAL is operated based on adiabatic switching principle. To indicate the circuit effectiveness, numerous analyses are carried out on different complementary metal oxide semiconductor (CMOS) technology nodes. Logic circuits, viz., NOT and NAND are analyzed and simulated using the traditional CMOS design style and some popular adiabatic logic design techniques: two-phase clocked adiabatic static CMOS logic (2PASCL), diode free adiabatic logic (DFAL), adiabatic dynamic CMOS logic (ADCL), two-phase adiabatic dynamic CMOS logic (2PADCL), quasi-static energy recovery logic (QSERL), and clocked CMOS adiabatic logic (CCAL). The results are compared with the proposed design (IDFAL) at various operating frequencies. The results revealed that the IDFAL inverter circuit has the least power delay product (PDP) among the reported adiabatic design methodologies and saves 91.59 % over the counter-part CMOS inverter at 16 nm high-performance predictive technologies (HP_PTM).

Transmission Line Effects of Long Gate-to-Gate Interconnections in Adiabatic Quantum-Flux-Parametron Logic Circuits

Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic family that utilizes adiabatic switching of logic gates. At present, a pure inductance is used to model a gate-to-gate interconnection in AQFP logic circuits. However, it is necessary to consider the transmission line effects when the interconnection length becomes long to take into account the propagation delay. This study investigated the transmission line effects of a long gate-to-gate interconnection in AQFP logic circuits. We observed reflection effects in a long transmission line between AQFP gates. These effects induced errors when the interconnection length exceeded several hundred micrometers. We adopted a damping resistance to stabilize the reflection effect to realize an error-free long gate-to-gate interconnection. The circuit simulations confirmed that a damping resistance connected in parallel to the transmission line effectively stabilizes the reflection effect, enabling an interconnection length that is longer than 1 mm. We fabricated AQFP buffer chains that included a long transmission line with and without a parallel damping resistance, and measured their bit error rates. The results showed that the parallel damping resistance effectively improves the bit error rate at high frequencies.

Design and Demonstration of a Superconducting Field-Programmable Gate Array Using Adiabatic Quantum-Flux-Parametron Logic and Memory

Adiabatic quantum-flux-parametron (AQFP) logic is a promising technology for future energy-efficient, high- performance information processing systems because it has significantly low power consumption due to the adiabatic switching of Josephson junctions. We are developing a high-performance field-programmable gate array (FPGA) using superconducting AQFP circuits to reduce its energy consumption. The all-AQFP FPGA consists of logic blocks, switch blocks, connection blocks, and memory using AQFP circuits. In particular, the memory is composed of AQFP buffer chains, enabling high-density and low-power memory. The switch blocks can perform data routing as well as several logic functions, including majority, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</small> , and <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">or</small> functions, which increases the design flexibility of the all-AQFP FPGA. We fabricated a one-unit all-AQFP FPGA and demonstrated its reconfigurable operation at low speed. It was found that much lower power consumption can be achieved in the new FPGA than in the other superconducting FPGAs.

Partitioning of Iron Between Liquid and Crystalline Phases of (Mg,Fe)O

AbstractThe density contrast between crystals and coexisting liquids is key to understanding the evolution of the magma ocean. While crystals remain denser than isochemical liquids in most oxide and silicate systems over the pressure range of Earth's mantle, element partitioning, particularly of abundant heavy elements such as iron, can alter the buoyancy. We use molecular dynamics simulations based on spin‐polarized density functional theory and adiabatic switching to determine the free energy of iron substitution in liquid and crystalline (Mg,Fe)O and the distribution coefficient. We find that iron is strongly incompatible with a distribution coefficient less than 0.3 over the mantle pressure range. We find that the crystal is buoyant with respect to coexisting liquid at pressures exceeding 50 GPa. The high‐spin to low‐spin transition has an important influence on the distribution coefficient, which decreases with increasing pressure up to 80 GPa, and then increases on further increase of pressure.

Adiabatic Quantum-Flux-Parametron: A Tutorial Review

The adiabatic quantum-flux-parametron (AQFP) is an energy-efficient superconductor logic element based on the quantum flux parametron. AQFP circuits can operate with energy dissipation near the thermodynamic and quantum limits by maximizing the energy efficiency of adiabatic switching. We have established the design methodology for AQFP logic and developed various energy-efficient systems using AQFP logic, such as a low-power microprocessor, reversible computer, single-photon image sensor, and stochastic electronics. We have thus demonstrated the feasibility of the wide application of AQFP logic in future information and communications technology. In this paper, we present a tutorial review on AQFP logic to provide insights into AQFP circuit technology as an introduction to this research field. We describe the historical background, operating principle, design methodology, and recent progress of AQFP logic.

A Mixer-First Receiver With Class-F Adiabatic Switching

This letter introduces the use of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">class-</i> F adiabatic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">switching</i> in a mixer-first 2.45-GHz ISM-band receiver. By using the principle of adiabatic switching with a class-F VCO, a resonant multiharmonic drive for an N-path-based mixer-first receiver is generated, resulting in a reduced power consumption while maintaining a good mixer noise figure (NF). To optimize the area, coupled inductors in the VCO are used. By employing a switched capacitor (SC) feedback network in the baseband (BB) amplifier, a proper input matching and flexible common-mode (CM) bias is achieved. A packaged chip implemented in 28-nm CMOS achieves a low-power consumption of 3.5 mW with a gain of 22 dB and an NF of 7.4 dB.

Low-Latency Adiabatic Quantum-Flux-Parametron Circuit Integrated With a Hybrid Serializer/Deserializer

Adiabatic quantum-flux-parametron (AQFP) logic is an ultra-low-power superconductor logic family. AQFP logic gates are powered and clocked by dedicated clocking schemes using ac excitation currents to implement an energy-efficient switching process, adiabatic switching. We have proposed a low-latency clocking scheme, delay-line clocking, and demonstrated basic AQFP logic gates. In order to test more complex circuits, a serializer/deserializer (SerDes) should be incorporated into the AQFP circuit under test, since the number of input/output (I/O) cables is limited by equipment. Therefore, in the present study we propose and develop a novel SerDes for testing delay-line-clocked AQFP circuits by combining AQFP and rapid single-flux-quantum (RSFQ) logic families, which we refer to as the AQFP/RSFQ hybrid SerDes. The hybrid SerDes comprises RSFQ shift registers to facilitate the data storage during serial-to-parallel and parallel-to-serial conversion. Furthermore, all the component circuits in the hybrid SerDes are clocked by the identical excitation current to synchronize the AQFP and RSFQ parts. We fabricate and demonstrate a delay-line-clocked AQFP circuit (8-to-3 encoder, which is the largest delay-line-clocked circuit ever designed) integrated with the hybrid SerDes at 4.2 K up to 4.5 GHz. Our measurement results indicate that the hybrid SerDes enables the testing of delay-line-clocked AQFP circuits with only a few I/O cables and is thus a powerful tool for the development of very large-scale integration AQFP circuits.

On-the-fly adiabatically switched semiclassical initial value representation molecular dynamics for vibrational spectroscopy of biomolecules.

Semiclassical (SC) vibrational spectroscopy is a technique capable of reproducing quantum effects (such as zero-pointenergies, quantum resonances, and anharmonic overtones) from classical dynamics runs even in the case of very large dimensional systems. In a previous study [Conte et al. J. Chem. Phys. 151, 214107 (2019)], a preliminary sampling based on adiabatic switching has been shown to be able to improve the precision and accuracy of semiclassical results for challenging model potentials and small molecular systems. In this paper, we investigate the possibility to extend the technique to larger (bio)molecular systems whose dynamics must be integrated by means of ab initio "on-the-fly" calculations. After some preliminary tests on small molecules, we obtain the vibrational frequencies of glycine improving on pre-existing SC calculations. Finally, the new approach is applied to 17-atom proline, an amino acid characterized by a strong intramolecular hydrogen bond.

GHZ-like states in the Qubit-Qudit Rabi model

We study a Rabi type Hamiltonian system in which a qubit and a dd-level quantum system (qudit) are coupled through a common resonator. In the weak and strong coupling limits the spectrum is analysed through suitable perturbative schemes. The analysis show that the presence of the multilevels of the qudit effectively enhance the qubit-qudit interaction. The ground state of the strongly coupled system is found to be of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the qubit-qudit strong coupling, the nature of the specific tripartite entanglement of the GHZ state suppresses the bipartite entanglement. We analyze the system dynamics under quenching and adiabatic switching of the qubit-resonator and qudit-resonator couplings. In the quench case, we found that the non-adiabatic generation of photons in the resonator is enhanced by the number of levels in the qudit. The adiabatic control represents a possible route for preparation of GHZ states. Our analysis provides relevant information for future studies on coherent state transfer in qubit-qudit systems.

Exploring quantum adiabatic switching among impurity-modulated states in doped quantum dots: Role of Gaussian white noise

Current inquiry explores the time-dependent quantum adiabatic switching (TDQAS) of impurity doped quantum dot (QD) under the aegis of Gaussian white noise (GWN). The QAS has been performed among the impurity-modulated states of QD using several switching functions (SFs). The time-evolution of switching has been monitored with the help of overlap function and quantum information entropy (QIE). The SFs appear to recover the impurity-modulated eigenstates of QD corresponding to the final Hamiltonian starting from the analogous QD eigenstates corresponding to the initial Hamiltonian. The switching paths have been found to be comprising of important physical attributes of overlap function and QIE. These subtleties of the switching paths and the efficiency of switching/recovery depend on the nature of the SF itself and the characteristics of noise. The study deems importance since impurities have become inalienable part of QD systems for immense technological applications where presence of noise could invite additional delicacies.

Adiabatic Switching Among Quantum Dot Eigenstates: Role of Anharmonicity and Gaussian White Noise

Current study inquires the time‐dependent quantum adiabatic switching (TDQAS) among the quantum dot (QD) eigenstates under the aegis of Gaussian white noise (GWN) with special emphasis on anharmonicity that may be present in the QD potential. The initial and the final eigenstates are distinguished by different values of magnetic field strength, confinement potential, anisotropy, and anharmonicity. The QAS has been conducted using four different switching functions (SFs), e.g., square, exponential, sinusoidal, and logarithmic. The time development of switching has been monitored with the help of overlap function and quantum information entropy (QIE). The SFs appear to recover the eigenstates of QD corresponding to the final Hamiltonian. The switching paths comprise features such as enhancement, depletion, maximization, minimization, and crossover of the overlap function and entropy. These characteristics of switching paths depend on presence/absence of noise, its pathway of application (additive/multiplicative), and symmetry (odd/even) of the anharmonic potential. The dependence on the type of SF used, however, has been found to be not much significant unless the exclusive role of noise strength on switching path is observed. The study merits importance in view of immense technological applications of QD‐based systems where the noise‐anharmonicity interplay may be exploited to a great extent.

Beyond the normal mode picture: the importance of the reactant’s intramolecular mode coupling in quasiclassical trajectory simulations

In quasiclassical trajectory simulations of bimolecular reactions of polyatomic molecules, the sets of initial coordinates and momenta of the colliding molecules generated by the widely used normal mode sampling (NMS) are generally nonstationary and evolve during the initial free flight of the reactants. For several isotopologues of the CH4 + H abstraction reaction, the calculated cross sections were found to oscillate as a function of the initial reactant separation. The arising ambiguity can be removed by averaging over an entire period of such oscillations (1PA). Adiabatic switching (AS) produces stationary ensembles of initial states, allowing one to generate unambiguous reaction probabilities and cross sections regardless of the choice of coordinate system used in the zeroth-order harmonic Hamiltonian. In this work the accuracy of the 1PA method was tested against AS-based reactivity parameters. Overall, 1PA provides a reasonably good correction to the non-stationarity of the initial states generated by NMS, but in extreme cases the cross sections are overestimated by up to 70%, thus the accuracy of 1PA varies currently unpredictably and is often sensitive to the choice of coordinates used for NMS. Therefore, it seems advisable to use adiabatic switching to prepare initial states in quasiclassical trajectory simulations.

High-fidelity method for a single-step N -bit Toffoli gate in trapped ions

Conditional multiqubit gates are a key component for elaborate quantum algorithms. In a recent work, Rasmussen et al. [Phys. Rev. A 101, 022308 (2020)] proposed an efficient single-step method for a prototypical multiqubit gate, a Toffoli gate, based on a combination of Ising interactions between control qubits and an appropriate driving field on a target qubit. Trapped ions are a natural platform to implement this method, since Ising interactions mediated by phonons have been demonstrated in increasingly large ion crystals. However, the simultaneous application of these interactions and the driving field required for the gate results in undesired entanglement between the qubits and the motion of the ions, reducing the gate fidelity. In this work, we propose a solution based on adiabatic switching of these phonon-mediated Ising interactions. We study the effects of imperfect ground-state cooling and use spin-echo techniques to undo unwanted phase accumulation in the achievable fidelities. For gates coupling to all axial modes of a linear crystal, we calculate high-fidelity $(&gt;99%)$ $N$-qubit rotations with $N=3--7$ ions cooled to their ground state of motion and a gate time below 1 ms. Finally, we study the effect of laser intensity fluctuations and find that the proposed gate requires intensity stabilization with subpercentage noise levels. The high fidelities obtained also for large crystals could make the gate competitive with gate-decomposed, multistep variants of the $N$-qubit Toffoli gate, at the expense of requiring ground-state cooling of the ion crystal.

An Adiabatic Superconductor Comparator With 46 nA Sensitivity

Adiabatic quantum-flux-parametron (AQFP) circuits can operate with extremely small energy dissipation (∼1 zJ per junction at 5 GHz) and high sensitivity (∼1 μA) owing to adiabatic switching. Thus, AQFP logic is suitable to use as readout interfaces for cryogenic detectors, such as superconducting nanowire single-photon detectors (SSPDs). In order to extend the application of AQFP logic to various detectors, it is crucial to achieve even better sensitivity because some detectors, such as WSi SSPDs and transition edge sensors (TESs), require sub-μA sensitivity. In the present study, we propose a high-sensitivity AQFP comparator with a current transformer (CT), which increases the equivalent input current and thereby improves the sensitivity. Numerical simulation shows that the proposed comparator achieves a sensitivity approximately six times better than that of a conventional AQFP comparator. Furthermore, we demonstrate a sensitivity of 46 nA at 4.2 K for a sampling frequency of 500 Hz in the experiment.