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A Polynomial-Time Classical Algorithm for Noisy Quantum Circuits
We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g., the computational basis). Our approach is based upon the intuition that noise exponentially damps nonlocal correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by keeping track of only the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasipolynomial time, so long as the distribution anticoncentrates. A number of implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: For constant noise rates, any quantum circuit for which error mitigation succeeds in polynomial-time on most input states can also be classically simulated in polynomial-time on most input states. Our algorithms scale exponentially in the inverse noise rate, which is fundamental and makes them impractical for current quantum devices.
A review of crosstalk polymorphic circuits and their scalability
Using a control variable, the functionality of Polymorphic circuits can be modified, making them adaptable and useful for reconfiguring circuit behavior — all the way from gate level to system level. State-of-the art polymorphic circuits are based on custom non-linear circuit design or emerging devices such as ambipolar FET, configurable magnetic devices etc. While some of these approaches are inefficient in performance, others involve exotic devices. The Crosstalk computing based polymorphic circuits offer a fresh perspective. In Crosstalk, the interconnect interference between nanoscale metal lines is intentionally engineered to exhibit the programmable Boolean logic behavior. This approach relies on the coupling between metal lines and not on the transistors for computing, resulting in better scalability, security by obscurity, and fault tolerance by reconfiguration. Our novel approach is backed by the mathematical formulation that conveys the rationale to generalize and achieve a wide variety of polymorphic circuits. Our experiments, including design, simulation, and Power Performance Area (PPA) characterization results indicate that crosstalk circuits provide significant improvement in transistor count (about 3x), switching energy (2x), and speed (1.5x) for polymorphic logic circuits. In the best-case scenario, the transistor count reduction is 5x. This paper presents Crosstalk computing’s fundamentals, polymorphism and the scalability aspects to compete/co-exist with CMOS for digital logic implementations below 10 nm. Our scalability study uses Open Source 7 nm PDK, considers all process variation aspects and accommodates worst-case scenarios. The study results for various benchmark circuits show that the Crosstalk technology is a viable alternative to CMOS for digital logic implementations below 10 nm, having 48% density, 57% power, and 10% performance gains over equivalent CMOS counterparts. Finally, we compare Crosstalk Polymorphic Circuit design technique with similar approaches described in related works and discuss its features and constraints.
Exact block encoding of imaginary time evolution with universal quantum neural networks
We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.
Modeling strategy for progressive failure prediction in lithium-ion batteries under mechanical abuse
The prediction for the internal failure of lithium-ion batteries (LIBs) under external mechanical abuse loading remains a challenge for safe design. This paper systematically studies the modeling approach for progressive failure simulation and short-circuit prediction. Hemispherical indentation experiments are conducted on a battery specimen containing 5 representative sandwich (RS) layers to examine the deformation and progressive failure behavior of battery components. Three different models, viz, a high-fidelity detailed model, an intermediate homogenized model and a fully homogenized model, are developed and employed to simulate the progressive failure in a multi-layer battery specimen. The simulation results obtained using the three models all correlate well with experimental phenomena, capturing the overall stress-strain response and ultimate failure of the battery structure. The numerical results can help us understand the failure behavior and the mechanism for mechanical abuse-induced short circuit in LIBs. The feasibility of the three models for use in progressive failure prediction is compared by analyzing the capability of the models in predicting the critical failure events, the computational efficiency of the models, and the feasibility to implement coupled mechanical-electrochemical-thermal simulations. The results of this work provide useful insights on practical choices for the modeling strategy and safety design of LIBs under mechanical abuse conditions.
Stochastic fracture generation and thermo-hydro-mechanical modeling in an equivalent continuum framework for enhanced geothermal systems
Enhanced geothermal systems (EGS) involve fracturing low permeability material to establish well connectivity and then injecting and circulating fluid into the fractured subsurface for geothermal power production. Changes in fracture aperture from contraction of the cooling matrix rock may alter network connectivity and risk thermal short-circuiting. Thermo-hydro-mechanical (THM) models are a useful tool to study these processes. However, as fracture networks are complex, and data may be limited, fracture networks in THM models are often stochastically generated. Given reliance on stochastic fracture networks and THM modeling to represent the subsurface and assess productivity of EGS, increased understanding of the influence of such statistically derived fracture networks on flow and heat transport in THM models is needed. Here, a new fracture process model is developed in the reactive transport code PFLOTRAN to stochastically generate fracture families and simulate changes in fracture aperture over time due to temperature changes of the rock matrix. Sixty-four different fracture networks ranging from well to poorly-connected, are modeled in PFLOTRAN with and without mechanical processes (THM vs TH). Results indicate that for well-connected fracture networks, thermal short-circuiting is less of a concern due to the abundance of available alternative flowpaths. For poorly-connected fracture networks, inclusion of mechanical processes showed steep thermal drawdown coincident with increase in fracture aperture along developing colder flowpaths, demonstrating the risk of thermal short-circuiting. Simulations with additional, larger fractures engineered to establish connectivity in a poorly-fractured subsurface, indicate that while stochastic variation of fracture orientation of the background network had limited influence, such variation in the engineered fractures significantly affected flow and heat transport.
Qutrit and qubit circuits for three-flavor collective neutrino oscillations
We explore the utility of qutrits and qubits for simulating the flavor dynamics of dense neutrino systems. The evolution of such systems impacts some important astrophysical processes, such as core-collapse supernovae and the nucleosynthesis of heavy nuclei. Many-body simulations require classical resources beyond current computing capabilities for physically relevant system sizes. Quantum computers are therefore a promising candidate to efficiently simulate the many-body dynamics of collective neutrino oscillations. Previous quantum simulation efforts have primarily focused on properties of the two-flavor approximation due to their direct mapping to qubits. Furthermore, we present new quantum circuits for simulating three-flavor neutrino systems on qutrit- and qubit-based platforms, and demonstrate their feasibility by simulating systems of two, four, and eight neutrinos on IBM and Quantinuum quantum computers.
Improving quantum simulation efficiency of final state radiation with dynamic quantum circuits
Not Available
Model Based Predictive Control for Frequency Support in Multi-port Autonomous Reconfigurable Solar Plants
Primary frequency support functionality can be an added advantage for any new grid integrated power electronics resource. With increased penetration of power electronics resources, inertial and primary frequency response capabilities are decreasing. In this research paper, an advanced model-based predictive control (MBPC) algorithm for providing frequency support to a new topology of integrated photovoltaic(PV), batterybased energy storage systems (ESS), and high-voltage direct current (HV dc) systems called multi-port autonomus reconfigurable solar (MARS) plants is based on the synchronverter-based control. The simulation of MARS-HV dc system with proposed control strategy is simulated and validated for MARS connected to low short circuit ratio (SCR) grids in PSCAD/EMTDC simulation environment. The control algorithm proposed showcases better performance in terms of frequency nadir improvement and frequency steady state improvemnt with respect to no frequency control.
Maximum power point tracking for a multi-layered piezoelectric heel charger with a levered mechanism toward impact-based energy harvesting
The piezoelectric footstep energy harvester does not always work at its maximum power point when the external load is fixed, as the optimal load changes when the walking excitation alters. Thus, the harvesting efficiency is downgraded largely in real-life scenarios compared to in-lab experiments and theoretical or numerical predictions due to the mismatch between the actual load and the optimal load. To address this issue, the concept of Maximum Power Point Tracking (MPPT) is investigated in this paper and the circuit design is implemented for a multi-layered levered piezoelectric footstep energy harvester (heel charger). The proposed event-driven MPPT circuit interface with a customized buck converter aims to maximize the power gained from daily walking using the heel charger to power a fixed load, such as smart insole or shoes. The MPPT circuit design is conceptually simulated and then tested with the heel charger to further validate if it works at its maximum power point when the frequency of the input excitation alters. Results show that the extracted power from the heel charger connected to a fixed resistance load with MPPT implementation is improved up to 300% compared to the one without MPPT implementation in simulation and up to 180% in the experiment when connected to a fixed load. The difference between simulation and experimental results is due to the optimization of using voltage sources as the heel charger and the control signals (pulse width modulation) from the microcontroller in the simulation.
Spatiotemporal pattern detection, generation, and computation with circuits
Abstract Implementations of neurons, delays, and synapse circuits are presented with simulations. These neural elements are used to create two small spiking neural networks, the Rate-Window and Order-Biased clusters, which are capable of detecting simple two-spike spatiotemporal patterns. A simple pattern detecting network (SPDN) is created by combining the Rate-Window and Order-Biased clusters, where clusters are small spiking neural networks, and its simple pattern detection ability is demonstrated in simulation. The SPDN is used to implement a complex pattern detecting network (CPDN) and its complex pattern detection ability is demonstrated in simulation. Methods for generating arbitrary spatiotemporal patterns are presented. The CPDN and spatiotemporal pattern generation methods are then used to implement a novel spatiotemporal computing paradigm based on detecting and responding to spatiotemporal symbols. A simulation of a spatiotemporal half adder is presented to demonstrate the computing paradigm.
Dynamics of qudit gates and effects of spectator modes on optimal control pulses
Qudit gates for high-dimensional quantum computing can be synthesized with high precision using numerical quantum optimal control techniques. Large circuits are broken down into modules and the tailored pulses for each module can be used as primitives for a qudit compiler. Application of the pulses of each module in the presence of extra modes may decrease their effectiveness due to crosstalk. In this paper, we address this problem by simulating qudit dynamics for circuit quantum electrodynamics systems. As a test case, we take pulses for single-qudit swap gates optimized in isolation and then apply them in the presence of spectator modes each of which are in Fock states. We provide an experimentally relevant scaling formula that can be used as a bound on the fidelity decay. Our results show that frequency shift from spectator mode populations has to be ≲ 0.1 % of the qudit's nonlinearity in order for high-fidelity single-qudit gates to be useful in the presence of occupied spectator modes.
Binary operations on neuromorphic hardware with application to linear algebraic operations and stochastic equations
Abstract Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses—so-called neuromorphic systems—is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement operations. We use the mechanisms to construct a neuromorphic, binary matrix multiplication algorithm that may be used as a primitive for linear differential equation integration, deep networks, and other standard calculations. We also construct a random walk circuit and apply it in Brownian motion simulations. We study how both algorithms scale in circuit size and iteration time.
Enhanced Inductance and Winding Loss Model for Coupled Inductors
An enhanced model for coupled inductors with significant fringing effect is developed in the form of equivalent circuit. The equivalent circuit is derived from a physical model that captures the flux paths through a leakage inductor and two mutual inductors on the primary and secondary side. A mutual winding resistor is added in parallel with the mutual inductor to model the winding loss affected by the fringing flux that penetrates the winding. The equivalent circuit is verified by finite-element simulation (FES) and successfully predicts the open-circuit winding loss and winding loss variation with phase-shift impact.
Large-signal Stability Analysis of Grid-forming Inverters with Equivalent-circuit Models
Here, this paper proposes an energy function-based direct method for large-signal stability assessment of grid-forming (GFM) inverters leveraging an equivalent-circuit representation of all involved control- and physical-layer dynamics. Three different primary controls, a standard inner-current outer-voltage cascaded-control architecture, output LCL filter, and reference-current saturation limiting are featured in the modeling and analysis framework. A composite energy function for the GFM inverter is obtained by summing up individual energy contributions gleaned from the circuit representation. The approach can readily be generalized to different primary controls, output-filter arrangements, and current limiters since it is based on a circuit-theoretic foundation. Numerical simulations validate the efficacy of the approach in estimating the critical clearing time following a large-signal disturbance.
Spread Spectrum Time Domain Reflectometry (SSTDR) Digital Twin Simulation of Photovoltaic Systems for Fault Detection and Location
Utilizing spread spectrum time domain reflectometry (SSTDR) to detect, locate, and characterize faults in photovoltaic (PV) systems is examined in this paper. We present a method to obtain the model parameters that are needed to produce digital twin SSTDR responses for PV systems. The digital twin SSTDR responses could be used to predict faults within the PV systems. Here, the model parameters are the reflection and transmission coefficients at each impedance discontinuity in the PV system along with the propagation coefficients across each PV cable segment. We obtain model parameter by applying inverse modeling techniques to experimental SSTDR data associated with PV systems. Our model parameters can be used in any digital twin simulation method for modeling reflectometry in frequency-dependent and complex loads. For validation, we used the model parameters in a graph network simulation engine and adapted it to be used for SSTDR digital twin simulations in PV systems. We produced simulations for 0 to 10 PV modules connected in series. We also simulated SSTDR responses for open circuit disconnections in a PV setup containing 10 PV modules in series. Results show that all but one simulated disconnect locations match experimental disconnection locations of the same setup with an error of less than 5%.
Real-time Implementation of Grid Code Compliant Grid Edge Energy Management System
Integrated distributed energy resources (DER) in a distribution system need to follow grid codes to avoid violations that result in DER/circuit segment disconnection. To comply with grid code requirements at the grid edge level, network constrained grid edge energy management system (EMS) can be deployed. The objective of grid edge EMS is to provide economic solution for active and reactive power DER setpoints at each dispatch interval and ensure voltage regulation to support secure interconnection of the grid edge segment to the distribution system with multiple inverter based DER units. In this work, real-time simulation of grid code compliant grid edge EMS is deployed in a realistic feeder circuit segment. For real-time simulation, communication between the grid edge EMS and DERs is done exploiting IEC 61850-7-420. It enables interoperability among different DERs and grid edge EMS. No prior art has deployed IEC 61850-7-420 GOOSE communication protocol for grid edge EMS. Conversion of IEC 61850 GOOSE messages to Modbus communication protocol is also performed to communicate with grid edge EMS in commodity-off the shelf embedded boards in this work. The real-time simulation in OPAL-RT real-time digital simulator shows the out-performance of grid edge EMS by reducing the voltage violation in the distribution circuit.
Observable measurement-induced transitions
One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across the entire system. As the measurement density is increased, a phase transition occurs that is characterized by the disentanglement of different parts of the system. Unfortunately, this transition is impossible to observe experimentally for macroscopic systems because it requires an exponentially costly full tomography of the many-body wave function or a comparison with the simulation on an oracle classical computer. In this work we report the discovery of another measurement-induced phase transition that can be observed experimentally if quantum dynamics can be reversed. On one side of this phase transition the quantum information encoded in some part of the Hilbert space is fully recovered after the time inversion. On the other side, all quantum information is corrupted. This transition also manifests itself as the change in the behavior of the probability to observe the same measurement outcome in the process that consists of identical blocks repeated many times. In each block the unitary evolution is followed by the measurement. On one side of the transition the probability decreases exponentially with the number of repetitions, on the other it tends to a constant as the number of repetitions is increased. We confirm the existence of the proposed phase transition through numerical simulations of realistic quantum circuits and analytical calculations using an effective random-matrix theory model.