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Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers

We present a novel input scheme for general second-quantized Hamiltonians of relativistic or non-relativistic many-fermion systems. This input scheme incorporates the fermionic anticommutation relations, particle number variations, and respects the symmetries of the Hamiltonian. Based on our input scheme, we propose a hybrid quantum-classical framework for spectral calculations on future quantum hardwares. We provide explicit circuit designs and the associated gate cost. We demonstrate our hybrid framework by solving the low-lying spectra of 42 Ca and 46 Ca. Our input scheme provides new pathways to solving the spectra and dynamics of the relativistic and nonrelativistic many-fermion systems via first-principles approaches.

Hybrid spectral calculation framework↗

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping

We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $η$ particles and $N$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O(η^2\sqrt{N})$ $T$-gates, outperforming alternative algorithms when $η ≲ \sqrt{N}$. To achieve such scaling, we require $O(\sqrt{N})$ dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford $+T$ gates and study the impact of noise on the prepared state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Associative Pattern Recognition In Analog VLSI Circuits

Winner-take-all circuit selects best-match stored pattern. Prototype cascadable very-large-scale integrated (VLSI) circuit chips built and tested to demonstrate concept of electronic associative pattern recognition. Based on low-power, sub-threshold analog complementary oxide/semiconductor (CMOS) VLSI circuitry, each chip can store 128 sets (vectors) of 16 analog values (vector components), vectors representing known patterns as diverse as spectra, histograms, graphs, or brightnesses of pixels in images. Chips exploit parallel nature of vector quantization architecture to implement highly parallel processing in relatively simple computational cells. Through collective action, cells classify input pattern in fraction of microsecond while consuming power of few microwatts.

Tawel, Raoul↗

Peak Prediction Using Multi Layer Perceptron (MLP) for Edge Computing ASICs Targeting Scientific Applications

High data rate detectors play an integral part in scientific research and their development is actively pursued at High Energy Physics (HEP) facilities around the world. Edge Machine Learning (ML) offers the ability to reduce data rates by integrating ML algorithms into Application Specific Integrated Circuits (ASICs) on the front end electronics. In this work, we explore a set of neural network architectures for predicting the peak amplitudes in the detector's sensor response. We have designed and synthesized several MLP based neural networks comparing their inference accuracy, power consumption, and area targeting for minimal latency. The neural networks are synthesized in a commercial 65nm process. The effect of quantizing the network's weights and biases on hardware performance and area is reported. We also conduct design space exploration to compare between design alternatives

47 OTHER INSTRUMENTATION↗

Unification of finite symmetries in the simulation of many-body systems on quantum computers

Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can result in significant overhead due to the exponentially growing size of some symmetry groups as the number of particles increases. Quantum computers hold the promise of achieving exponential speedup in simulating quantum many-body systems; however, a general method for utilizing symmetries in quantum simulations has not yet been established. In this work, we present a unified framework for incorporating symmetry group transforms on quantum computers to simulate many-body systems. The core of our approach lies in the development of efficient quantum circuits for symmetry-adapted projection onto irreducible representations of a group or pairs of commuting groups. We provide resource estimations for common groups, including the cyclic and permutation groups. Our algorithms demonstrate the capability to prepare coherent superpositions of symmetry-adapted states and to perform quantum evolution across a wide range of models in condensed-matter physics and ab initio electronic structure in quantum chemistry. Specifically, we execute a symmetry-adapted quantum subroutine for small molecules in first-quantization on noisy hardware and demonstrate the emulation of symmetry-adapted quantum phase estimation for preparing coherent superpositions of quantum states in various irreducible representations of a symmetry group. In addition, we present a discussion of open problems regarding treating symmetries in digital quantum simulations of many-body systems, paving the way for future systematic investigations into leveraging symmetries quantumly for practical quantum advantage. The broad applicability and rigorous resource estimation for symmetry transformations make our framework appealing for achieving provable quantum advantage on fault-tolerant quantum computers, especially for symmetry-related properties.

quantum algorithms↗

Lidar Luminance Quantizer

This innovation addresses challenges in lidar imaging, particularly with the detection scheme and the shapes of the detected signals. Ideally, the echoed pulse widths should be extremely narrow to resolve fine detail at high event rates. However, narrow pulses require wideband detection circuitry with increased power dissipation to minimize thermal noise. Filtering is also required to shape each received signal into a form suitable for processing by a constant fraction discriminator (CFD) followed by a time-to-digital converter (TDC). As the intervals between the echoes decrease, the finite bandwidth of the shaping circuits blends the pulses into an analog signal (luminance) with multiple modes, reducing the ability of the CFD to discriminate individual events

Quilligan, Gerard↗

A high accuracy all-angle gyroscope readout using quantized flux

Means are described to use SQUID magnetometer flux counting and the London moment of a spherical superconducting gyroscope to read out the gyroscope spin axis direction to an accuracy of at least 23 bits per quadrant. The system is discussed in analogy to optical fringe counting as applied to distance measurement. Several methods of applying both analog and digital SQUID magnetometers to the readout problem are given, as well as limitations on each. Described are two methods of increasing the flux available for measurement: magnetizing the gyroscope with a trapped field, and optimizing readout circuit inductances. Finally, the same principle on which the gyroscope readout is based is applied to a description of a high accuracy, flux counting, digital angle encoder.

Anderson, J. T.↗

High resolution angular sensor

Specifications for the pointing stabilization system of the large space telescope were used in an investigation of the feasibility of reducing ring laser gyro output quantization to the sub-arc-second level by the use of phase locked loops and associated electronics. Systems analysis procedures are discussed and a multioscillator laser gyro model is presented along with data on the oscillator noise. It is shown that a second order closed loop can meet the measurement noise requirements when the loop gain and time constant of the loop filter are appropriately chosen. The preliminary electrical design is discussed from the standpoint of circuit tradeoff considerations. Analog, digital, and hybrid designs are given and their applicability to the high resolution sensor is examined. the electrical design choice of a system configuration is detailed. The design and operation of the various modules is considered and system block diagrams are included. Phase 1 and 2 test results using the multioscillator laser gyro are included.

Gneses, M. I.↗

Development of a Two Dimensional Synthetic Aperture Radiometer at L-Band

A radiometer that uses aperture synthesis in two dimensions is being built as part of research under NASA's Instrument Incubator Program. The instrument development team consists of engineers at the Goddard Space Flight Center, the University of Massachusetts and Quadrant Engineering. This will be an aircraft instrument operating at L-band which builds on the heritage of ESTAR. The choice of L-band was made because the problem of achieving adequate resolution in space is most critical at this wavelength and because a polarimetric, conical scanning airborne radiometer for future experiments to validate soil moisture and ocean salinity retrieval algorithms is not currently available. The instrument will be designed to fly on the NASA P-3 aircraft in a nadir pointing mode, although other options are possible. The antenna will consist of an array of modules arranged in a rectangular grid. Each module will be comprised of a printed circuit dual-polarized patch and integrated receiver. The distribution of modules within the rectangular array will be adjustable so that several different imaging configurations (e.g. "+","Y", "T") can be employed. The integrated receiver will provide amplification and conversion to IF. The IF signal will be routed to a processor where the required correlations performed. The I and Q channels will be created digitally and the correlations will be done digitally in this processor. The digitization will be done with sufficient bits to study the effects of quantization on radiometer performance. A computer/controller will store the data for conversion to an image and will also perform temperature control and other data interfacing and housekeeping tasks. The instrument is currently in the bread boarding phase of development. A design of the critical components has been completed and hardware is being assembled to test the individual elements. It is expected that a complete 2-channel correlator will be tested by the summer of 2000 and that the complete instrument will be ready for flight tests the following summer (2001).

LeVine, D. M.↗

Development of a Two Dimensional Synthetic Aperture Radiometer at L-Band

A radiometer that uses aperture synthesis in two dimensions is being built as part of research under NASA's Instrument Incubator Program. The instrument development team consists of engineers at the Goddard Space Flight Center, the University of Massachusetts and Quadrant Engineering. This will be an aircraft instrument operating at L-band which builds on the heritage of Electronically Steered Thinned Array Radiometer (ESTAR). This instrument is a next step in the development of aperture synthesis (STAR technology) to meet the goal of a future mission to monitor soil moisture globally from space. The instrument will be designed to fly on the NASA P-3 aircraft in a nadir pointing mode, although other options are possible. The antenna will consist of an array of modules in a rectangular grid. Each module will be comprised of a printed circuit dual-polarized patch and integrated receiver. The distribution of modules within the rectangular array will be adjustable so that several different imaging configurations (e.g. '+', 'Y', 'T') can be employed. The integrated receiver will provide amplification and conversion to infrared (IF). The IF signal will be routed to a processor where the required correlations performed. The I and Q channels will be created digitally and the correlations will be done digitally in this processor. The digitization will be done with sufficient bits to study the effects of quantization on radiometer performance. A computer/controller will store the data for conversion to an image and will also perform temperature control and other data interfacing and housekeeping tasks. The design of critical components has been completed and hardware is being assembled to test the individual elements. It is expected that a complete two-channel correlator will be tested by the end of 2000 and that the complete instrument will be ready for flight tests the following summer (2001).

LeVine, D. M.↗

Waveform processing using neural network algorithms on the front-end electronics

In a multi-channel radiation detector readout system, waveform sampling, digitization, and raw data transmission to the data acquisition system constitute a conventional processing chain. The deposited energy on the sensor is estimated by extracting peak amplitudes, area under pulse envelopes from the raw data, and starting times of signals or time of arrivals. However, such quantities can be estimated using machine learning algorithms on the front-end Application-Specific Integrated Circuits (ASICs), often termed as “edge computing”. Edge computation offers enormous benefits, especially when the analytical forms are not fully known or the registered waveform suffers from noise and imperfections of practical implementations. In this work, we aim to predict peak amplitude from a single waveform snippet whose rising and falling edges containing only 3 to 4 samples. We thoroughly studied two well-accepted neural network algorithms, Multi-Layer Perceptron (MLP) and Convolutional Neural Network (CNN) by varying their model sizes. Further, to better fit front-end electronics, neural network model reduction techniques, such as network pruning methods and variable-bit quantization approaches, were also studied. By combining pruning and quantization, our best performing model has the size of 1.5 KB, reduced from 16.6 KB of its full model counterpart. It can reach mean absolute error of 0.034 comparing to that of a naive baseline of 0.135. Such parameter-efficient and predictive neural network models established feasibility and practicality of their deployment on front-end ASICs.

47 OTHER INSTRUMENTATION↗

Improved Autoassociative Neural Networks

Improved autoassociative neural networks, denoted nexi, have been proposed for use in controlling autonomous robots, including mobile exploratory robots of the biomorphic type. In comparison with conventional autoassociative neural networks, nexi would be more complex but more capable in that they could be trained to do more complex tasks. A nexus would use bit weights and simple arithmetic in a manner that would enable training and operation without a central processing unit, programs, weight registers, or large amounts of memory. Only a relatively small amount of memory (to hold the bit weights) and a simple logic application- specific integrated circuit would be needed. A description of autoassociative neural networks is prerequisite to a meaningful description of a nexus. An autoassociative network is a set of neurons that are completely connected in the sense that each neuron receives input from, and sends output to, all the other neurons. (In some instantiations, a neuron could also send output back to its own input terminal.) The state of a neuron is completely determined by the inner product of its inputs with weights associated with its input channel. Setting the weights sets the behavior of the network. The neurons of an autoassociative network are usually regarded as comprising a row or vector. Time is a quantized phenomenon for most autoassociative networks in the sense that time proceeds in discrete steps. At each time step, the row of neurons forms a pattern: some neurons are firing, some are not. Hence, the current state of an autoassociative network can be described with a single binary vector. As time goes by, the network changes the vector. Autoassociative networks move vectors over hyperspace landscapes of possibilities.

Hand, Charles↗

All-Digital Baseband 65nm PLL/FPLL Clock Multiplier using 10-cell Library

PLLs for clock generation are essential for modern circuits, to generate specialized frequencies for many interfaces and high frequencies for chip internal operation. These circuits depend on analog circuits and careful tailoring for each new process, and making them fault tolerant is an incompletely solved problem. Until now, all digital PLLs have been restricted to sampled data DSP techniques and not available for the highest frequency baseband applications. This paper presents the design and preliminary evaluation of an all-digital baseband technique built entirely with an easily portable 10-cell digital library. The library is also described, as it aids in research and low volume design porting to new processes. The advantages of the digital approach are the wide variety of techniques available to give varying degrees of fault tolerance, and the simplicity of porting the design to new processes, even to exotic processes that may not have analog capability. The only tuning parameter is digital gate delay. An all-digital approach presents unique problems and standard analog loop stability design criteria cannot be directly used. Because of the quantization of frequency, there is effectively infinite gain for very small loop error feedback. The numerically controlled oscillator (NCO) based on a tapped delay line cannot be reliably updated while a pulse is active in the delay line, and ordinarily does not have enough frequency resolution for a low-jitter output.

Shuler, Robert L., Jr.↗

ALL-Digital Baseband 65nm PLL/FPLL Clock Multiplier Using 10-Cell Library

PLLs for clock generation are essential for modern circuits, to generate specialized frequencies for many interfaces and high frequencies for chip internal operation. These circuits depend on analog circuits and careful tailoring for each new process, and making them fault tolerant is an incompletely solved problem. Until now, all digital PLLs have been restricted to sampled data DSP techniques and not available for the highest frequency baseband applications. This paper presents the design and preliminary evaluation of an all-digital baseband technique built entirely with an easily portable 10-cell digital library. The library is also described, as it aids in research and low volume design porting to new processes. The advantages of the digital approach are the wide variety of techniques available to give varying degrees of fault tolerance, and the simplicity of porting the design to new processes, even to exotic processes that may not have analog capability. The only tuning parameter is digital gate delay. An all-digital approach presents unique problems and standard analog loop stability design criteria cannot be directly used. Because of the quantization of frequency, there is effectively infinite gain for very small loop error feedback. The numerically controlled oscillator (NCO) based on a tapped delay line cannot be reliably updated while a pulse is active in the delay line, and ordinarily does not have enough frequency resolution for a low-jitter output.

Schuler, Robert L., Jr.↗

Root-Raised Cosine Filter Implementation That Uses Canonical Signed Digits for High-Speed Digital Filter Applications

NASA Lewis Research Center's Space Communications Division has been investigating high-speed digital filters that can operate at a higher speed than those in current use for a digital modulator and demodulator (modem). Using the Canonical Signed Digits (CSD) number representation for filter coefficients is a very effective way to increase the filter's speed while reducing complexity in the digital filter hardware design. This approach is a good alternative to using an expensive parallel-processing design technique or custom, application-specific integrated circuits. Such integrated circuits may not be suitable for applications that require filter speeds faster than what application-specific integrated circuits digital signal processors can offer for a dedicated channel. When a communication channel is a dedicated, multiplication process--a costly, time-consuming process--it can be greatly simplified by a replacement of the filter coefficients with CSD numbers. A computer code written with the MATLAB software package runs the program and generates CSD-represented filter coefficients that are based on minimizing minimum mean square errors. Also, the Alta Group of Cadence's Signal Processing Workstation is used to simulate and analyze the CSD filter responses. The impulse response of the root-raised cosine filter that is used as a base model is defined. From this filter, a set of coefficients is sampled and stored in a file. For the all coefficients, the optimal CSD number for each coefficient is searched on the basis of the minimum-mean-square-errors criterion. Because the distribution of CSD numbers is not uniform, quantization errors tend to be bigger for coefficients greater than 1/2. To offset errors that occur in a region of coefficients between 1/2 to 1 and to better represent fractions with CSD numbers, an extra nonzero digit is allowed for any coefficients exceeding 1/2. This will greatly improve frequency response as well as intersymbol interference at the receiver. The frequency response of a set of collected CSD-represented filter coefficients was compared with the same filter that was conventionally implemented. Analyses show CSD-implemented filters perform as well as conventional filters. Comparison of eye diagrams and bit-error-rate curves between CSD filters and traditionally implemented filters are almost indistinguishable. However, filter complexity was reduced from almost 3.5 to 1 for CSD filters. Complete computer simulation results are available. In the near future, work will focus on building actual working digital filter hardware in a field programmable gate array (FPGA).

Kim, Heechul↗

Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗

NASA Tech Briefs, July 2010

Topics covered include: Wirelessly Interrogated Wear or Temperature Sensors; Processing Nanostructured Sensors Using Microfabrication Techniques; Optical Pointing Sensor; Radio-Frequency Tank Eigenmode Sensor for Propellant Quantity Gauging; High-Temperature Optical Sensor; Integral Battery Power Limiting Circuit for Intrinsically Safe Applications; Configurable Multi-Purpose Processor; Squeezing Alters Frequency Tuning of WGM Optical Resonator; Automated Computer Access Request System; Range Safety for an Autonomous Flight Safety System; Fast and Easy Searching of Files in Unisys 2200 Computers; Parachute Drag Model; Evolutionary Scheduler for the Deep Space Network; Modular Habitats Comprising Rigid and Inflatable Modules; More About N2O-Based Propulsion and Breathable-Gas Systems; Ultrasonic/Sonic Rotary-Hammer Drills; Miniature Piezoelectric Shaker for Distribution of Unconsolidated Samples to Instrument Cells; Lunar Soil Particle Separator; Advanced Aerobots for Scientific Exploration; Miniature Bioreactor System for Long-Term Cell Culture; Electrochemical Detection of Multiple Bioprocess Analytes; Fabrication and Modification of Nanoporous Silicon Particles; High-Altitude Hydration System; Photon Counting Using Edge-Detection Algorithm; Holographic Vortex Coronagraph; Optical Structural Health Monitoring Device; Fuel-Cell Power Source Based on Onboard Rocket Propellants; Polar Lunar Regions: Exploiting Natural and Augmented Thermal Environments; Simultaneous Spectral Temporal Adaptive Raman Spectrometer - SSTARS; Improved Speed and Functionality of a 580-GHz Imaging Radar; Bolometric Device Based on Fluxoid Quantization; Algorithms for Learning Preferences for Sets of Objects; Model for Simulating a Spiral Software-Development Process; Algorithm That Synthesizes Other Algorithms for Hashing; Algorithms for High-Speed Noninvasive Eye-Tracking System; and Adapting ASPEN for Orbital Express.

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