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Juqbox.jl

The Juqbox.jl package implements functionality for solving the quantum optimal control problem for realizing logical gates in closed quantum systems. The dynamics of the quantum system is modeled by Schroedinger's equation, which takes to form of a linear system of ordinary differential equations (ODE). Juqbox.jl solves this ODE by numerical time stepping and applies a gradient-based optimization technique to determine control pulses for driving an initial state to a final state, according to the desired logical gate transformation. To evaluate the gradient, Juqbox.jl applies the ``first discretize, then optimize'' approach based on a discrete adjoint time stepping technique. The actual optimization is performed by the open source Ipopt libaray. Juqbox.jl is written in the Julia programming language which, among many other features, provides a convenient interface to the Ipopt library.

PETERSSON, NILSA.↗

DALG: A program for test pattern generation in combinational logical circuits

A user's manual for a computer program DALG which generates test patterns for detecting faults in combinational logic circuits containing up to 200 logical gates is presented. The gates may be of logical types AND, OR, NAND, NOR, NOT, or Exclusive OR is presented. The faults may be any one gate or input struck at a fixed value (0 or 1). In addition to test pattern generation DALG will also determine whether or not the given test pattern will detect given faults in a circuit. Sample problems are given along with input data sheets and printed output to illustrate the capabilities of the program.

Source record↗

Efficient Multiplexer FPGA Block Structures Based on G4FETs

Generic structures have been conceived for multiplexer blocks to be implemented in field-programmable gate arrays (FPGAs) based on four-gate field-effect transistors (G(sup 4)FETs). This concept is a contribution to the continuing development of digital logic circuits based on G4FETs and serves as a further demonstration that logic circuits based on G(sup 4)FETs could be more efficient (in the sense that they could contain fewer transistors), relative to functionally equivalent logic circuits based on conventional transistors. Results in this line of development at earlier stages were summarized in two previous NASA Tech Briefs articles: "G(sup 4)FETs as Universal and Programmable Logic Gates" (NPO-41698), Vol. 31, No. 7 (July 2007), page 44, and "Efficient G4FET-Based Logic Circuits" (NPO-44407), Vol. 32, No. 1 ( January 2008), page 38 . As described in the first-mentioned previous article, a G4FET can be made to function as a three-input NOT-majority gate, which has been shown to be a universal and programmable logic gate. The universality and programmability could be exploited to design logic circuits containing fewer components than are required for conventional transistor-based circuits performing the same logic functions. The second-mentioned previous article reported results of a comparative study of NOT-majority-gate (G(sup 4)FET)-based logic-circuit designs and equivalent NOR- and NAND-gate-based designs utilizing conventional transistors. [NOT gates (inverters) were also included, as needed, in both the G(sup 4)FET- and the NOR- and NAND-based designs.] In most of the cases studied, fewer logic gates (and, hence, fewer transistors), were required in the G(sup 4)FET-based designs. There are two popular categories of FPGA block structures or architectures: one based on multiplexers, the other based on lookup tables. In standard multiplexer- based architectures, the basic building block is a tree-like configuration of multiplexers, with possibly a few additional logic gates such as ANDs or ORs. Interconnections are realized by means of programmable switches that may connect the input terminals of a block to output terminals of other blocks, may bridge together some of the inputs, or may connect some of the input terminals to signal sources representing constant logical levels 0 or 1. The left part of the figure depicts a four-to-one G(sup 4)FET-based multiplexer tree; the right part of the figure depicts a functionally equivalent four-to-one multiplexer based on conventional transistors. The G(sup 4)FET version would contains 54 transistors; the conventional version contains 70 transistors.

Vatan, Farrokh↗

Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

Here, we show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on “thermodynamic codes” to general local spin and different irreducible representations using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy under generic noise on any known 𝑑 sites, under independent and identically distributed noise, and under heralded 𝑑-local erasures. We demonstrate that this family of codes protects a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.

quantum error correction↗

Encoding Scheme Reduces Hardware Requirements

Shift register time-shared in proposed error-correcting code for tape-storage systems. Error-correcting code logic for blocks of 256-bit data words implemented by 14-stage-time-shared shift register, two 4,096bit RAM's and logic gates. Encoding and decoding logic implement generator polynomial that defines error-correcting code, and error correction based on algorithm also implemented by logic.

Sasnowitz, H.↗

Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic States

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-König bound for $n$-dimensional topological stabilizer codes. In this work, we extend topological Pauli stabilizer codes to a broad class of $n$-dimensional Clifford hierarchy stabilizer codes. These codes correspond to the $(n+1)$D Dijkgraaf-Witten gauge theories with non-Abelian topological order. We construct transversal non-Clifford gates through automorphism symmetries represented by cup products. In 2D, we obtain the first transversal non-Clifford logical gates including T and CS for Clifford stabilizer codes, using the automorphism of the twisted $\mathbb{Z}_2^3$ gauge theory (equivalent to $\mathbb{D}_4$ topological order). We also combine it with the just-in-time decoder to fault-tolerantly prepare the logical T magic state in $O(d)$ rounds via code switching. In 3D, we construct a transversal logical $\sqrt{\text{T}}$ gate in a non-Clifford stabilizer code at the third level of the Clifford hierarchy, located on a tetrahedron corresponding to a twisted $\mathbb{Z}_2^4$ gauge theory. Furthermore, our constructions surpass the Bravyi-König bound by achieving the logical gates in the $(n+1)$-th level of Clifford hierarchy in $n$ spatial dimension.

Kobayashi, Ryohei [Institute for Advanced Study, P↗

Two mechanisms for the spontaneous emergence, execution, and reprogramming of chemical logic circuits

A key question in origin-of-life research is how primitive life or life-like systems obtained reusable and reprogrammable machinery of processing information to respond to various environmental and internal stimuli. One strategy to approach this question is to view living systems as universal chemical computers. This approach focuses upon uncovering how reusable and reprogrammable chemical NOT, AND, and OR logic gates could appear under prebiotically possible scenarios where simple chemicals and second- or lower-order reactions are more frequent than macromolecules and higher-order reactions. In this article, we theoretically model two generic mechanisms of forming Boolean gates based on geochemically plausible reaction systems that could have preceded complex biopolymers. The mechanisms exploit simple bistable autocatalytic systems to encode binary variables and use heterogeneous dilution rates to differentially activate or deactivate autocatalysis in different reactors. We found that NOT, AND, and OR gates, as well as more complex logic circuits, can spontaneously arise from connected, well-mixed flow reactors based on (i) catalysis by a heterodimer between mutually inhibitory autocatalysts or (ii) selectively permeable tunnels connecting reactors. Our results suggest that simple machinery can support the prebiotic emergence of complex chemical logic circuits and provide new guides for experimentally actualizing chemical computation.

Zhen Peng↗

NNSA MSIIP Intern Biweekly Report - #3

These couple of weeks I continued doing solvent tests with the 3D printed actuators. I made measurements and organized the data obtained from the tests. I was also able to get a logic gate design that worked according to the logic and was able to start printing and modifying the design. I've been understanding more about what parts of the design it would be best to modify and why certain ideas do not work versus others. I've been communicating with my mentor when I make edits to the design to ensure I keep moving forward with it and make it look closer and closer to what we need it to. I've continued to attend the seminars held by the department and learned more about the different methods of 3d printing and the different projects that are being worked on here.

36 MATERIALS SCIENCE↗

Silicon validation of evolution-designed circuits

This paper is the first to report on a silicon implementation of circutis evolved in simulation. Several circuits were evolved an fabricated in 0.5 micron CMOS process; this paper focuses on results of logical gates evolved at transistor level. It discusses the steps taken in order to increase the chances of robust and portable designs, summarizes the results of characterization tests based on chip measurements, and comments on the performance comparing to simulations.

evolutionary algorithms↗

Dynamic variable precision computation

A conversion unit converts operands from a conventional number system that represents each binary number in the operands as one bit to redundant number system (RNS) operands that represent each binary number as a plurality of bits. An arithmetic logic unit performs an arithmetic operation on the RNS operands in a direction from a most significant bit (MSB) to a least significant bit (LSB). The arithmetic logic unit stops performing the arithmetic operation prior to performing the arithmetic operation on a target binary number indicated by a dynamic precision associated with the RNS operands. In some cases, a power supply provides power to bit slices in the arithmetic logic unit and a clock signal generator provides clock signals to the bit slices. Gate logic is configured to gate the power or the clock signals provided to a subset of the bit slices.

97 MATHEMATICS AND COMPUTING↗

Assurance of Complex Electronics. What Path Do We Take?

Many of the methods used to develop software bare a close resemblance to Complex Electronics (CE) development. CE are now programmed to perform tasks that were previously handled in software, such as communication protocols. For instance, Field Programmable Gate Arrays (FPGAs) can have over a million logic gates while system-on-chip (SOC) devices can combine a microprocessor, input and output channels, and sometimes an FPGA for programmability. With this increased intricacy, the possibility of "software-like" bugs such as incorrect design, logic, and unexpected interactions within the logic is great. Since CE devices are obscuring the hardware/software boundary, we propose that mature software methodologies may be utilized with slight modifications to develop these devices. By using standardized S/W Engineering methods such as checklists, missing requirements and "bugs" can be detected earlier in the development cycle, thus creating a development process for CE that will be easily maintained and configurable based on the device used.

FROM↗

Software Process Assurance for Complex Electronics

Complex Electronics (CE) now perform tasks that were previously handled in software, such as communication protocols. Many methods used to develop software bare a close resemblance to CE development. Field Programmable Gate Arrays (FPGAs) can have over a million logic gates while system-on-chip (SOC) devices can combine a microprocessor, input and output channels, and sometimes an FPGA for programmability. With this increased intricacy, the possibility of software-like bugs such as incorrect design, logic, and unexpected interactions within the logic is great. With CE devices obscuring the hardware/software boundary, we propose that mature software methodologies may be utilized with slight modifications in the development of these devices. Software Process Assurance for Complex Electronics (SPACE) is a research project that used standardized S/W Assurance/Engineering practices to provide an assurance framework for development activities. Tools such as checklists, best practices and techniques were used to detect missing requirements and bugs earlier in the development cycle creating a development process for CE that was more easily maintained, consistent and configurable based on the device used.

Plastow, Richard A.↗

Software Process Assurance for Complex Electronics (SPACE)

Complex Electronics (CE) are now programmed to perform tasks that were previously handled in software, such as communication protocols. Many of the methods used to develop software bare a close resemblance to CE development. For instance, Field Programmable Gate Arrays (FPGAs) can have over a million logic gates while system-on-chip (SOC) devices can combine a microprocessor, input and output channels, and sometimes an FPGA for programmability. With this increased intricacy, the possibility of software-like bugs such as incorrect design, logic, and unexpected interactions within the logic is great. Since CE devices are obscuring the hardware/software boundary, we propose that mature software methodologies may be utilized with slight modifications in the development of these devices. Software Process Assurance for Complex Electronics (SPACE) is a research project that looks at using standardized S/W Assurance/Engineering practices to provide an assurance framework for development activities. Tools such as checklists, best practices and techniques can be used to detect missing requirements and bugs earlier in the development cycle creating a development process for CE that will be more easily maintained, consistent and configurable based on the device used.

Plastow, Richard A.↗

CADAT logic simulation program

CADAT Logic Simulation Program (LOGSIM) checks functional correctness of electronic logic circuit by simulating circuit at logic gate level. LOGSIM also checks propagation delay through logic nets and indicates any timing or "race" problems.

Mitchell, C. L.↗

Filling the Assurance Gap on Complex Electronics

Many of the methods used to develop software bare a close resemblance to Complex Electronics (CE) development. CE are now programmed to perform tasks that were previously handled by software, such as communication protocols. For example, the James Webb Space Telescope will use Field Programmable Gate Arrays (FPGAs), which can have over a million logic gates, to send telemetry. System-on-chip (SoC) devices, another type of complex electronics, can combine a microprocessor, input and output channels, and sometimes an FPGA for programmability. With this increased intricacy, the possibility of software-like bugs such as incorrect design, logic, and unexpected interactions within the logic is great. Since CE devices are obscuring the hardware/software boundary, mature software methodologies have been proposed, with slight modifications, to develop these devices. By using standardized S/W Engineering methods such as checklists, missing requirements and bugs can be detected earlier in the development cycle, thus creating a development process for CE that can be easily maintained and configurable based on the device used.

Plastow, Richard A.↗

An Efficient, FPGA-Based, Cluster Detection Algorithm Implementation for a Strip Detector Readout System in a Time Projection Chamber Polarimeter

A fundamental challenge in a spaceborne application of a gas-based Time Projection Chamber (TPC) for observation of X-ray polarization is handling the large amount of data collected. The TPC polarimeter described uses the APV-25 Application Specific Integrated Circuit (ASIC) to readout a strip detector. Two dimensional photoelectron track images are created with a time projection technique and used to determine the polarization of the incident X-rays. The detector produces a 128x30 pixel image per photon interaction with each pixel registering 12 bits of collected charge. This creates challenging requirements for data storage and downlink bandwidth with only a modest incidence of photons and can have a significant impact on the overall mission cost. An approach is described for locating and isolating the photoelectron track within the detector image, yielding a much smaller data product, typically between 8x8 pixels and 20x20 pixels. This approach is implemented using a Microsemi RT-ProASIC3-3000 Field-Programmable Gate Array (FPGA), clocked at 20 MHz and utilizing 10.7k logic gates (14% of FPGA), 20 Block RAMs (17% of FPGA), and no external RAM. Results will be presented, demonstrating successful photoelectron track cluster detection with minimal impact to detector dead-time.

Polarimeter↗

SCB Quantum Computers Using iSWAP and 1-Qubit Rotations

Units of superconducting circuitry that exploit the concept of the single- Cooper-pair box (SCB) have been built and are undergoing testing as prototypes of logic gates that could, in principle, constitute building blocks of clocked quantum computers. These units utilize quantized charge states as the quantum information-bearing degrees of freedom. An SCB is an artificial two-level quantum system that comprises a nanoscale superconducting electrode connected to a reservoir of Cooper-pair charges via a Josephson junction. The logical quantum states of the device, .0. and .1., are implemented physically as a pair of charge-number states that differ by 2e (where e is the charge of an electron). Typically, some 109 Cooper pairs are involved. Transitions between the logical states are accomplished by tunneling of Cooper pairs through the Josephson junction. Although the two-level system contains a macroscopic number of charges, in the superconducting regime, they behave collectively, as a Bose-Einstein condensate, making possible a coherent superposition of the two logical states. This possibility makes the SCB a candidate for the physical implementation of a qubit. A set of quantum logic operations and the gates that implement them is characterized as universal if, in principle, one can form combinations of the operations in the set to implement any desired quantum computation. To be able to design a practical quantum computer, one must first specify how to decompose any valid quantum computation into a sequence of elementary 1- and 2-qubit quantum gates that are universal and that can be realized in hardware that is feasible to fabricate. Traditionally, the set of universal gates has been taken to be the set of all 1-qubit quantum gates in conjunction with the controlled-NOT (CNOT) gate, which is a 2-qubit gate. Also, it has been known for some time that the SWAP gate, which implements square root of the simple 2-qubit exchange interaction, is as computationally universal as is the CNOT operation.

Williams, Colin↗