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Digest of technical papers/Digest of technical papers - IEEE International Solid-State Circuits Conference

29.3 A 48GHz 5.6mW Gate-Level-Pipelined Multiplier Using Single-Flux Quantum Logic

Ikki Nagaoka, Masamitsu Tanaka, Koji Inoue, Akira Fujimaki

Published Feb 1, 2019• 45 citations
Publisher

Abstract

A multiplier based on superconductor single-flux-quantum (SFQ) logic is demonstrated up to 48GHz with the measured power consumption of 5.6 mW. The multiplier performs 8 × 8-bit signed multiplication every clock cycle. The design is based on a bit-parallel, gate-level-pipelined structure that exploits ultimately high-throughput performance of SFQ logic. The test chip fabricated using a 1.0-μm, 9-layer process consists of 20,251 Nb/AlOx/Nb Josephson junctions (JJs). The correctness of operation is verified by on-chip high-speed testing.

DOI
10.1109/isscc.2019.8662351

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A multiplier based on superconductor single-flux-quantum (SFQ) logic is demonstrated up to 48GHz with the measured power consumption of 5.6 mW. The multiplier performs 8 × 8-bit signed multiplication every clock cycle. The design is based on a bit-parallel, gate-level-pipelined structure that exploits ultimately high-throughput performance of SFQ logic. The test chip fabricated using a 1.0-μm, 9-layer process consists of 20,251 Nb/AlOx/Nb Josephson junctions (JJs). The correctness of operation is verified by on-chip high-speed testing.
A high-throughput 4$\boldsymbol{\times }4−bitmultiplierwasdemonstratedusinganextremelycarefultimingdesignforlow−voltagerapidsingle−flux−quantum(LV−RSFQ)logic.Thedesignconsidersthelengthsofallwires,biasdependencyofthedelays,andloaddependencyofthesignalsplitters.ThekeyistointentionallyusebothJosephsontransmissionlinesandpassivetransmissionlinesforgate−to−gatewiring,evenovershortdistances,toformthesamestructurewiringastheclocklines.Thestructureofthemultiplierisbasedonabit−parallel,gate−levelpipelinetoexploitthroughput.ThetestchipwasfabricatedusingtheAIST10−kA/cm4-bit multiplier was demonstrated using an extremely careful timing design for low-voltage rapid single-flux-quantum (LV-RSFQ) logic. The design considers the lengths of all wires, bias dependency of the delays, and load dependency of the signal splitters. The key is to intentionally use both Josephson transmission lines and passive transmission lines for gate-to-gate wiring, even over short distances, to form the same structure wiring as the clock lines. The structure of the multiplier is based on a bit-parallel, gate-level pipeline to exploit throughput. The test chip was fabricated using the AIST 10-kA/cm4−bitmultiplierwasdemonstratedusinganextremelycarefultimingdesignforlow−voltagerapidsingle−flux−quantum(LV−RSFQ)logic.Thedesignconsidersthelengthsofallwires,biasdependencyofthedelays,andloaddependencyofthesignalsplitters.ThekeyistointentionallyusebothJosephsontransmissionlinesandpassivetransmissionlinesforgate−to−gatewiring,evenovershortdistances,toformthesamestructurewiringastheclocklines.Thestructureofthemultiplierisbasedonabit−parallel,gate−levelpipelinetoexploitthroughput.ThetestchipwasfabricatedusingtheAIST10−kA/cm\boldsymbol{^2},Nb/AlOx/Nb,9−Nb−layerAdvancedProcess2.Themeasuredmaximumoperatingfrequency,throughput,andpowerconsumptionwithoutcoolingcostinthehigh−speedon−chiptestwere52GHz,52G−operationspersecond(GOPS),and134, Nb/AlOx/Nb, 9-Nb-layer Advanced Process 2. The measured maximum operating frequency, throughput, and power consumption without cooling cost in the high-speed on-chip test were 52 GHz, 52 G-operations per second (GOPS), and 134,Nb/AlOx/Nb,9−Nb−layerAdvancedProcess2.Themeasuredmaximumoperatingfrequency,throughput,andpowerconsumptionwithoutcoolingcostinthehigh−speedon−chiptestwere52GHz,52G−operationspersecond(GOPS),and134\boldsymbol{\mu }W,respectively.AlthoughtheswitchingspeedoftheJosephsonjunctionswasreducedby40W, respectively. Although the switching speed of the Josephson junctions was reduced by 40W,respectively.AlthoughtheswitchingspeedoftheJosephsonjunctionswasreducedby40\boldsymbol{\%}$owing to the low-voltage operation, the obtained clock frequency was as high as that demonstrated with the standard bias voltage. The energy efficiency was 381 tera-operations per second per watt (TOPS/W) at 4.2 K. Further improvement in energy efficiency is expected by using low-voltage half-flux-quantum (LV-HFQ) circuits and shrinking the size of Josephson junctions.
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence at high speed. FFT can convert a signal from time domain to frequency domain, and is wildly used in digital signal processing field. In this paper, a high-speed, low-power FFT processor is demonstrated up to 47.8GHz with the measured power consumption of 5.3mW, using single-flux quantum (SFQ) logic. This is the first complete FFT processor implementation using superconducting technology, performing 8-point 7-bit FFT in a bit-serial computing manner. The test chip fabricated using a 1.0 μm 9-layer process consists of 17 455 Nb/AlOx/Nb Josephson junctions (JJs), rendering itself the largest superconducting digital circuit capable of iterative data computing. The correct operation of the chip has been experimentally confirmed at a maximum operating frequency of 47.8GHz (word speed 8GHz) by conducting on-chip high-speed testing.
A design of a 32 × 32-bit 4-bit bit-slice integer multiplier for rapid single-flux quantum microprocessors is shown. The multiplier carries out both signed and unsigned multiplication. It is designed with synchronous concurrent-flow clocking and target frequency of 50 GHz using the AIST 1.0-μm Nb/AlOx/Nb, nine-layer advanced process 2 fabrication technology with a critical current density of 10 kA/cm2. It consists of 56 885 Josephson junctions. The area is 12.00 × 6.65 mm2. The simulation results show correct operation with frequency of 50 GHz at the dc bias voltage of 2.5 mV. The throughput is 3.125 × 109multiplications per second.
Single-flux-quantum (SFQ) technology is a novel technology where binary information is represented by a single flux. It enables us to realize high-speed, low-power SFQ logic circuits, surpassing conventional complementary metal-oxide-silicon (CMOS) technology. We proposed an SFQ packet switch to avoid the bottlenecks in broadband networks of the future. To demonstrate high-speed operation of an SFQ logic circuit and its application to our switch architecture, we designed a cross/bar switch. It consists of 13 logic gates and 581 Josephson junctions were used in the layout. We confirmed correct operations up to 33 GHz in simulation. We placed the switch circuit in an on-chip test system for high-speed (over 10 GHz) test. Including I/O circuits, the system as a whole consists of 1236 Josephson junctions. The chip was fabricated by using NEC's standard Nb process. We carried out an on-chip test and found correct operations up to 35 GHz.
Recently, we proposed a new data-path architecture, named a large-scale reconfigurable data-path (LSRDP), based on single-flux-quantum (SFQ) circuits, to establish a fundamental technology for future high-end computers. In this architecture, a large number of SFQ floating-point units (FPUs) are used as core components, and their high performance and low power consumption are essential. In this research, we implemented an SFQ half-precision bit-serial floating-point multiplier (FPM) with a target clock frequency of 50GHz, using the AIST 10kA/cm2 Nb process. The FPM was designed, based on a systolic-array architecture. It contains 11,066 Josephson junctions, including on-chip high-speed test circuits. The size and power consumption of the FPM are 6.66mm × 1.92mm and 2.83mW, respectively. Its correct operation was confirmed at a maximum frequency of 93.4GHz for the exponent part and of 72.0GHz for the significand part by on-chip high-speed tests.