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Cryogenic Memory Array based on Ferroelectric SQUID and Heater Cryotron

Shamiul Alam, Md Mazharul Islam, Md Shafayat Hossain, Kai Ni, Vijaykrishnan Narayanan, Ahmedullah Aziz

Published Jun 26, 2022• 15 citations
Publisher

Abstract

Cryogenic (cryo) memory devices, designed to operate at/below 4 Kelvin (K) temperature, is a prime enabler of practical quantum computing systems, and superconducting (SC) electronic platforms (Figs. 1(a), (b)) [1]. The state-of-the-art quantum algorithms require many arbitrary rotations which demand a large memory to store program instructions [2]. SC qubits (used in most of the existing quantum computing systems) are highly sensitive to noise and hence, to protect the qubit states from thermal disturbances, they are placed at a few milli-Kelvin (mK) temperature. Furthermore, to preserve the integrity of the quantum states, the SC qubits undergo continuous error correction schemes, requiring extensive memory and bandwidth [2]. Superconducting electronics (SCE) (targeted towards space applications, and high-performance computing) outperforms the conventional CMOS counterparts in terms of speed and energy-efficiency (Fig. 1(c)) [3]. Decades of research efforts have given rise to three major categories (and several sub-variants) of cryo-memories based on SC, non-SC, and hybrid technologies (Fig. 2) [2], [4]–[6]. However, the existing variants suffer from one or more of the following challenges - (i) limited scalability, (ii) process complexity, (iii) bulky peripherals, (iv) array-level interference, (v) volatility, and (vi) speed incompatibility. Therefore, a scalable cryo-memory system remains elusive. To address these existing issues, here, we present a novel cryo-memory system utilizing -(i) the polarization-induced Cooper-pair [7] modulation in a ferroelectric$(FE)$superconducting quantum interference device (SQUID) (Fig. 3(a)) [8], and (ii) current controlled$SC\leftrightarrow non-SC$switching in a heater cryotron$(hTron)$(Fig. 4) [4]. Discrete prototypes of these devices have been demonstrated recently, but their coupled interactions (which we harness in our work) were never explored before.

DOI
10.1109/drc55272.2022.9855813

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Cryogenic (cryo) memory devices, designed to operate at/below 4 Kelvin (K) temperature, is a prime enabler of practical quantum computing systems, and superconducting (SC) electronic platforms (Figs. 1(a), (b)) [1]. The state-of-the-art quantum algorithms require many arbitrary rotations which demand a large memory to store program instructions [2]. SC qubits (used in most of the existing quantum computing systems) are highly sensitive to noise and hence, to protect the qubit states from thermal disturbances, they are placed at a few milli-Kelvin (mK) temperature. Furthermore, to preserve the integrity of the quantum states, the SC qubits undergo continuous error correction schemes, requiring extensive memory and bandwidth [2]. Superconducting electronics (SCE) (targeted towards space applications, and high-performance computing) outperforms the conventional CMOS counterparts in terms of speed and energy-efficiency (Fig. 1(c)) [3]. Decades of research efforts have given rise to three major categories (and several sub-variants) of cryo-memories based on SC, non-SC, and hybrid technologies (Fig. 2) [2], [4]–[6]. However, the existing variants suffer from one or more of the following challenges - (i) limited scalability, (ii) process complexity, (iii) bulky peripherals, (iv) array-level interference, (v) volatility, and (vi) speed incompatibility. Therefore, a scalable cryo-memory system remains elusive. To address these existing issues, here, we present a novel cryo-memory system utilizing -(i) the polarization-induced Cooper-pair [7] modulation in a ferroelectric(FE)(FE)(FE)superconducting quantum interference device (SQUID) (Fig. 3(a)) [8], and (ii) current controlledSC↔non−SCSC\leftrightarrow non-SCSC↔non−SCswitching in a heater cryotron(hTron)(hTron)(hTron)(Fig. 4) [4]. Discrete prototypes of these devices have been demonstrated recently, but their coupled interactions (which we harness in our work) were never explored before.
Ferroelectric Superconducting Quantum Interference Devices (Fe-SQUIDs) have recently gained attention as a transformative technology for superconducting computing, offering voltage-controlled switching that is essential for large-scale digital circuits. This unique technology has the potential to drive advancements in cryogenic computing by enabling scalable memory systems and voltage-controlled logic circuits. These innovations are critical for the realization of large-scale quantum computers and hold significant promise for high-performance computing and space exploration. In this article, we explore how Fe-SQUIDs, integrated with heater cryotrons (hTrons), can be harnessed to develop key components of computing systems. These include non-volatile memory, voltage-controlled logic circuits, in-memory matrix-vector multiplication systems, and ternary content-addressable memory. We also examine how changes in the key characteristics of Fe-SQUIDs and hTrons influence the performance of these applications, providing insights into the design and optimization of next-generation superconducting hardware.
Cryogenic (cryo) memory blocks are envisioned to be crucial components for - (i) scalable quantum computing systems with> 1000 qubits [1], and (ii) superconducting (SC) single flux quantum (SFQ) systems [2]. Decades of research has led to a whole host of cryo-memory variants (SC, non-SC, and hybrid), and more are being actively explored. Despite having such massive interest in the search for cryo-storage solutions, the design possibilities for compatible sense amplifiers (SA) remain largely unexplored. The existing approaches for cryogenic sensing are mostly agnostic to the unique properties of the memory array [3]–[5]. For example, the recently proposed SC and twistronic memories promise seamless compatibility with the cryogenic processors in terms of speed, power, and temperature range [4]–[7]. However, they rely on current-driven read operation, and necessitate voltage-based sensing. Therefore, a current-based cryo-SA [3] cannot be used for these emerging cryo-memory variants. In this work, we propose a voltage sense amplifier (VSA) for cryogenic memories utilizing the Josephson junction field effect transistor (JJFET) [8] as the primary component, and the heater cryotron (hTron) [4], [9] as an auxiliary entity. We exploit their coupled interactions to sense ultra-low (< 1 mV) voltage difference (customary for many cryo-memory technologies [4]–[7]) between the binary memory states (0/1) at/below 4 Kelvin temperature.
The recent progress in quantum computing and space exploration led to a surge in interest in cryogenic electronics. Superconducting devices such as Josephson junction, Josephson field effect transistor, cryotron, and superconducting quantum interference device (SQUID) are traditionally used to build cryogenic logic gates. However, due to the superconducting nature, gate-voltage-based control of these devices is extremely difficult. Even more challenging is to cascade the logic gates because most of these devices require current bias for their operation. Therefore, these devices are not as convenient as the semiconducting transistors to design logic gates. Here, to overcome these challenges, we propose a ferroelectric SQUID (FeSQUID) based voltage-controlled logic gates. FeSQUID exhibits two different critical current levels for two different voltage-switchable polarization states of the ferroelectric. We utilize the polarization-dependent (hence, voltage-controllable) superconducting to resistive switching of FeSQUID to design Boolean logic gates such as Copy, NOT, AND, and OR gates. The operations of these gates are verified using a Verilog-A-based compact model of FeSQUID. Finally, to demonstrate the fanning out capability of FeSQUID-based logic family, we simulate a two-input XOR gate using FeSQUID-based NOT, AND, and OR gates. Together with the ongoing progress on FeSQUID-based non-volatile memory, our designed FeSQUID-based logic family will enable all FeSQUID-based cryogenic computer, ensuring minimum mismatch between logic and memory blocks in terms of speed, power consumption, and fabrication process.
Superconducting (SC) electronics (SCE) is one of the major requirements to develop a large-scale practical quantum computing system. (Figs. 1(a)) [1]. Currently, a room temperature conventional computer is used as the control processor which requires a huge number of lossy interconnects to connect with the qubits placed at a few millikelvin temperatures. This, in turn, limits the scalability of the quantum computing system up to hundreds of qubits which is not enough to achieve the full potential [2]. Therefore, along with a suitable cryogenic memory, a cryogenic (preferably superconducting) control processor is required to develop a quantum computing system with thousands of qubits. Moreover, SCE offers ultra-fast (hundreds of gigahertz) and highly energy efficient (sub attojoule/bit) performance [3]. Therefore, SCE is projected to achieve the department of energy (DOE) exascale goal which the conventional supercomputers failed to achieve (Fig. 1(b)) [4]. However, Josephson junction-based SC circuits suffer from limited integration density due to flux trapping, difficulty in driving large impedances, fanning out digital signals, and operating in noisy environments [5]. To address these existing issues, here, we present a novel reconfigurable SC logic circuit using a nano-cryotron (nTron) that can perform 1-input copy, 2-input AND and OR, and 3-input majority logic functionalities. This work can enable the implementation of highly scalable and energy-efficient SC processor since the use of only one device. To achieve the reconfigurable nature of the logic circuit, we utilize the multi-gate switching of nTron.
Superconducting electronics are among the most promising alternatives to conventional CMOS technology, thanks to the ultra-fast speed and ultra-high energy efficiency of the superconducting devices. Having a cryogenic control processor is also a crucial requirement for scaling the existing quantum computers up to thousands of qubits. Despite showing outstanding speed and energy efficiency, Josephson junction-based circuits suffer from several challenges such as flux trapping leading to limited scalability, difficulty in driving high impedances, and so on. Three-terminal cryotron devices have been proposed to solve these issues, which can drive high impedances (>100 kΩ) and are free from any flux trapping issue. In this work, we develop a reconfigurable logic circuit using a heater cryotron (hTron). In conventional approaches, the number of devices to perform a logic operation typically increases with the number of inputs. However, here, we demonstrate a single hTron device-based logic circuit that can be reconfigured to perform 1-input copy and NOT, 2-input AND and OR, and 3-input majority logic operations by choosing suitable biasing conditions. Consequently, we can perform any processing task with a much smaller number of devices. Also, since we can perform different logic operations with the same circuit (same layout), we can develop a camouflaged system where all the logic gates will have the same layout. Therefore, this proposed circuit will ensure enhanced hardware security against reverse engineering attacks.
The core of a quantum computer is a quantum processor, which is composed of quantum bits (qubits). Qubits can be implemented in many flavors, but they are fragile, and their state has a tendency to decay in time. To be usable for computation, qubits must be corrected in real time by a classical controller. The controller must also see that desired computations are executed. Today, the control of qubits is performed at room temperature (RT) by racks of instruments, while the qubits operate at several tens of milli-Kelvin. To ensure compactness and, eventually, scalability, we have proposed and implemented CMOS circuits designed to operate at a few degrees Kelvin. This makes complex thermalization circuits unnecessary, potentially enabling superconductive interconnects, which would enable virtually zero resistance and low thermal conductivity. Cryogenic CMOS, or cryo-CMOS, technology was chosen to achieve classical control due to its scalable nature and overall miniaturization opportunities. Cryo-CMOS circuits and systems need to be carefully designed to ensure strict power budgets, while achieving quite advanced specifications in terms of noise and bandwidth. We review the requirements of a classical controller and cryo-CMOS circuits and systems developed for spin qubits in our lab. Results and perspectives are presented with a discussion about a road map for the future.