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IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP)

Improving Emulation of Quantum Algorithms using Space-Efficient Hardware Architectures

Naveed Mahmud, Esam El‐Araby

Published Jul 1, 2019• 2 citations
Publisher

Abstract

With rapid advancement in quantum computing technology, continuous efforts are being directed to simulation and emulation of quantum algorithms on classical platforms. A well-known limitation to classical emulation of quantum circuits is scalability. Existing hardware emulators implement gate-based circuit models of quantum circuits that result in heavy resource utilization and degrade the scalability of the system. Also, current quantum emulation hardware use fixedpoint arithmetic, which has an adverse effect on accuracy when the system is scaled up. In this work, we employ a complexmultiply-and-accumulate (CMAC) and lookup-based emulation approach that greatly reduces resource utilization and improves system scalability in terms of number of emulated qubits. We demonstrate emulation of up to 16 fully-entangled qubits which is highest among existing work. We design fully-pipelined, highthroughput hardware architectures that use floating-point precision for higher accuracy. Experimental evaluation and analysis of the architectures in terms of speed and area is also provided. The emulator is prototyped on a high-performance reconfigurable computing (HPRC) system and our results demonstrate quantitative improvement over existing Field-Programmable-Gate-Array (FPGA)-based hardware emulators.

DOI
10.1109/asap.2019.000-1

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With rapid advancement in quantum computing technology, continuous efforts are being directed to simulation and emulation of quantum algorithms on classical platforms. A well-known limitation to classical emulation of quantum circuits is scalability. Existing hardware emulators implement gate-based circuit models of quantum circuits that result in heavy resource utilization and degrade the scalability of the system. Also, current quantum emulation hardware use fixedpoint arithmetic, which has an adverse effect on accuracy when the system is scaled up. In this work, we employ a complexmultiply-and-accumulate (CMAC) and lookup-based emulation approach that greatly reduces resource utilization and improves system scalability in terms of number of emulated qubits. We demonstrate emulation of up to 16 fully-entangled qubits which is highest among existing work. We design fully-pipelined, highthroughput hardware architectures that use floating-point precision for higher accuracy. Experimental evaluation and analysis of the architectures in terms of speed and area is also provided. The emulator is prototyped on a high-performance reconfigurable computing (HPRC) system and our results demonstrate quantitative improvement over existing Field-Programmable-Gate-Array (FPGA)-based hardware emulators.
Quantum algorithms can be efficiently emulated on classical hardware such as field programmable gate arrays (FPGAs), achieving significant speedup over software simulations. However, the increase in the required hardware resources for emulating quantum systems becomes a critical limitation as the number of qubits is increased. In this paper, we propose a scalable emulation framework for modeling quantum algorithms on FPGAs that employs efficient resource scheduling such as space and space-time scheduling. In addition, full floating point precision arithmetic and dataflow non-linear (dynamic) pipelining are also used to achieve higher accuracy and higher throughput. We propose scalable and optimized hardware architectures for Quantum Fourier Transform (QFT) and Grover's search algorithm and demonstrate the scalability of our framework by scaling the system up to 5 fully-entangled qubits. A multi-node (multi-FPGA), state-of-the-art high-performance reconfigurable computer (HPRC) was used for implementation of the proposed architectures. Our experimental results show that by employing efficient resource scheduling techniques, the hardware resource constraints could be mitigated and the proposed emulation framework could be made feasible for emulation of more complex, larger-scale quantum algorithms while maintaining higher accuracy and throughput than existing work.
The general approach for emulating quantum algorithms on classical platforms has been through representing them as gate-based quantum circuits. However, direct implementation of quantum circuits significantly increases the hardware resource utilization and system latency of classical emulators. In this paper, we investigate multiple implementation models alternative to conventional emulation approaches, as feasible solutions to the scalability problem in classical emulation of quantum circuits. In the first model, the quantum circuit functionality is reduced to equivalent, arithmetic (multiply-and-accumulate) operations and combined with two computation methods, based on lookup and dynamic generation. In the second model, a kernel operation is extracted from the quantum circuit based on its functionality, and the kernel is iterated through all input quantum states. The proposed emulation models provide space and time optimizations, significantly reducing resource utilizations and latencies and improving scalability. We use these models to develop a highly scalable hardware emulator that is based on reconfigurable technology for efficient simulations of full quantum algorithms and circuits. Our hardware implementations support single precision floating point arithmetic for improved accuracy, and contain fully pipelined designs for high throughput. We investigate quantum algorithms such as quantum Fourier transform and quantum wavelet transform and explore different hardware architectures and optimizations. Experimental results and analysis are provided for the architectures in terms of resource consumption and emulation time. The experiments are carried out on a high-performance reconfigurable computing system and the obtained results show that the proposed emulator is feasible for running and testing a variety of quantum algorithms.
Quantum hardware emulators using field programmable gate arrays (FPGAs) have been demonstrated to efficiently exploit the inherent parallelism of quantum algorithms and perform better than sequential software simulators. However, one key problem in mapping quantum circuits on FPGAs is the exponential increase in resource requirements with the increase in the number of quantum bits (qubits). As a result, the precision of hardware emulators is often reduced to save resources and accommodate larger quantum circuits which results in lower accuracy and lower throughput. In this paper, we present a full precision FPGA quantum emulator that uses 32-bit floating-point arithmetic and has a fully pipelined architecture. Our emulator is capable of emulating an entangled 4-qubit quantum system performing Quantum Fourier Transform, Grover's Search algorithms on a single FPGA node. Our experimental work was conducted on a highly scalable multi-node (multi-FPGA) state-of-the-art high-performance reconfigurable computer (HPRC). Experimental results show that our emulator is functionally accurate and has a higher operating frequency relative to other emulators. For emulating larger-scale circuits we propose using a multi-node architecture scheme with low latency, high bandwidth inter-node communication.
Hardware emulation of quantum systems can mimic more efficiently the parallel behaviour of quantum computations, thus allowing higher processing speed-up than software simulations. In this paper, an efficient hardware emulation method that employs a serial-parallel hardware architecture targeted for field programmable gate array (FPGA) is proposed. Quantum Fourier transform and Grover’s search are chosen as case studies in this work since they are the core of many useful quantum algorithms. Experimental work shows that, with the proposed emulation architecture, a linear reduction in resource utilization is attained against the pipeline implementations proposed in prior works. The proposed work contributes to the formulation of a proof-of-concept baseline FPGA emulation framework with optimization on datapath designs that can be extended to emulate practical large-scale quantum circuits.
Contemporary quantum computers face many critical challenges that limit their usefulness for practical applications. A primary limiting factor is classical-to-quantum (C2Q) data encoding, which requires specific circuits for quantum state initialization. The required state initialization circuits are often complex and violate decoherence constraints, particularly for I/O intensive applications. Existing Noisy Intermediate-Scale Quantum (NISQ) devices are noise-sensitive and have low quantum bit (qubit) counts, thus limiting the applicability of C2Q circuits for encoding large and realistic datasets. This has made the study of complete and realistic circuits that include data encoding challenging and has also led to a heavy dependency on costly and resource-intensive simulations on classical platforms. In this work, we propose a cost-effective, classical-hardware-accelerated framework for realistic and complete emulation of quantum algorithms. The emulation framework incorporates components for the critical C2Q data encoding process, as well as architectures for quantum algorithms such as the quantum Haar transform (QHT). The framework is used to investigate optimizations for C2Q and QHT algorithms, and the corresponding optimized quantum circuits are presented. The framework is implemented on a High-Performance Reconfigurable Computer (HPRC) which emulates the proposed QHT circuits combined with proposed C2Q data encoding methods. For performance benchmarks, CPU-based emulations and simulations on a state-of-the-art quantum computing simulator are also carried out. Results show that the proposed hardware-accelerated emulation framework is more efficient in terms of speed and scalability compared to CPU-based emulation and simulation.
Quantum computers are regarded as the future of computing, as they are believed to be capable of solving extremely complex problems that are intractable on conventional digital computers. However, near-term quantum computers are prone to a plethora of noise sources that are difficult to mitigate, possibly limiting their scalability and precluding us from running any useful algorithms. Quantum emulation is an alternative approach that uses classical analog hardware to emulate the properties of superposition and entanglement, thereby mimicking quantum parallelism to attain similar speeds. By contrast, the use of classical digital hardware, such as field programmable gate arrays (FPGA), is less inefficient at emulating a quantum computer, as it does not take advantage of the fundamentally analog nature of quantum states. Consequently, this approach adds an inherent hardware overhead that also prevents scaling. In this work, an energy-efficient quantum emulator based on analog circuits realized in UMC 180-nm CMOS technology is proposed along with the design methodologies for a scalable computing architecture. A six-fold improvement in power consumption was observed over the FPGA-based approach for a ten-qubit emulation of Grover's search algorithm. The proposed emulator is also about 400 times faster than a Ryzen 5600x six-core processor performing a simulation of six-qubit Grover's search algorithm