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International Conference on Solid State Devices and Materials (SSDM)

Large-Scale Quantum Computing Emulation Based on Unitary Macro-Operations

Yosuke Goto, Minoru Fujishima

Published Sep 18, 2007• 0 citations
Publisher
DOI
10.7567/ssdm.2006.c-3-1

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Quantum computing has attracted many research studies to solve non-deterministic polynomial (NP) problems at high speed. However, large-scale quantum computing has not been realized yet. In this study, a new emulation method is proposed, where qubits are replaced with classical bits that use unitary macro-operations, which are a combination of quantum operations at the principal stage of the quantum computing process for executing several-hundred-qubit operations in a large-scale emulation. As a result, a quantum computing emulator has been successfully fabricated, and a 64-bit factorization was demonstrated with only 40 kbits of classical memory, where 320 qubits are required with Shor's algorithm in a quantum computer.
In this paper we present a novel approach to emulating a universal quantum computer with a classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any modality (e.g., acoustic, electromagnetic, etc), but we focus our discussion here on electronic signals. Unitary gate operations are performed using analog electronic circuit devices, such as four-quadrant multipliers, operational amplifiers, and analog filters, although non-unitary operations may be performed as well. In this manner, the Hilbert space structure of the quantum state, as well as a universal set of gate operations, may be fully emulated classically. The required bandwidth scales exponentially with the number of qubits, however, thereby limiting the scalability of the approach, but the intrinsic parallelism, ease of construction, and classical robustness to decoherence may nevertheless lead to capabilities and efficiencies rivaling that of current high performance computers.
To emulate a quantum computation on a classical computer i.e. the evolution of the unitary operations on the wave function of the particle in quantum mechanics, we have to perform unitary matrix and normalized vector multiplications in the high-level programming languages of Python, C++, Java, etc. Quantum Libraries already available perform the matrix-vector multiplication in the backend using the numpy libraries of Python like Qiskit or use a C++ wrapper to further optimize the runtime it as in Qiskit-Aer Simulators. Since a fully functioning fault-tolerant computer is decades away, it is in our best interest to design new quantum algorithms and develop accelerator test beds for Quantum Emulations. All the quantum computer operations can be emulated on a classical computer, with the only downside being that the matrix multiplications scale up as O (N3) in runtime. In contrast, the quantum computer scales it up as O (N2log2N), where N = 2n, where N is the matrix dimension, where n is the number of qubits, so the runtime for quantum emulations on the classical computer increases exponentially with increase in number of qubits and increases linearly with increase in number of depths, complexity wise. Though it is not possible to change the exponential index, it is possible to reduce the runtime for quantum emulations on classical computers by use of GPU and Alveo Accelerator Cards, and also code optimization on the software side like using a C++ wrapper. In this paper, we will benchmark the matrix-matrix multiplications on HPC Accelerator Cards varying the qubit size and the depth of the quantum circuit and provide a universal mathematical equation for the runtime on the GPU and Alveo Vector Cards for two variables of qubit size and quantum circuit depth. So a theoretical limit on qubit size and qubit depth exactly can be established for quantum emulations on present classical supercomputers.