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arXiv:1211.4086 · Journal of Physics Conference Series

A multiprecision C++ library for matrix-product-state simulation of quantum computing: Evaluation of numerical errors

Akira SaiToh

Published Aug 12, 2013• 6 citations
arXivHTMLPDF

Abstract

The time-dependent matrix-product-state (TDMPS) simulation method has been used for numerically simulating quantum computing for a decade. We introduce our C++ library ZKCM_QC developed for multiprecision TDMPS simulations of quantum circuits. Besides its practical usability, the library is useful for evaluation of the method itself. With the library, we can capture two types of numerical errors in the TDMPS simulations: one due to rounding errors caused by the shortage in mantissa portions of floating-point numbers; the other due to truncations of nonnegligible Schmidt coefficients and their corresponding Schmidt vectors. We numerically analyze these errors in TDMPS simulations of quantum computing.

DOI
10.1088/1742-6596/454/1/012064

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The time-dependent matrix-product-state (TDMPS) simulation method has been used for numerically simulating quantum computing for a decade. We introduce our C++ library ZKCM_QC developed for multiprecision TDMPS simulations of quantum circuits. Besides its practical usability, the library is useful for evaluation of the method itself. With the library, we can capture two types of numerical errors in the TDMPS simulations: one due to rounding errors caused by the shortage in mantissa portions of floating-point numbers; the other due to truncations of nonnegligible Schmidt coefficients and their corresponding Schmidt vectors. We numerically analyze these errors in TDMPS simulations of quantum computing.
The time-dependent matrix-product-state (TDMPS) simulation method has been known as one of fast simulation methods to study time-evolving quantum systems. Here, I report recent development of my open-source C++ library named ZKCM QC designed for TDMPS simulations of quantum circuits with arbitrary floating-point precision. Simulation performance is reported for well-known quantum algorithms. In addition, it is numerically shown that a trust-worthy simulation should be performed in multiprecision and should not involve truncations of nonzero Schmidt coefficients.
Recent improvements in the ZKCM and ZKCM_QC libraries are presented in this announcement. ZKCM was released as a C++ library for multiprecision matrix computation and ZKCM_QC was developed as its extension for matrix-product-state (MPS) simulation of quantum circuits. Their parallel processing extensions using OpenMP and CUDA were briefly reported in a previous contribution [A. SaiToh, to appear in Proc. CCP2023]. Here, their most recent developments are reported, which include the employments of advanced FFT and Moore-Penrose inverse routines.
Recent improvements in the ZKCM and ZKCM_QC libraries are presented in this announcement. ZKCM was released as a C++ library for multiprecision matrix computation and ZKCM_QC was developed as its extension for matrix-product-state (MPS) simulation of quantum circuits. Their parallel processing extensions using OpenMP and CUDA were briefly reported in a previous contribution [A. SaiToh, to appear in Proc. CCP2023]. Here, their most recent developments are reported, which include the employments of advanced FFT and Moore-Penrose inverse routines.
Simulating quantum error correction (QEC) circuits including non-Clifford gates at scale is important to accelerate progress toward fault-tolerant quantum computing. Here we demonstrate that matrix product state (MPS) techniques can handle many QEC circuits exactly and without restriction on gate types. Crucially, we find that MPS efficiency depends sensitively on implementation choices, and we introduce a series of targeted optimizations that reduce bond dimensions and simulation time by several orders of magnitude compared to naive approaches. We illustrate this with examples including: (a) a rotated surface code quantum memory up to distance 11, (b) logical Bell-state preparation up to distance 9, (c) a 15-to-1 magic-state distillation circuit including hundreds of QEC rounds that we optimize to be simulated with only 11 logical qubits (187 physical qubits) and a maximal bond dimension of 64 in under 40 seconds, and (d) a narrow, deep random circuit that scales linearly with the number of T gates. These results demonstrate the importance of circuit-level optimizations and position MPS as a valuable complement to near-Clifford simulators for QEC circuits.
QwaveMPS is an open-source Python library for simulating one-dimensional quantum many-body waveguide systems using matrix product states (MPS). It provides a user-friendly interface for constructing, evolving, and analyzing quantum states and operators, facilitating studies in quantum physics and quantum information with waveguide-QED systems. This approach enables efficient, scalable simulations by focusing computational resources on the most relevant parts of the quantum system. Thus, one can study a wide range of complex dynamical interactions, including time-delayed feedback effects in the non-Markovian regime and deeply nonlinear systems, at a highly reduced computational cost compared to full Hilbert space approaches, making it both practical and convenient to model a variety of open waveguide-QED systems (in Markovian and non-Markovian regimes), treating quantized atoms and quantized photons on an equal footing. The QwaveMPS package automates the waveguide-QED-specific tensor-network operations, including construction of the time-bin evolution operator from physical parameters, the swap network required for delayed interactions, orthogonality-center and truncation management, the matrix-product factorization of NNN-photon Fock-state inputs, and the evaluation of single-time and two-time field observables (such as the second-order quantum correlation function) at chosen points along the waveguide.
A C++ library, named ZKCM, has been developed for the purpose of multiprecision matrix calculations, which is based on the GNU MP and MPFR libraries. It is especially convenient for writing programs involving tensor-product operations, tracing-out operations, and singular-value decompositions. Its extension library, ZKCM_QC, for simulating quantum computing has been developed using the time-dependent matrix-product-state simulation method. This report gives a brief introduction to the libraries with sample programs.