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Register a new userA multiprecision C++ library for matrix-product-state simulation of quantum computing: Evaluation of numerical errors
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Authors
Akira SaiToh
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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.
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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.
ZKCM is a C++ library developed for the purpose of multiprecision matrix computation, on the basis of the GNU MP and MPFR libraries. It provides an easy-to-use syntax and convenient functions for matrix manipulations including those often used in numerical simulations in quantum physics. Its extension library, ZKCM_QC, is developed for simulating quantum computing using the time-dependent matrix-product-state simulation method. This paper gives an introduction about the libraries with practical sample programs.
Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space and find accurate solutions. Here we propose a quantum inspired K-means clustering algorithm which first maps the classical data into quantum states represented as matrix product states, and then minimize the loss function using the variational matrix product states method in the enlarged space. We demonstrate the performance of this algorithm by applying it to several commonly used machine learning datasets and show that this algorithm could reach higher prediction accuracies and that it is less likely to be trapped in local minima compared to the classical K-means algorithm.
A quantum algorithm to simulate the real time dynamics of two-flavor massive Gross-Neveu model is presented in Schrodinger picture. We implement the simulation on a classic computer by applying the matrix product state representation. The real time evolutions of up to four particles on a site in initial state are figured out in space-time coordinate. The state evolutions are effectively affected by fermion mass and coupling constant of the model. Especially when the mass of fermion is small enough and the coupling is strong enough, the fundamental fermions evolve synchronistically in space from the two-fermion and four-fermion initial states. These are also the conditions on which the bound states made up of fundamental fermion pairs were found to arise automatically in the literatures.
We compare the efficiency of different matrix product state (MPS) based methods for the calculation of two-time correlation functions in open quantum systems. The methods are the purification approach [1] and two approaches [2,3] based on the Monte-Carlo wave function (MCWF) sampling of stochastic quantum trajectories using MPS techniques. We consider a XXZ spin chain either exposed to dephasing noise or to a dissipative local spin flip. We find that the preference for one of the approaches in terms of numerical efficiency depends strongly on the specific form of dissipation.
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