相关论文: Simulating quantum computation by contracting tens…
Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…
We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected…
A general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more…
We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement is bounded for any bipartite split along an edge of the tree. This is achieved by expanding the {\em time-evolving block decimation}…
Classical simulation of quantum circuits is a critical tool for validating quantum hardware and probing the boundary between classical and quantum computational power. Existing state-of-the-art methods, notably tensor network approaches,…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size $n^{O(1)}$ and treewidth $O(\log^i n)$ can be simulated by a…
We show that any quantum circuit of treewidth $t$, built from $r$-qubit gates, requires at least $\Omega(\frac{n^{2}}{2^{O(r\cdot t)}\cdot \log^4 n})$ gates to compute the element distinctness function. Our result generalizes a…
We show a similarity between two different classical simulation methods for measurement based quantum computation -- one relying on a low entanglement (tree tensor network) representation of the computer's state, and the other a tensor…
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…
Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…
In this paper, we study quantum algorithms for computing the exact value of the treewidth of a graph. Our algorithms are based on the classical algorithm by Fomin and Villanger (Combinatorica 32, 2012) that uses $O(2.616^n)$ time and…
Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a…
Simulation of quantum computing on supercomputers is a significant research topic, which plays a vital role in quantum algorithm verification, error-tolerant verification and other applications. Tensor network contraction based on density…
It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results…
Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN)…
The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly.…
It is not currently known if quantum Turing machines can efficiently simulate probabilistic computations in the space-bounded case. In this paper we show that space-bounded quantum Turing machines can efficiently simulate a limited class of…