相关论文: Clifford Circuits Augmented Grassmann Matrix Produ…

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…

We introduce an exact mapping of Clifford (stabilizer) random tensor networks (RTNs) and monitored quantum circuits, onto a statistical mechanics model. With Haar unitaries, the fundamental degrees of freedom ('spins') are permutations…

Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…

We present a tensor-network approach for the strong-coupling expansion of two-dimensional QCD with staggered quarks at non-zero chemical potential. After expanding the Boltzmann factor in the gauge and fermion actions, all gauge fields can…

We propose a new framework of topological complexity to study the computational complexity of quantum circuits and tensor networks. Within this framework, we establish the Quon Classical Simulation (QCS) for hybrid Clifford-Matchgate…

Hamiltonian simulation is a key quantum algorithm for modeling complex systems. To implement a Hamiltonian simulation, it is typically decomposed into a list of Pauli strings, each corresponds to an RZ rotation gate with many Clifford…

We consider a fermionic system for which there exist a single-reference configuration-interaction (CI) expansion of the ground state wave function that converges, albeit not necessarily rapidly, with respect to excitation number. We show…

Since quantum computing is currently in the NISQ-Era, compilation strategies to reduce the number of gates executed on specific hardware are required. In this work, we utilize the concept of synthesis of a data structure called Clifford…

We review the basic ideas of the Tensor Renormalization Group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent…

We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a…

Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents' approximation. The utility of such robust…

The conventional circuit paradigm, utilizing a limited number of gates to construct arbitrary quantum circuits, is hindered by significant noise overhead. For instance, the standard gate paradigm employs two CNOT gates for the partial…

Variational Quantum Algorithms are promising candidates for near-term quantum computing, yet they face scalability challenges due to barren plateaus, where gradients vanish exponentially relative to system size. Recent conjectures suggest…

Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…

Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…

We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum…

Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum…

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…

We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…

Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…