Related papers: Simulating quantum circuits using tree tensor netw…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…
Circuit optimization is a fundamental task for practical applications of near-term quantum computers. In this work we address this challenge through the powerful lenses of tensor network theory. Our approach involves the full…
Classical simulations of quantum circuits are vital for assessing potential quantum advantage and benchmarking devices, yet they require sophisticated methods to avoid the exponential growth of resources. Tensor network approaches, in…
Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
In the framework of quantum computational tensor network [D. Gross and J. Eisert, Phys. Rev. Lett. {\bf98}, 220503 (2007)], which is a general framework of measurement-based quantum computation, the resource many-body state is represented…
Tensor network methods are incredibly effective for simulating quantum circuits. This is due to their ability to efficiently represent and manipulate the wave-functions of large interacting quantum systems. We describe the challenges faced…
We present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a…
As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…
CNOT circuits are a common building block of general quantum circuits. The problem of synthesizing and optimizing such circuits has received a lot of attention in the quantum computing literature. This problem is especially challenging for…
We present a practical course targeting graduate students with prior knowledge of the basics of quantum computing. The practical aims to deepen students' understanding of fundamental concepts in quantum computing by implementing quantum…
The ability to selectively measure, initialize, and reuse qubits during a quantum circuit enables a mapping of the spatial structure of certain tensor-network states onto the dynamics of quantum circuits, thereby achieving dramatic resource…
We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…
A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological…
Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient…
We present a classical protocol, using the matrix product state representation, to simulate cluster-state quantum computation at a cost polynomial in the number of qubits in the cluster and exponential in d -- the width of the cluster. We…