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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…
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}…
The simulation of the spectra measured in nuclear magnetic resonance (NMR) spectroscopy experiments is a computationally non-trivial problem which, due to its natural interpretation as a quantum spin problem, maps in a straightforward way…
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.…
In this proof-of-concept paper we show that tensor product approach is efficient for control of large quantum systems, such as Heisenberg spin wires, which are essential for emerging quantum computing technologies. We compute optimal…
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…
Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently…
An application of quantum cloning to optimally interface a quantum system with a classical observer is presented, in particular we describe a procedure to perform a minimal disturbance measurement on a single qubit by adopting a 1->2…
The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to…
We demonstrate that a tensor product structure and optical analogy of quantum entanglement can be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using the classical analogy, we discuss…
This paper presents an efficient and scalable tensor network framework for quantum kernel circuit simulation, alleviating practical costs associated with increasing qubit counts and data size. The framework enables systematic large-scale…
Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them…
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 multi-step N->M probabilistic optimal universal cloning protocol is presented together with the experimental realization of the (1 -> 3) and (2 -> 3) machines. Since the present method exploits the bosonic nature of the photons,…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
A quantum processing unit (QPU) must contain a large number of high quality qubits to produce accurate results for problems at useful scales. In contrast, most scientific and industry classical computation workloads happen in parallel on…
A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli…
Circuit knitting offers a promising path to the scalable execution of large quantum circuits by breaking them into smaller sub-circuits whose output is recombined through classical postprocessing. However, current techniques face excessive…
We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix…