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This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
Quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, and machine-learning applications. However, to capitalize on those promises, complex design flows composed of…
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.…
Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. Yet the most interesting systems are often complex, such that simulating their…
As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can…
In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine.…
Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
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…
Quantum coherence allows for reduced-memory simulators of classical processes. Using recent results in single-shot quantum thermodynamics, we derive a minimal work cost rate for quantum simulators that is quasistatically attainable in the…
Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily…
This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences…
Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle…
The use of $d$-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Molecular Nanomagnets are ideal spin systems to…
We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In…
We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of…
We prove that quantum Turing machines are strictly superior to probabilistic Turing machines in function computation for any space bound $ o(\log(n)) $.
We show that certain computational algorithms can be simulated on a quantum computer with exponential efficiency and be insensitive to phase errors. Our explicit algorithm simulates accurately the classical chaotic dynamics for…
Today, people are looking forward to get an awesome computational power. This kind of desire can be answered by quantum computing. By adopting quantum mechanics theory, it can generate a very fast computation result. As known, quantum…