Related papers: From estimation of quantum probabilities to simula…
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…
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…
Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
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.…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine…
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
In breakthrough work, Bravyi, Gosset, and K\"{o}nig (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
Quantum simulations consist in the intentional reproduction of physical or unphysical models into another more controllable quantum system. Beyond establishing communication vessels between unconnected fields, they promise to solve complex…
We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient…
Simulating quantum systems using classical computing equipment has been a significant research focus. This work demonstrates that circuits as large and complex as the random circuit sampling (RCS) circuits published as a part of Google's…
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…
This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system…
One of the core research questions in the theory of quantum computing is to find out to what precise extent the classical simulation of a noisy quantum circuits is possible and where potential quantum advantages can set in. In this work, we…