Related papers: Sampling of globally depolarized random quantum ci…
Output probability distributions of several sub-universal quantum computing models cannot be classically efficiently sampled unless some unlikely consequences occur in classical complexity theory, such as the collapse of the polynomial-time…
A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer,…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
Quantum Supremacy is a demonstration of a computation by a quantum computer that can not be performed by the best classical computer in a reasonable time. A well-studied approach to demonstrating this on near-term quantum computers is to…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling, that is beyond the practical reach of modern supercomputers. We examine the…
Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…
Results on the hardness of approximate sampling are seen as important stepping stones towards a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include…
A critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB…
It is known that several sub-universal quantum computing models, such as the IQP model, the Boson sampling model, the one-clean qubit model, and the random circuit model, cannot be classically simulated in polynomial time under certain…
We introduce a new family of quantum circuits in Continuous Variables and we show that, relying on the widely accepted conjecture that the polynomial hierarchy of complexity classes does not collapse, their output probability distribution…
A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers,…
Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical…
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…
Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$, how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately,…
Recent work by Bravyi, Gosset, and Koenig showed that there exists a search problem that a constant-depth quantum circuit can solve, but that any constant-depth classical circuit with bounded fan-in cannot. They also pose the question: Can…
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy…