Related papers: Quantum supremacy and hardness of estimating outpu…
As Moore's law reaches its limits, quantum computers are emerging with the promise of dramatically outperforming classical computers. We have witnessed the advent of quantum processors with over $50$ quantum bits (qubits), which are…
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…
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…
Noise is the defining feature of the NISQ era, but it remains unclear if noisy quantum devices are capable of quantum speedups. Quantum supremacy experiments have been a major step forward, but gaps remain between the theory behind these…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
We consider the hardness of computing additive approximations to output probabilities of random quantum circuits. We consider three random circuit families, namely, Haar random, $p=1$ QAOA, and random IQP circuits. Our results are as…
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…
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…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we…
Near-term feasibility, classical hardness, and verifiability are the three requirements for demonstrating quantum advantage; most existing quantum advantage proposals achieve at most two. A promising candidate recently proposed is through…
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…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy"…
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,…
Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of…
Recent experiments completed by collaborating research groups from Google, NASA Ames, UC Santa Barbara, and others provided compelling evidence that quantum supremacy has finally been achieved on a superconducting quantum processor. The…
Estimating the entropy of probability distributions and quantum states is a fundamental task in information processing. Here, we examine the hardness of this task for the case of probability distributions or quantum states produced by…
The recent paper [F. Arute et al. Nature {\bf 574}, 505 (2019)] considered exact classical sampling of the output probability distribution of the globally depolarized random quantum circuit. In this paper, we show three results. First, we…