Related papers: The hardness of quantum spin dynamics
Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is…
Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce…
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial…
The fundamental principles of quantum mechanics, such as its probabilistic nature, allow for the theoretical ability of quantum computers to generate statistically random numbers, as opposed to classical computers which are only able to…
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…
One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
Since the advent of quantum mechanics, classical probability interpretations have faced significant challenges. A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of…
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…
We study the classical complexity of the exact Boson Sampling problem where the objective is to produce provably correct random samples from a particular quantum mechanical distribution. The computational framework was proposed by Aaronson…
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.…
Quantum supremacy is the ability of quantum processors to outperform classical computers at certain tasks. In digital random quantum circuit approaches for supremacy, the output distribution produced is described by the Porter-Thomas (PT)…
Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically…
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…
We introduce a quantum algorithm for efficient biased sampling of the rare events generated by classical memoryful stochastic processes. We show that this quantum algorithm gives an extreme advantage over known classical biased sampling…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical…
Sampling from probability distributions of quantum circuits is a fundamentally and practically important task which can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In the present work, we examine…
We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater…