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We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
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…
The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient…
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…
Classical simulations of quantum circuits are limited in both space and time when the qubit count is above 50, the realm where quantum supremacy reigns. However, recently, for the low depth circuit with more than 50 qubits, there are…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Optimization of circuits is an essential task for both quantum and classical computers to improve their efficiency. In contrast, classical logic optimization is known to be difficult, and a lot of heuristic approaches have been developed so…
Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…
We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum…
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…
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and…
Despite the rapid development of quantum computing these years, state-of-the-art quantum devices still contain only a very limited number of qubits. One possible way to execute more realistic algorithms in near-term quantum devices is to…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Quantum computers allow a near-exponential speed-up for specific applications when compared to classical computers. Despite recent advances in the hardware of quantum computers, their practical usage is still severely limited due to a…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Digital quantum simulation is a promising application for quantum computers. Their free programmability provides the potential to simulate the unitary evolution of any many-body Hamiltonian with bounded spectrum by discretizing the time…