Related papers: Anticoncentrated $n$-bit distribution from $\log(n…
While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote…
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…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
Random Number Generators are critical components of modern cryptosystems. Quantum Random Number Generators (QRNG) have emerged to provide high-quality randomness for these applications. Here we describe a scheme to extract random numbers…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
Gaussian Boson Sampling (GBS) generate random samples of photon-click patterns from a class of probability distributions that are hard for a classical computer to sample from. Despite heroic demonstrations for quantum supremacy using GBS,…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
Quantum algorithms have the ability to reduce runtime for executing tasks beyond the capabilities of classical algorithms. Therefore, identifying the resources responsible for quantum advantages is an interesting endeavour. We prove that…
Gaussian Boson Sampling (GBS) is a promising candidate for demonstrating quantum computational advantage and can be applied to solving graph-related problems. In this work, we propose Markov chain Monte Carlo-based algorithms to sample from…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
We describe quantum circuits with only $\widetilde{\cal O}(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary (e.g., molecular) orbitals. With ${\cal O}(\lambda / \epsilon)$…
The intrinsic random nature of quantum physics offers novel tools for the generation of random numbers, a central challenge for a plethora of fields. Bell non-local correlations obtained by measurements on entangled states allow for the…
Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be…
Fast quantum algorithms can solve important computational problems more efficiently than classical algorithms. However, little is known about whether quantum computing can speed up solving geometric problems. This article explores quantum…
We introduce an explicit construction for a key distribution protocol in the Quantum Computational Timelock (QCT) security model, where one assumes that computationally secure encryption may only be broken after a time much longer than the…
We introduce "holographic shadows", a new class of randomized measurement schemes for classical shadow tomography that achieves the optimal scaling of sample complexity for learning geometrically local Pauli operators at any length scale,…
In the development of quantum technologies, nonclassical states have been playing a pivotal role, as quantum advantage cannot be obtained without appropriate utilization of nonclassicality. In the present work, we consider a hybrid coherent…
In the past decades, Random Electrodynamics (also called Stochastic Electrodynamics) has been used to study the classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation. Random Electrodynamics (RED)…
One of the core challenges of research in quantum computing is concerned with the question whether quantum advantages can be found for near-term quantum circuits that have implications for practical applications. Motivated by this mindset,…
We consider the problem of decoding corrupted error correcting codes with NC$^0[\oplus]$ circuits in the classical and quantum settings. We show that any such classical circuit can correctly recover only a vanishingly small fraction of…