Related papers: Quantum Proofs
We define a general formulation of quantum PCPs, which captures adaptivity and multiple unentangled provers, and give a detailed construction of the quantum reduction to a local Hamiltonian with a constant promise gap. The reduction turns…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
Motivated by notions of quantum heuristics and by average-case rather than worst-case algorithmic analysis, we define quantum computational advantage in terms of individual problem instances. Inspired by the classical notions of Kolmogorov…
One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…
We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the Consistency of Local Density…
The instantaneous quantum polynomial time model (or the IQP model) is one of promising models to demonstrate a quantum computational advantage over classical computers. If the IQP model can be efficiently simulated by a classical computer,…
Nuclear Magnetic Resonance (NMR) has provided a valuable experimental testbed for quantum information processing (QIP). Here, we briefly review the use of nuclear spins as qubits, and discuss the current status of NMR-QIP. Advances in the…
Zero-Knowledge (ZK) protocols have been intensely studied due to their fundamental importance and versatility. However, quantum information's inherent differences significantly alter the landscape, necessitating a re-examination of ZK…
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic…
$ \newcommand{\Xlin}{\mathcal{X}} \newcommand{\Zlin}{\mathcal{Z}} \newcommand{\C}{\mathbb{C}} $We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers,…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in…
Quantum information concepts and quantum technologies have opened the prospect to probe quantum gravity in table-top experiments. Many proposals rely on witnessing entanglement generation as a means to probe whether gravity is a quantum…
An overarching milestone of quantum machine learning (QML) is to demonstrate the advantage of QML over all possible classical learning methods in accelerating a common type of learning task as represented by supervised learning with…
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 information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical Quantum Information Processing (QIP) holds particular…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Quantum cloud computing is emerging as a popular model for users to experience the power of quantum computing through the internet, enabling quantum computing as a service. The question is, when the scale of the computational problems…
In known constructions of classical zero-knowledge protocols for NP, either of zero-knowledge or soundness holds only against computationally bounded adversaries. Indeed, achieving both statistical zero-knowledge and statistical soundness…
In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…