Related papers: Efficient Quantum Pseudorandomness from Hamiltonia…

This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…

While one-way functions (OWFs) serve as the minimal assumption for computational cryptography in the classical setting, in quantum cryptography, we have even weaker cryptographic assumptions such as pseudo-random states, and EFI pairs,…

Randomness is a fundamental feature of quantum mechanics, which is an invaluable resource for both classical and quantum technologies. Practical quantum random number generators (QRNG) usually need to trust their devices, but their security…

Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of…

We prove that recognizing the phase of matter of an unknown quantum state is quantum computationally hard. More specifically, we show that the quantum computational time of any phase recognition algorithm must grow exponentially in the…

Random circuit sampling (RCS) is a leading approach to demonstrate quantum advantage, with its believed classical hardness rooted in anticoncentration of output distributions and average-case hardness of probability estimation. Here we show…

One of the main challenges in the field of quantum simulation and computation is to identify ways to certify the correct functioning of a device when a classical efficient simulation is not available. Important cases are situations in which…

In this paper we explore the possibility of fundamental tests for coherent state optical quantum computing gates [T. C. Ralph, et. al, Phys. Rev. A \textbf{68}, 042319 (2003)] using sophisticated but not unrealistic quantum states. The…

As quantum computing matures into a practical paradigm, the need for secure and private quantum computation on untrusted hardware becomes increasingly urgent. While classical fully homomorphic encryption has enabled computation over…

This work focuses on optimizing the gates of a quantum circuit with a given topology to approximate the unitary time evolution governed by a Hamiltonian. Recognizing that unitary matrices form a mathematical manifold, we employ Riemannian…

The rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozen of qubits. This success poses a strong demand on efficient and reliable methods for characterization and…

Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…

We study the computational complexity of the Guided Local Hamiltonian problem: given a local Hamiltonian $H$ together with a classical description of a guiding state that has non-negligible overlap with the ground state of $H$, estimate the…

One of the most fundamental results in classical cryptography is that the existence of Pseudo-Random Generators (PRG) that expands $k$ bits of randomness to $k+1$ bits that are pseudo-random implies the existence of PRG that expand $k$ bits…

Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…

The technology of Quantum Computing (QC) is continuously evolving, as researchers explore new technologies and the public gains access to quantum computers with an increasing number of qubits. In addition, the research community and…

Common random string model is a popular model in classical cryptography. We study a quantum analogue of this model called the common Haar state (CHS) model. In this model, every party participating in the cryptographic system receives many…

This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…

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 propose a mechanism for reaching pseudorandom quantum states, computationally indistinguishable from Haar random, with shallow log-n depth quantum circuits, where n is the number of qudits. We argue that $\log n$ depth 2-qubit-gate-based…