Related papers: How to Construct Random Unitaries
Pseudorandom unitaries (PRUs) are ensembles of efficiently implementable unitary operators that cannot be distinguished from Haar random unitaries by any quantum polynomial-time algorithm with query access to the unitary. We present a…
Pseudorandom unitaries (PRUs), one of the key quantum pseudorandom notions, are efficiently computable unitaries that are computationally indistinguishable from Haar random unitaries. While there is evidence to believe that PRUs are weaker…
We study the (in)feasibility of quantum pseudorandom notions in a quantum analog of the random oracle model, where all the parties, including the adversary, have oracle access to the same Haar random unitary. In this model, we show the…
Random unitaries sampled from the Haar measure serve as fundamental models for generic quantum many-body dynamics. Under standard cryptographic assumptions, recent works have constructed polynomial-size quantum circuits that are…
Pseudorandom quantum states (PRSs) and pseudorandom unitaries (PRUs) possess the dual nature of being efficiently constructible while appearing completely random to any efficient quantum algorithm. In this study, we establish fundamental…
We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered…
The quantum Haar random oracle model is an idealized model where every party has access to a single Haar random unitary and its inverse. We construct strong pseudorandom unitaries in the quantum Haar random oracle model. This strictly…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
We consider the task of constructing pseudorandom unitaries (PRUs) with scalable security, i.e. families in which the security parameter may vary independently of the dimension (or input bit-length). It is not known whether scalable PRUs…
This paper, for the first time, addresses the questions related to the connections between the quantum pseudorandomness and quantum hardware assumptions, specifically quantum physical unclonable functions (qPUFs). Our results show that the…
We introduce the pseudorandom quantum authentication scheme (PQAS), an efficient method for encrypting quantum states that relies solely on the existence of pseudorandom unitaries (PRUs). The scheme guarantees that for any eavesdropper with…
We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over $n$ qubits in $\log n$ depth. In a similar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in…
There are various notions of quantum pseudorandomness, such as pseudorandom unitaries (PRUs), pseudorandom state generators (PRSGs) and pseudorandom function-like state generators (PRFSGs). Unlike classical pseudorandomness, where different…
Understanding how fast physical systems can resemble Haar-random unitaries is a fundamental question in physics. Many experiments of interest in quantum gravity and many-body physics, including the butterfly effect in quantum information…
We explore a very simple distribution of unitaries: random (binary) phase -- Hadamard -- random (binary) phase -- random computational-basis permutation. We show that this distribution is statistically indistinguishable from random Haar…
In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
We show how to construct pseudorandom permutations (PRPs) that remain secure even if the adversary can query the permutation, both in the forward and reverse directions, on a quantum superposition of inputs. Such quantum-secure PRPs have…
In this work we give an efficient construction of unitary $k$-designs using $\tilde{O}(k\cdot poly(n))$ quantum gates, as well as an efficient construction of a parallel-secure pseudorandom unitary (PRU). Both results are obtained by giving…
Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects…