Related papers: Efficient simulation of random states and random u…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
Efficiently sampling a quantum state that is hard to distinguish from a truly random quantum state is an elementary task in quantum information theory that has both computational and physical uses. This is often referred to as pseudorandom…
The emergence of randomness from unitary quantum dynamics is a central problem across diverse disciplines, ranging from the foundations of statistical mechanics to quantum algorithms and quantum computation. Physical systems are invariably…
The interest in post-quantum cryptography - classical systems that remain secure in the presence of a quantum adversary - has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and…
Pseudorandom states (PRS) are an important primitive in quantum cryptography. In this paper, we show that subset states can be used to construct PRSs. A subset state with respect to $S$, a subset of the computational basis, is \[…
We introduce a new notion called ${\cal Q}$-secure pseudorandom isometries (PRI). A pseudorandom isometry is an efficient quantum circuit that maps an $n$-qubit state to an $(n+m)$-qubit state in an isometric manner. In terms of security,…
A long-standing problem in quantum optimal control is finding an optimal pulse structure that leads to an efficient exploration of the unitary space with a minimal number of optimization parameters. We solve this problem by constructing…
We consider deterministic and {\em randomized} quantum algorithms simulating $e^{-iHt}$ by a product of unitary operators $e^{-iA_jt_j}$, $j=1,...,N$, where $A_j\in\{H_1,...,H_m\}$, $H=\sum_{i=1}^m H_i$ and $t_j > 0$ for every $j$.…
We construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom…
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size…
We introduce the problem of unitarization. Unitarization is the problem of taking $k$ input quantum circuits that produce orthogonal states from the all $0$ state, and create an output circuit implementing a unitary with its first $k$…
State-of-the-art classical neural networks are observed to be vulnerable to small crafted adversarial perturbations. A more severe vulnerability has been noted for quantum machine learning (QML) models classifying Haar-random pure states.…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…
A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…
The nature of randomness and complexity growth in systems governed by unitary dynamics is a fundamental question in quantum many-body physics. This problem has motivated the study of models such as local random circuits and their…
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
We investigate the generation of quantum states and unitary operations that are ``random'' in certain respects. We show how to use such states to estimate the average fidelity, an important measure in the study of implementations of quantum…