Related papers: Approximate Randomization of Quantum States With F…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. We propose a novel scheme where identical copies of a quantum state are measured jointly so that all Pauli…
We provide more sample-efficient versions of some basic routines in quantum data analysis, along with simpler proofs. Particularly, we give a quantum "Threshold Search" algorithm that requires only $O((\log^2 m)/\epsilon^2)$ samples of a…
Pure quantum states are often approximately encoded as classical bit strings such as those representing probability amplitudes and those describing circuits that generate the quantum states. The crucial quantity is the minimum length of…
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…
Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…
We construct a probabilistic quantum cloning machine by a general unitary-reduction operation. With a postselection of the measurement results, the machine yields faithful copies of the input states. It is shown that the states secretly…
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…
We introduce $k$-local quasi-quantum states: a superset of the regular quantum states, defined by relaxing the positivity constraint. We show that a $k$-local quasi-quantum state on $n$ qubits can be 1-1 mapped to a distribution of…
Subsets of F_2^n that are eps-biased, meaning that the parity of any set of bits is even or odd with probability eps close to 1/2, are powerful tools for derandomization. A simple randomized construction shows that such sets exist of size…
Quantum computers promise to solve important problems faster than conventional computers. However, unleashing this power has been challenging. In particular, design automation runs into (1) the probabilistic nature of quantum computation…
Entanglement is not only the most intriguing feature of quantum mechanics, but also a key resource in quantum information science. The entanglement content of random pure quantum states is almost maximal; such states find applications in…
We consider a one-dimensional wire in gaussian random potential. By treating the spatial direction as imaginary time, we construct a `minimal' zero-dimensional quantum system such that the local statistical properties of the wire are given…
We propose new optimality criterion for the estimation of state-dependent cloning. We call this measure the relative error because the one compares the errors in the copies with contiguous size taking into account the similarity of states…
We investigate the approximate quantum state sharing protocol based on random unitary channels, which is secure against any exterior or interior attackers in principle. Although the protocol leaks small information for a security parameter…
A standard approach to generate random pure quantum states relies on sampling from the Haar measure. However, the entanglement properties of such states present a fundamental challenge for their general applicability. Here, we introduce the…
We prove that the local eigenvalue statistics for $d=1$ random band matrices with fixed bandwidth and, for example, Gaussian entries, is given by a Poisson point process and we identify the intensity of the process. The proof relies on an…
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…
We give an approximation algorithm for Quantum Max-Cut which works by rounding an SDP relaxation to an entangled quantum state. The SDP is used to choose the parameters of a variational quantum circuit. The entangled state is then…
We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within…