Related papers: Fast Quantum Algorithms for Trace Distance Estimat…
Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition,…
Classically, the edit distance of two length-$n$ strings can be computed in $O(n^2)$ time, whereas an $O(n^{2-\epsilon})$-time procedure would falsify the Orthogonal Vectors Hypothesis. If the edit distance does not exceed $k$, the running…
The problem of finding \emph{distance} between \emph{pattern} of length $m$ and \emph{text} of length $n$ is a typical way of generalizing pattern matching to incorporate dissimilarity score. For both Hamming and $L_1$ distances only a…
In quantum mechanics, measuring the expectation value of a general observable has an inherent statistical uncertainty that is quantified by variance or mean squared error of measurement outcome. While the uncertainty can be reduced by…
Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
Recent work has shown that $n$-qubit quantum states output by circuits with at most $t$ single-qubit non-Clifford gates can be learned to trace distance $\epsilon$ using $\mathsf{poly}(n,2^t,1/\epsilon)$ time and samples. All prior…
Quantum tomography is a fundamental technique for characterizing, benchmarking, and verifying quantum states and devices. It plays a crucial role in advancing quantum technologies and deepening our understanding of quantum mechanics.…
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the optimal strategy that minimizes the total probability of error. This leads to the identification of the…
Quantum process tomography, the task of estimating an unknown quantum channel, is a central problem in quantum information theory. A long-standing open question is to determine the optimal number of uses of an unknown channel required to…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\mathrm{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum…
One of the simplest and most effective classical machine learning algorithms is the $k$-nearest neighbors algorithm ($k$NN) which classifies an unknown test state by finding the $k$ nearest neighbors from a set of $M$ train states. Here we…
The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…
In this article we extend results from our previous work [Bendersky, de la Torre, Senno, Figueira and Ac\'in, Phys. Rev. Lett. 116, 230406 (2016)] by providing a protocol to distinguish in finite time and with arbitrarily high success…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…