Related papers: Optimal algorithms for learning quantum phase stat…
Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
Estimating properties of unknown unitary operations is a fundamental task in quantum information science. While full unitary tomography requires a number of samples to the unknown unitary scaling linearly with the dimension (implying…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling clearly limits our ability to do tomography to systems with no more than a few qubits and has been used to…
Recent results have established dramatic advantages in learning properties of quantum states when a quantum computer is available to process or jointly measure multiple copies of the unknown quantum state. Learning tasks can be accomplished…
The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm…
Understanding the computational complexity of learning efficient classical programs in various learning models has been a fundamental and important question in classical computational learning theory. In this work, we study the…
We revisit the problem of learning mixtures of spherical Gaussians. Given samples from mixture $\frac{1}{k}\sum_{j=1}^{k}\mathcal{N}(\mu_j, I_d)$, the goal is to estimate the means $\mu_1, \mu_2, \ldots, \mu_k \in \mathbb{R}^d$ up to a…
We study the problem of efficiently learning an unknown $n$-qubit unitary channel in diamond distance given query access. We present a general framework showing that if Pauli operators remain low-complexity under conjugation by a unitary,…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased…
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a…
As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum computation has stimulated much recent interest in algorithms…
We initiate the study of sample-optimal quantum state tomography with minimal disturbance to the samples. Can we efficiently learn a precise description of a quantum state through sequential measurements of samples while at the same time…
Quantum signal processing (QSP) represents a real scalar polynomial of degree $d$ using a product of unitary matrices of size $2\times 2$, parameterized by $(d+1)$ real numbers called the phase factors. This innovative representation of…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
Quantum phase classification is a fundamental problem in quantum many-body physics, traditionally approached using order parameters or quantum machine learning techniques such as quantum convolutional neural networks (QCNNs). However, these…
We propose an approach to measure the quantum phase of an electron in a non-Abelian system using the algorithm of Quantum Phase Estimation (QPE). The discrete-path systems were previously studied in the context of square or rectangular…
We show that measuring pairs of qubits in the Bell basis can be used to obtain a simple quantum algorithm for efficiently identifying an unknown stabilizer state of n qubits. The algorithm uses O(n) copies of the input state and fails with…