Related papers: Another generalization of Hadamard test: Optimal s…
We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…
Quantum machine learning models are designed for performing learning tasks. Some quantum classifier models are proposed to assign classes of inputs based on fidelity measurements. Quantum Hadamard test is a well-known quantum algorithm for…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…
We propose a method to conduct uniform inference for the (optimal) value function, that is, the function that results from optimizing an objective function marginally over one of its arguments. Marginal optimization is not Hadamard…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…
We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2{+}d$ elements…
Partial observability is a common challenge in many reinforcement learning applications, which requires an agent to maintain memory, infer latent states, and integrate this past information into exploration. This challenge leads to a number…
Quantum state tomography is the fundamental physical task of learning a complete classical description of an unknown state of a quantum system given coherent access to many identical samples of it. The complexity of this task is commonly…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
Efficient estimation of nonlinear functions of quantum states is crucial for various key tasks in quantum computing, such as entanglement spectroscopy, fidelity estimation, and feature analysis of quantum data. Conventional methods using…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
We study the problem of estimating the value of a known smooth function $f$ at an unknown point $\boldsymbol{\mu} \in \mathbb{R}^n$, where each component $\mu_i$ can be sampled via a noisy oracle. Sampling more frequently components of…
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary maximum…
We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution, or more generally, any unital…
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd,…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…