Related papers: Learning quantum states and unitaries of bounded g…
In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a…
We analyze the complexity of quantum state verification in the context of solving systems of linear equations of the form $A \vec x = \vec b$. We show that any quantum operation that verifies whether a given quantum state is within a…
We introduce and explore the notion of texture of an arbitrary quantum state, in a selected basis. In the first part of this letter we develop a resource theory and show that state texture is adequately described by an easily computable…
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…
The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
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…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
Quantum process tomography (QPT) methods aim at identifying a given quantum process. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the…
Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent…
To obtain a complete description of a quantum system, one usually employs standard quantum state tomography, which however requires exponential number of measurements to perform and hence is impractical when the system's size grows large.…
Learning properties of quantum states from measurement data is a fundamental challenge in quantum information. The sample complexity of such tasks depends crucially on the measurement primitive. While shadow tomography achieves…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. While various tomographic methods such as classical shadow and MPS tomography have shown…
We consider the problem of learning $N$ identical copies of an unknown $n$-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly $d$ neighboring vertices. Here, we…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states or simple mixed states,…
Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum…
The identification of an unknown quantum gate is a significant issue in quantum technology. In this paper, we propose a quantum gate identification method within the framework of quantum process tomography. In this method, a series of pure…