Related papers: Learning the Complexity of Weakly Noisy Quantum St…
We give a polynomial time algorithm that, given copies of an unknown quantum state $\vert\psi\rangle=U\vert 0^n\rangle$ that is prepared by an unknown constant depth circuit $U$ on a finite-dimensional lattice, learns a constant depth…
We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical…
In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term…
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 conventional approach to understanding the characteristics of an unknown quantum state involves having numerous identical independent copies of the system in that state. However, we demonstrate that gleaning insights into specific…
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…
The dependence of quantum algorithms on state fidelity is difficult to characterize analytically and is best explored experimentally as hardware scales and noisy simulations become intractable. While low fidelity states are often…
We describe a resource-efficient approach to studying many-body quantum states on noisy, intermediate-scale quantum devices. We employ a sequential generation model that allows us to bound the range of correlations in the resulting…
The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which…
A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16,…
Quantum mechanics provides cryptographic primitives whose security is grounded in hardness assumptions independent of those underlying classical cryptography. However, existing proposals require low-noise quantum communication and…
Noise in quantum systems is a major obstacle to implementing many quantum algorithms on large quantum circuits. In this work, we study the effects of noise on the Rademacher complexity of quantum circuits, which is a measure of statistical…
The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum…
We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the…
Access to quantum computing is steadily increasing each year as the speed advantage of quantum computers solidifies with the growing number of usable qubits. However, the inherent noise encountered when running these systems can lead to…
Ubiquitous in quantum computing is the step to encode data into a quantum state. This process is called quantum state preparation, and its complexity for non-structured data is exponential on the number of qubits. Several works address this…
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…
Entanglement plays an indispensable role in numerous quantum information and quantum computation tasks, underscoring the need for efficiently verifying entangled states. In recent years, quantum state verification has received increasing…
Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and…
Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state…