Related papers: Stabiliser states are efficiently PAC-learnable
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements --…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of…
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient…
Quantum State Tomography is the task of inferring the state of a quantum system from measurement data. A reliable tomography scheme should not only report an estimate for that state, but also well-justified error bars. These may be…
In order to leverage the full power of quantum noise squeezing with unavoidable decoherence, a complete understanding of the degradation in the purity of squeezed light is demanded. By implementing machine learning architecture with a…
With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the…
The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown $d$-dimensional quantum state through POVMs. Yet, these states are rarely static; they evolve due to factors such as measurements,…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
Quantum state tomography is a powerful, but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as…
Quantum state tomography is a fundamental task in quantum computing, involving the reconstruction of an unknown quantum state from measurement outcomes. Although essential, it is typically introduced at the graduate level due to its…
We describe an algorithm for quantum state tomography that converges in polynomial time to an estimate, together with a rigorous error bound on the fidelity between the estimate and the true state. The result suggests that state tomography…
This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably…
It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum…
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…
We present a protocol that allows the estimation of any density matrix element for continuous-variable quantum states, without resorting to the complete reconstruction of the full density matrix. The algorithm adaptatively discretizes the…
Gate-model quantum computers can allow quantum computations in near-term implementations. The stabilization of an optimal quantum state of a quantum computer is a challenge, since it requires stable quantum evolutions via a precise…