Related papers: On the statistical complexity of quantum circuits
A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical…
For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…
For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…
In this work, we investigate the relation between different notions of quantum complexity, namely, circuit and spread complexity and physically meaningful quantities such as the particle content of the quantum state and the variances of…
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…
Magic states are essential for universal quantum computation and are widely viewed as a key source of quantum advantage, yet in realistic devices they are inevitably noisy. In this work, we characterize how noise on injected magic resources…
The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple…
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
We propose a general method to operationally quantify the resourcefulness of quantum channels via channel discrimination, an important information processing task. A main result is that the maximum success probability of distinguishing a…
Quantum reservoir computing offers a promising approach to the utilization of complex quantum dynamics in machine learning. Statistical noise inevitably arises in real settings of quantum reservoir computing (QRC) due to the practical…
A critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
Quantum magic resources, or nonstabilizerness, are a central ingredient for universal quantum computation. In noisy many-body systems, the interplay between these resources and errors leads to sharp magic phase transitions. However, the…
Quantum resource theories are a powerful framework to characterize and quantify relevant quantum phenomena and identify processes that optimize their use for different tasks. Here, we define a resource measure for magic, the sought-after…
Quantum simulation is a cornerstone application of quantum computing, yet how fundamental quantum resources--entanglement and non-stabilizerness (``magic")--shape simulation fidelity remains an open question. In this work, we establish a…