Related papers: Efficient Monte Carlo characterization of quantum …

We show that the minimum experimental effort to characterize the proper functioning of a quantum device scales as 2^n for n qubits and requires classical computational resources ~ n^2 2^{3n}. This represents an exponential reduction…

For certain quantum operations acting on qubits, there exist bases of measurement operators such that estimating the average fidelity becomes efficient. The number of experiments required is then independent of system size and the classical…

Standard Monte Carlo computation is widely known to exhibit a canonical square-root convergence speed in terms of sample size. Two recent techniques, one based on control variate and one on importance sampling, both derived from an…

The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a…

While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…

Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…

Experimental implementations of quantum information processing have now reached a level of sophistication where quantum process tomography is impractical. The number of experimental settings as well as the computational cost of the data…

Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…

There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction…

We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…

In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…

Recently, Huggins et. al. [Nature, 603, 416-420 (2022)] devised a general projective Quantum Monte Carlo method suitable for implementation on quantum computers. This hybrid approach, however, relies on a subroutine -the computation of the…

The Clifford operators are an important and well-studied subset of quantum operations, in both the qubit and higher-dimensional qudit cases. While there are many ways to characterize this set, this paper aims to provide an ideal…

Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…

We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic…

Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and…

We present a Monte Carlo method to compute efficiently susceptibilites or covariances of two physical variables. The method relies on a generalization of the exchange cluster algorithm to any model of interacting particles with any $2$-body…

Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…

High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…