Related papers: Rademacher complexity of noisy quantum circuits
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…
It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…
Noise detrimentally affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, LOWESA (low weight efficient simulation…
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as $1/N^2$ with the number of particles involved---substantially surpassing the $1/N$-scaling characteristic to…
We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to…
Noisy, intermediate-scale quantum computers come with intrinsic limitations in terms of the number of qubits (circuit "width") and decoherence time (circuit "depth") they can have. Here, for the first time, we demonstrate a recently…
Simulating noisy quantum circuits is vital in designing and verifying quantum algorithms in the current NISQ (Noisy Intermediate-Scale Quantum) era, where quantum noise is unavoidable. However, it is much more inefficient than the classical…
Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from…
Existing lower bounds on redundancy in fault-tolerant quantum circuits are applicable when both the input and the intended output are quantum states. These bounds may not necessarily hold, however, when the input and the intended output are…
Evaluating the reliability of noisy quantum circuits is essential for implementing quantum algorithms on noisy quantum devices. However, current quantum hardware exhibits diverse noise mechanisms whose compounded effects make accurate and…
Deep neural networks are over-parameterized, which implies that the number of parameters are much larger than the number of samples used to train the network. Even in such a regime deep architectures do not overfit. This phenomenon is an…
It has been known for almost 30 years that quantum circuits with interspersed depolarizing noise converge to the uniform distribution at $\omega(\log n)$ depth, where $n$ is the number of qubits, making them classically simulable. We show…
Reducing noise in quantum systems is a major challenge towards the application of quantum technologies. Here, we propose and demonstrate a scheme to reduce noise using a quantum autoencoder with rigorous performance guarantees. The quantum…
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be…
The main challenge of quantum computing on its way to scalability is the erroneous behaviour of current devices. Understanding and predicting their impact on computations is essential to counteract these errors with methods such as quantum…
Quantum errors in noisy environments remain a major obstacle to advancing quantum information technology. In this work, we expand a recently developed geometric framework, originally utilized for analyzing noise accumulation and creating…
We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm.…
We formally study the effects of a restricted single-qubit noise model inspired by real quantum hardware, and corruption in quantum training data, on the performance of binary classification using quantum circuits. We find that, under the…