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Undesired coupling to the surrounding environment destroys long-range correlations on quantum processors and hinders the coherent evolution in the nominally available computational space. This incoherent noise is an outstanding challenge to…
Classical simulation of quantum computation has often been viewed as the method to determine where the horizon of quantum supremacy is located---that is, where quantum computation can no longer be simulated by classical methods. As of now,…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
The System of Linear Equations Problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\kappa$ of $A$, a vector $b$, a Hermitian matrix $M$ and an accuracy $\epsilon$, and the task is to estimate $x^\dagger…
Quantum machine learning applies principles such as superposition and entanglement to data processing and optimization. Variational quantum models operate on qubits in high-dimensional Hilbert spaces and provide an alternative approach to…
Quantum computation promises to execute certain computational tasks on time scales much faster than any known algorithm on an existing classical computer, for example calculating the prime factors of large integers. Recently a research team…
In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble…
Quantum Kernels are projected to provide early-stage usefulness for quantum machine learning. However, highly sophisticated classical models are hard to surpass without losing interpretability, particularly when vast datasets can be…
The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage…
Quantum machine learning promises to efficiently solve important problems. There are two persistent challenges in classical machine learning: the lack of labeled data, and the limit of computational power. We propose a novel framework that…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
Quantum metric learning enhances machine learning by mapping classical data to a quantum Hilbert space with maximal separation between classes. However, on current NISQ hardware, this mapping process itself is prone to errors and could be…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
We show that noiseless random quantum circuits pass the linear cross-entropy benchmark (LXEB) test with high probability. If the circuits are linear depth, and thus form unitary 4-designs, the LXEB test is passed with probability…
As machine learning models grow more complex and their applications become more high-stakes, tools for explaining model predictions have become increasingly important. This has spurred a flurry of research in model explainability and has…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold.…
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…
Boson Sampling represents a promising witness of the supremacy of quantum systems as a resource for the solution of computational problems. The classical hardness of Boson Sampling has been related to the so called Permanent-of-Gaussians…
This paper proves that the computational power of quantum interactive proof systems, with a double-exponentially small gap in acceptance probability between the completeness and soundness cases, is precisely characterized by EXP, the class…