Related papers: Quartic quantum speedups for planted inference

We study the effects of quantum noise in hybrid quantum-classical solver for sparse systems of linear equations using quantum random walks, applied to stoquastic Hamiltonian matrices. In an ideal noiseless quantum computer, sparse matrices…

We prove that the generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted. The algorithms speeding up these problems, amplitude amplification and amplitude…

Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…

There has been increasing interest in developing efficient quantum algorithms for hard classical problems. The Network Signal Coordination (NSC) problem is one such problem known to be NP complete. We implement Grover's search algorithm to…

In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…

Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…

Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…

The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…

There is mounting evidence of emergent phenomena in the capabilities of deep learning methods as we scale up datasets, model sizes, and training times. While there are some accounts of how these resources modulate statistical capacity, far…

We employ spectral analysis and compressed sensing to identify settings where a variational algorithm's cost function can be recovered purely classically or with minimal quantum computer access. We present theoretical and numerical evidence…

Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…

Linear optical quantum circuits with photon number resolving (PNR) detectors are used for both Gaussian Boson Sampling (GBS) and for the preparation of non-Gaussian states such as Gottesman-Kitaev-Preskill (GKP), cat and NOON states. They…

The learning parity with noise (LPN) problem is a well-established computational challenge whose difficulty is critical to the security of several post-quantum cryptographic primitives such as HQC and Classic McEliece. Classically, the…

Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we…

Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear…

We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…

Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…

Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in…

Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering…

In this perspective, we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best…