Related papers: An unconditional distribution learning advantage w…
We present a computational problem with the following properties: (i) Every instance can be solved with near-certainty by a constant-depth quantum circuit using only nearest-neighbor gates in 3D even when its implementation is corrupted by…
Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC$^0$) can solve with near certainty (probability $1 - o(1)$), but that any bounded fan-in constant-depth classical circuit (NC$^0$)…
We study random constant-depth quantum circuits in a two-dimensional architecture. While these circuits only produce entanglement between nearby qubits on the lattice, long-range entanglement can be generated by measuring a subset of the…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
We study quantum-classical separations between classical and quantum supervised learning models based on constant depth (i.e., shallow) circuits, in scenarios with and without noises. We construct a classification problem defined by a…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
The task of learning a probability distribution from samples is ubiquitous across the natural sciences. The output distributions of local quantum circuits form a particularly interesting class of distributions, of key importance both to…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation. In this paper we show a similar separation in the…
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a…
Through the two specific problems, the 2D hidden linear function problem and the 1D magic square problem, Bravyi et al. have recently shown that there exists a separation between $\mathbf{QNC^0}$ and $\mathbf{NC^0}$, where $\mathbf{QNC^0}$…
Quantum mechanics is inherently probabilistic in light of Born's rule. Using quantum circuits as probabilistic generative models for classical data exploits their superior expressibility and efficient direct sampling ability. However,…
Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum…
Quantum Machine Learning algorithms based on Variational Quantum Circuits (VQCs) are important candidates for useful application of quantum computing. It is known that a VQC is a linear model in a feature space determined by its…
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we…
Quantum advantage schemes probe the boundary between classically simulatable and classically intractable quantum dynamics. We explore the impact of mid-circuit measurements on the computational power of quantum circuits. To this effect, we…
Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in…
Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects…
The current generation of quantum computing technologies call for quantum algorithms that require a limited number of qubits and quantum gates, and which are robust against errors. A suitable design approach are variational circuits where…
In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term…