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We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
Quantum computers offer the potential for efficiently sampling from complex probability distributions, attracting increasing interest in generative modeling within quantum machine learning. This surge in interest has driven the development…
We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium…
The key factor currently limiting the advancement of computational power of electronic computation is no longer the manufacturing density and speed of components, but rather their high energy consumption. While it has been widely argued…
Most future quantum devices, including quantum computers, require control that is broadband, meaning that the rate of change of the time-dependent Hamiltonian is as fast or faster than the dynamics it generates. In many areas of quantum…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise.…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
We introduce a ``Statistical Query Sampling'' model, in which the goal of an algorithm is to produce an element in a hidden set $Ssubseteqbit^n$ with reasonable probability. The algorithm gains information about $S$ through oracle calls…
As quantum devices progress towards a quantum advantage regime, they become harder to benchmark. A particularly relevant challenge is to assess the quality of the whole computation, beyond testing the performance of each single operation.…
Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…
Due to the scarcity of quantum computing resources, researchers and developers have very limited access to real quantum computers. Therefore, judicious planning and utilization of quantum computer runtime are essential to ensure smooth…
Random circuit sampling (RCS) is a leading approach to demonstrate quantum advantage, with its believed classical hardness rooted in anticoncentration of output distributions and average-case hardness of probability estimation. Here we show…
Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…
Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
This paper concerns the problem of checking if two shallow (i.e., constant-depth) quantum circuits perform equivalent computations. Equivalence checking is a fundamental correctness question -- needed, e.g., for ensuring that…
Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs.…
Demonstrations of quantum computational advantage and benchmarks of quantum processors via quantum random circuit sampling are based on evaluating the linear cross-entropy benchmark (XEB). A key question in the theory of XEB is whether it…