Related papers: Unconditional Quantum Advantage for Sampling with …
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…
We prove several new lower bounds for constant depth quantum circuits. The main result is that parity (and hence fanout) requires log depth circuits, when the circuits are composed of single qubit and arbitrary size Toffoli gates, and when…
We prove that a classical computer can efficiently sample from the photon-number probability distribution of a Gaussian state prepared by using an optical circuit that is shallow and local. Our work generalizes previous known results for…
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…
Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling, that is beyond the practical reach of modern supercomputers. We examine the…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
We prove that $poly(t) \cdot n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on a $D$-dimensional lattice with n qudits are approximate $t$-designs in various measures. These include the "monomial"…
This paper studies a Shannon-theoretic version of the generalized distribution preserving quantization problem where a stationary and memoryless source is encoded subject to a distortion constraint and the additional requirement that the…
We prove that constant-depth quantum circuits are more powerful than their classical counterparts. To this end we introduce a non-oracular version of the Bernstein-Vazirani problem which we call the 2D Hidden Linear Function problem. An…
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.…
Estimating the entropy of probability distributions and quantum states is a fundamental task in information processing. Here, we examine the hardness of this task for the case of probability distributions or quantum states produced by…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
Random circuit sampling has become a popular means for demonstrating the superiority of quantum computers over classical supercomputers. While quantum chips are evolving rapidly, classical sampling algorithms are also getting better and…
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…
Despite fundamental interests in learning quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions…
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
We study the implementation of quantum channels with quantum computers while minimizing the experimental cost, measured in terms of the number of Controlled-NOT (C-NOT) gates required (single-qubit gates are free). We consider three…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer,…