Related papers: Unconditional Quantum Advantage for Sampling with …
Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this work, we present classical sampling algorithms for single-photon and…
This note introduces "Q-marginals", which are quantum states encoding some probability distribution in a manner suitable for use in Quantum Monte Carlo Integration (QMCI), and shows that these can be prepared directly from a classical…
Noise is one of the main obstacles to realizing quantum devices that achieve a quantum computational advantage. A possible approach to minimize the noise effect is to employ shallow-depth quantum circuits since noise typically accumulates…
We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device and channel noises has been missing.…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
Boson Sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be…
We establish new separations between the power of monotone and general (non-monotone) Boolean circuits: - For every $k \geq 1$, there is a monotone function in ${\sf AC^0}$ that requires monotone circuits of depth $\Omega(\log^k n)$. This…
In this paper, we introduce a classical algorithm for random sampling of permutations, drawing inspiration from the Steinhaus-Johnson-Trotter algorithm. Our approach takes a comprehensive view of permutation sampling by expressing them as…
The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. However, existing certification tests fall short, as they either suffer from systematic errors or do not…
Channel resolvability concerns the minimum resolution for approximating the channel output. We study the resolvability of classical-quantum channels in two settings, for the channel output generated from the worst input, and form the fixed…
It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results…
Quantum circuit simulators running on classical computers offer a vital platform for designing, testing, and optimizing quantum algorithms, driving innovation despite limited access to real quantum hardware. However, their scalability is…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
The present era of quantum processors with hundreds to thousands of noisy qubits has sparked interest in understanding the computational power of these devices and how to leverage it to solve practically relevant problems. For applications…
The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…
Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…
We prove new inner bounds for several multiterminal channels with classical inputs and quantum outputs. Our inner bounds are all proved in the one-shot setting, and are natural analogues of the best classical inner bounds for the respective…