Related papers: Interactive shallow Clifford circuits: quantum adv…
Despite its popularity, several empirical and theoretical studies suggest that the quantum approximate optimization algorithm (QAOA) has persistent issues in providing a substantial practical advantage. Numerical results for few qubits and…
Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually…
Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators is that they generally require less memory than their…
We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown…
Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical…
Recently Brakerski, Christiano, Mahadev, Vazirani and Vidick (FOCS 2018) have shown how to construct a test of quantumness based on the learning with errors (LWE) assumption: a test that can be solved efficiently by a quantum computer but…
Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical…
Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by non-unitary, dynamic circuits.…
Quantum computing carries significant potential for addressing practical problems. However, currently available quantum devices suffer from noisy quantum gates, which degrade the fidelity of executed quantum circuits. Therefore, quantum…
A recent line of work has shown the unconditional advantage of constant-depth quantum computation, or $\mathsf{QNC^0}$, over $\mathsf{NC^0}$, $\mathsf{AC^0}$, and related models of classical computation. Problems exhibiting this advantage…
Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively…
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…
Non-stabilizerness, alongside entanglement, is a crucial ingredient for fault-tolerant quantum computation and achieving a genuine quantum advantage. Despite recent progress, a complete understanding of the generation and thermalization of…
Current quantum computers suffer from a limited number of qubits and high error rates, limiting practical applicability. Different techniques exist to mitigate these effects and run larger algorithms. In this work, we analyze one of these…
Magic states are essential for universal quantum computation and are widely viewed as a key source of quantum advantage, yet in realistic devices they are inevitably noisy. In this work, we characterize how noise on injected magic resources…
We present two results on the subject of quantum contextuality and cohomology, and non-locality and quantum advantage with shallow circuits. Abramsky et al. showed that a range of examples of quantum contextuality is detected by a…
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…
The goal of benchmarking is to determine how far the output of a noisy system is from its ideal behavior; this becomes exceedingly difficult for large quantum systems where classical simulations become intractable. A common approach is to…
The conventional circuit paradigm, utilizing a limited number of gates to construct arbitrary quantum circuits, is hindered by significant noise overhead. For instance, the standard gate paradigm employs two CNOT gates for the partial…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…