Related papers: Average-case complexity versus approximate simulat…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
We study a subclass of the Instantaneous Quantum Polynomial-time (IQP) circuit with a varying density of two-qubit gates. In addition to a known anticoncentration regime, we identify novel parameter conditions where the model is classically…
Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-defined quantum complexity theory for these bosonic…
A crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can compute certain tasks that are impossible to reproduce by a classical computer with any reasonable resources. Such a…
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 present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a…
We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In…
We study the classical complexity of the exact Boson Sampling problem where the objective is to produce provably correct random samples from a particular quantum mechanical distribution. The computational framework was proposed by Aaronson…
Realizing computationally complex quantum circuits in the presence of noise and imperfections is a challenging task. While fault-tolerant quantum computing provides a route to reducing noise, it requires a large overhead for generic…
The states accepted by a quantum circuit are known as the witnesses for the quantum circuit's satisfiability. The assumption BQP does not equal QMA implies that no efficient algorithm exists for constructing a witness for a quantum circuit…
A critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB…
We introduce a new family of quantum circuits in Continuous Variables and we show that, relying on the widely accepted conjecture that the polynomial hierarchy of complexity classes does not collapse, their output probability distribution…
Simulation of quantum systems is notoriously challenging for classical computers, while quantum hardware is naturally well-suited for this task. However, the imperfections of contemporary quantum systems poses a considerable challenge in…
Sampling problems demonstrating beyond classical computing power with noisy intermediate scale quantum devices have been experimentally realized. In those realizations, however, our trust that the quantum devices faithfully solve the…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes…
Recently, quantum computing experiments have for the first time exceeded the capability of classical computers to perform certain computations -- a milestone termed "quantum computational advantage." However, verifying the output of the…