Related papers: The space "just above" BQP
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
The recent proliferation of NISQ devices has made it imperative to understand their computational power. In this work, we define and study the complexity class $\textsf{NISQ} $, which is intended to encapsulate problems that can be…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
The complexity class $PSPACE$ includes all computational problems that can be solved by a classical computer with polynomial memory. All $PSPACE$ problems are known to be solvable by a quantum computer too with polynomial memory and are,…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…
Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has…
Complexity theory traditionally studies the hardness of solving classical computational problems. In the quantum setting, it is also natural to consider a different notion of complexity, namely the complexity of physically preparing a…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
Instantaneous quantum polynomial time (IQP) is a model of (probably) non-universal quantum computation. Since it has been proven that IQP circuits are unlikely to be simulated classically up to a multiplicative error and an error in the…
What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate…
The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define "Quantum NP," the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill,…
A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…
Post-selection, the power of discarding all runs of a computation in which an undesirable event occurs, is an influential concept introduced to the field of quantum complexity theory by Aaronson (Proceedings of the Royal Society A, 2005).…
We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…
The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in…
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…
We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…
We introduce a novel software-oriented model of quantum computation motivated by the practical constraints of near-term quantum hardware. In this model, gates are specified by constraints expressed in terms of Pauli observables, with each…
In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_q$, for p and q prime. We first present a classification of these groups in five classes. Then, we…
We present a new quantum complexity class, called MQ^2, which is contained in AWPP. This class has a compact and simple mathematical definition, involving only polynomial-time computable functions and a unitarity condition. It contains both…