Related papers: Collapses in quantum-classical probabilistically c…
The structure of Collapse Models is investigated in the framework of Quantum Measure Theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach…
This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA=QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCMA. More…
We construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
The polynomial hierarchy has been widely studied in classical complexity theory. In this paper, we will generalize some commonly known results about the polynomial hierarchy to a version of the hierarchy extended to promise problems. This…
We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimization problems, generalizing the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many…
We generalize quantum-classical PCPs, first introduced by Weggemans, Folkertsma and Cade (TQC 2024), to allow for $q$ quantum queries to a polynomially-sized classical proof ($\mathsf{QCPCP}_{Q,c,s}[q]$). Exploiting a connection with the…
We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller…
QMA (Quantum Merlin Arthur) is the class of problems which, though potentially hard to solve, have a quantum solution which can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical…
We show that the Bub-Clifton uniqueness theorem for 'no collapse' interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the 'weak separability' assumption.
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
We give a corrected proof that if PP $\subseteq$ BQP/qpoly, then the Counting Hierarchy collapses, as originally claimed by [Aaronson 2006 arXiv:cs/0504048]. This recovers the related unconditional claim that PP does not have circuits of…
We begin by establishing structural results for several fundamental quantum complexity classes: p/mBQP, p/mQ(C)MA, $\text{p/mQSZK}_{\text{hv}}$, p/mQIP, p/mBQP/qpoly, p/mBQP/poly, and p/mPSPACE. This includes identifying complete problems,…
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus…
The specific advance of this work is to propose a mechanism by which superpositions collapse during measurement of the separated subsystems of entangled quantum states. It is shown how the phase that locks together entangled states plays a…