Related papers: BQP_p = PP for integer p > 2
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
In a series of recent works, an interesting quantum generative model based on parameterized instantaneous polynomial quantum (IQP) circuits has emerged as they can be trained efficiently classically using any loss function that depends only…
There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the…
We study the computational difficulty of computing the ground state degeneracy and the density of states for local Hamiltonians. We show that the difficulty of both problems is exactly captured by a class which we call #BQP, which is the…
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…
The pigeonhole principle: "If you put three pigeons in two pigeonholes at least two of the pigeons end up in the same hole" is an obvious yet fundamental principle of Nature as it captures the very essence of counting. Here however we show…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
The most peculiar, specifically quantum, features of quantum mechanics --- quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement --- are explained on a logical-geometrical…
Can the computational complexity theory of computer science and mathematics say something new about unresolved problems in quantum physics? Particularly, can the P versus NP question in the computational complexity theory be a factor in the…
The anthropic principle is an inevitable constraint on the space of possible theories. As such it is central to determining the limits of physics. In particular, we contend that what is ultimately possible in physics is determined by…
Motivated by understanding the power of quantum computation with restricted number of qubits, we give two complete characterizations of unitary quantum space bounded computation. First we show that approximating an element of the inverse of…
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…
Suppose $1 < p < \infty$. Carleson's Theorem states that the Fourier series of any function in $L^p[-\pi, \pi]$ converges almost everywhere. We show that the Schnorr random points are precisely those that satisfy this theorem for every $f…
Without invalidating quantum mechanics as a principle underlying the dynamics of a fundamental theory, it is possible to ask for even more basic dynamical laws that may yield quantum mechanics as the machinery needed for its statistical…
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…
A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this…
There has been considerable discussion of the claim by Stapp [Am. J. Phys. 65, 300 (1997)] that quantum theory is incompatible with locality. In this note I analyze the meaning of some of the statements used in this discussion.
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
We extend Beurling's invariant subspace theorem, by characterizing subspaces $K$ of the noncommutative $L^p$ spaces which are invariant with respect to Arveson's maximal subdiagonal algebras, sometimes known as noncommutative $H^\infty$. It…
Quantum mechanics permits nonlocality - both nonlocal correlations and nonlocal equations of motion - while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two…