Related papers: Realizable Circuit Complexity: Embedding Computati…

Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…

Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…

Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the…

Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…

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…

Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…

While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to nontrivial insights in general relativity, quantum information, and other areas. In this paper we show that if CTCs existed, then quantum…

Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…

We study a polynomial-time decision problem in which each input encodes a depth-$N$ causal execution in which a single non-duplicable token must traverse an ordered sequence of steps, revealing at most $O(1)$ bits of routing information at…

In breakthrough work, Bravyi, Gosset, and K\"{o}nig (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a…

Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…

We show a relation, based on parallel repetition of the Magic Square game, that can be solved, with probability exponentially close to $1$ (worst-case input), by $1D$ (uniform) depth $2$, geometrically-local, noisy (noise below a…

Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a…

We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…

The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine…

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have…

We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a 2D grid of logical qubits with nearest-neighbor logical operations. Embedding an input circuit's qubits in…

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…

Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…

We investigate whether there are inherent limits of parallelization in the (randomized) massively parallel computation (MPC) model by comparing it with the (sequential) RAM model. As our main result, we show the existence of hard functions…