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We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers,…

Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which…

It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…

The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous-variable quantum systems. In…

In the Quantum Supremacy regime, quantum computers may overcome classical machines on several tasks if we can estimate, mitigate, or correct unavoidable hardware noise. Estimating the error requires classical simulations, which become…

Quantum memories are key components of emerging quantum technologies. They are designed to store quantum states and retrieve them on demand without losing features such as superposition and entanglement. Verifying that a memory preserves…

Let L be a language decided by a constant-round quantum Arthur-Merlin (QAM) protocol with negligible soundness error and all but possibly the last message being classical. We prove that if this protocol is zero knowledge with a black-box,…

Efficiently entangling pairs of qubits is essential to fully harness the power of quantum computing. Here, we devise an exact protocol that simultaneously entangles arbitrary pairs of qubits on a trapped-ion quantum computer. The protocol…

This paper introduces quantum ``multiple-Merlin''-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical…

This paper introduces and studies a new model of computation called an Alternating Automatic Register Machine (AARM). An AARM possesses the basic features of a conventional register machine and an alternating Turing machine, but can carry…

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…

The recent physical realisation of quantum computers with dozens to hundreds of noisy qubits has given birth to an intense search for useful applications of their unique capabilities. One area that has received particular attention is…

The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…

Infinite time Turing machines (ITTMs) have been introduced by Hamkins and Lewis in their seminal article arXiv:math/9808093. The strength of the model comes from a limit rule which allows the ITTM to compute through ordinal stages. This…

An effective, accessible abstraction hierarchy has made using and programming computers possible for people across all disciplines. Establishing such a hierarchy for quantum programming is an outstanding challenge, especially due to a…

In a recent study (Ref. [1]), quantum annealing was reported to exhibit a scaling advantage for approximately solving Quadratic Unconstrained Binary Optimization (QUBO). However, this claim critically depends on the choice of classical…

Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…

We present a protocol which allows a client to have a server carry out a quantum computation for her such that the client's inputs, outputs and computation remain perfectly private, and where she does not require any quantum computational…

Tsetlin Machines (TMs) have emerged as a compelling alternative to conventional deep learning methods, offering notable advantages such as smaller memory footprint, faster inference, fault-tolerant properties, and interpretability. Although…