Related papers: On quantum and classical space-bounded processes w…
It is not currently known if quantum Turing machines can efficiently simulate probabilistic computations in the space-bounded case. In this paper we show that space-bounded quantum Turing machines can efficiently simulate a limited class of…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…
Fault-tolerant quantum computation requires non-destructive quantum measurements with classical feed-forward. Many experimental groups are actively working towards implementing such capabilities and so they need to be accurately evaluated.…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
The model of open quantum systems is adopted to describe the non-local dynamical behaviour of qubits processed by entangling gates. The analysis gets to the conclusion that a distinction between evaluation steps and task-oriented computing…
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity…
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…
Yao (1993) proved that quantum Turing machines and uniformly generated quantum circuits are polynomially equivalent computational models: $t \geq n$ steps of a quantum Turing machine running on an input of length $n$ can be simulated by a…
A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography.…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…