Related papers: Predicting quantum channels over general product d…
We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$…
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…
Adaptiveness is a key principle in information processing including statistics and machine learning. We investigate the usefulness of adaptive methods in the framework of asymptotic binary hypothesis testing, when each hypothesis represents…
We study the problem of learning nearly $(s,\epsilon)$-sparse unitaries, meaning that the Pauli spectrum is concentrated on at most $s$ components with at most $\epsilon$ residual mass in Pauli $\ell_1$-norm. This class generalizes…
The simplest building blocks for quantum computations are the qbit-qbit quantum channels. In this paper we analyse the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of classical…
The success probability of a quantum algorithm constructed from noisy quantum gates cannot be accurately predicted from single parameter metrics that compare noisy and ideal gates. We illustrate this concept by examining a system with…
We propose constructive approaches for the optimization of binary classical communication over a general noisy qubit quantum channel, for both the error probability and the classical capacity functionals. After showing that the optimal…
Neural Networks (NNs) have been extensively used for a wide spectrum of real-world regression tasks, where the goal is to predict a numerical outcome such as revenue, effectiveness, or a quantitative result. In many such tasks, the point…
Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates. Although these high numbers engender…
The task of finding a correctable encoding that protects against some physical quantum process is in general hard. Two main obstacles are that an exponential number of experiments are needed to gain complete information about the quantum…
The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code…
We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannon's original…
While many statistical properties of deep random quantum circuits can be deduced, often rigorously and other times heuristically, by an approximation to global Haar-random unitaries, the statistics of constant-depth random quantum circuits…
Real-world quantum systems interact with their environments, leading to the irreversible dynamics described by the Lindblad equation. Solutions to the Lindblad equation give rise to quantum channels $\Phi_t$ that characterize the evolution…
We present a new method for quantum process tomography. The method enables us to efficiently estimate, with fixed precision, any of the parameters characterizing a quantum channel. It is selective since one can choose to estimate the value…
Noise forms a central obstacle to effective quantum information processing. Recent experimental advances have enabled the tailoring of noise properties through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
The optimal measurement configuration, i.e., the optimal input quantum state and measurement in the form of a POVM with two elements, is investigated in this paper for qubit and generalized Pauli channels. The channel directions are defined…
Quantum operations, or quantum channels cannot be inverted in general. An arbitrary state passing through a quantum channel looses its fidelity with the input. Given a quantum channel ${\cal E}$, we introduce the concept of its…
We compare the effect of single qubit incoherent and coherent errors on the logical error rate of the Steane [[7,1,3]] quantum error correction code by performing an exact full-density-matrix simulation of an error correction step. We find…