10 research outputs found
Decoherence on a two-dimensional quantum walk using four- and two-state particle
We study the decoherence effects originating from state flipping and
depolarization for two-dimensional discrete-time quantum walks using four-state
and two-state particles. By quantifying the quantum correlations between the
particle and position degree of freedom and between the two spatial ()
degrees of freedom using measurement induced disturbance (MID), we show that
the two schemes using a two-state particle are more robust against decoherence
than the Grover walk, which uses a four-state particle. We also show that the
symmetries which hold for two-state quantum walks breakdown for the Grover
walk, adding to the various other advantages of using two-state particles over
four-state particles.Comment: 12 pages, 16 figures, In Press, J. Phys. A: Math. Theor. (2013
Asymptotic entanglement in a two-dimensional quantum walk
The evolution operator of a discrete-time quantum walk involves a conditional
shift in position space which entangles the coin and position degrees of
freedom of the walker. After several steps, the coin-position entanglement
(CPE) converges to a well defined value which depends on the initial state. In
this work we provide an analytical method which allows for the exact
calculation of the asymptotic reduced density operator and the corresponding
CPE for a discrete-time quantum walk on a two-dimensional lattice. We use the
von Neumann entropy of the reduced density operator as an entanglement measure.
The method is applied to the case of a Hadamard walk for which the dependence
of the resulting CPE on initial conditions is obtained. Initial states leading
to maximum or minimum CPE are identified and the relation between the coin or
position entanglement present in the initial state of the walker and the final
level of CPE is discussed. The CPE obtained from separable initial states
satisfies an additivity property in terms of CPE of the corresponding
one-dimensional cases. Non-local initial conditions are also considered and we
find that the extreme case of an initial uniform position distribution leads to
the largest CPE variation.Comment: Major revision. Improved structure. Theoretical results are now
separated from specific examples. Most figures have been replaced by new
versions. The paper is now significantly reduced in size: 11 pages, 7 figure
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
Journa
Breast cancer management pathways during the COVID-19 pandemic: outcomes from the UK ‘Alert Level 4’ phase of the B-MaP-C study
Abstract: Background: The B-MaP-C study aimed to determine alterations to breast cancer (BC) management during the peak transmission period of the UK COVID-19 pandemic and the potential impact of these treatment decisions. Methods: This was a national cohort study of patients with early BC undergoing multidisciplinary team (MDT)-guided treatment recommendations during the pandemic, designated ‘standard’ or ‘COVID-altered’, in the preoperative, operative and post-operative setting. Findings: Of 3776 patients (from 64 UK units) in the study, 2246 (59%) had ‘COVID-altered’ management. ‘Bridging’ endocrine therapy was used (n = 951) where theatre capacity was reduced. There was increasing access to COVID-19 low-risk theatres during the study period (59%). In line with national guidance, immediate breast reconstruction was avoided (n = 299). Where adjuvant chemotherapy was omitted (n = 81), the median benefit was only 3% (IQR 2–9%) using ‘NHS Predict’. There was the rapid adoption of new evidence-based hypofractionated radiotherapy (n = 781, from 46 units). Only 14 patients (1%) tested positive for SARS-CoV-2 during their treatment journey. Conclusions: The majority of ‘COVID-altered’ management decisions were largely in line with pre-COVID evidence-based guidelines, implying that breast cancer survival outcomes are unlikely to be negatively impacted by the pandemic. However, in this study, the potential impact of delays to BC presentation or diagnosis remains unknown