1,043 research outputs found
Scalability of Shor's algorithm with a limited set of rotation gates
Typical circuit implementations of Shor's algorithm involve controlled
rotation gates of magnitude where is the binary length of the
integer N to be factored. Such gates cannot be implemented exactly using
existing fault-tolerant techniques. Approximating a given controlled
rotation gate to within currently requires both
a number of qubits and number of fault-tolerant gates that grows polynomially
with . In this paper we show that this additional growth in space and time
complexity would severely limit the applicability of Shor's algorithm to large
integers. Consequently, we study in detail the effect of using only controlled
rotation gates with less than or equal to some . It is found
that integers up to length can be factored
without significant performance penalty implying that the cumbersome techniques
of fault-tolerant computation only need to be used to create controlled
rotation gates of magnitude if integers thousands of bits long are
desired factored. Explicit fault-tolerant constructions of such gates are also
discussed.Comment: Substantially revised version, twice as long as original. Two tables
converted into one 8-part figure, new section added on the construction of
arbitrary single-qubit rotations using only the fault-tolerant gate set.
Substantial additional discussion and explanatory figures added throughout.
(8 pages, 6 figures
A Quantitative Measure of Interference
We introduce an interference measure which allows to quantify the amount of
interference present in any physical process that maps an initial density
matrix to a final density matrix. In particular, the interference measure
enables one to monitor the amount of interference generated in each step of a
quantum algorithm. We show that a Hadamard gate acting on a single qubit is a
basic building block for interference generation and realizes one bit of
interference, an ``i-bit''. We use the interference measure to quantify
interference for various examples, including Grover's search algorithm and
Shor's factorization algorithm. We distinguish between ``potentially
available'' and ``actually used'' interference, and show that for both
algorithms the potentially available interference is exponentially large.
However, the amount of interference actually used in Grover's algorithm is only
about 3 i-bits and asymptotically independent of the number of qubits, while
Shor's algorithm indeed uses an exponential amount of interference.Comment: 13 pages of latex; research done at http://www.quantware.ups-tlse.fr
Role of beam propagation in Goos-H\"{a}nchen and Imbert-Fedorov shifts
We derive the polarization-dependent displacements parallel and perpendicular
to the plane of incidence, for a Gaussian light beam reflected from a planar
interface, taking into account the propagation of the beam. Using a
classical-optics formalism we show that beam propagation may greatly affect
both Goos-H\"{a}nchen and Imbert-Fedorov shifts when the incident beam is
focussed.Comment: 3 pages, 1 figure, submitted to Opt. Let
Quantum physics in neuroscience and psychology: a neurophysical model of mind–brain interaction:
Assessing the climate change impacts of biogenic carbon in buildings: a critical review of two main dynamic approaches
Wood is increasingly perceived as a renewable, sustainable building material. The carbon it contains, biogenic carbon, comes from biological processes; it is characterized by a rapid turnover
in the global carbon cycle. Increasing the use of harvested wood products (HWP) from sustainable forest management could provide highly needed mitigation efforts and carbon removals. However,
the combined climate change benefits of sequestering biogenic carbon, storing it in harvested wood products and substituting more emission-intensive materials are hard to quantify. Although different
methodological choices and assumptions can lead to opposite conclusions, there is no consensus on the assessment of biogenic carbon in life cycle assessment (LCA). Since LCA is increasingly relied
upon for decision and policy making, incorrect biogenic carbon assessment could lead to inefficient or counterproductive strategies, as well as missed opportunities. This article presents a critical review
of biogenic carbon impact assessment methods, it compares two main approaches to include time considerations in LCA, and suggests one that seems better suited to assess the impacts of biogenic carbon in buildings
Effects of imperfections for Shor's factorization algorithm
We study effects of imperfections induced by residual couplings between
qubits on the accuracy of Shor's algorithm using numerical simulations of
realistic quantum computations with up to 30 qubits. The factoring of numbers
up to N=943 show that the width of peaks, which frequencies allow to determine
the factors, grow exponentially with the number of qubits. However, the
algorithm remains operational up to a critical coupling strength
which drops only polynomially with . The numerical dependence of
on is explained by analytical estimates that allows to
obtain the scaling for functionality of Shor's algorithm on realistic quantum
computers with a large number of qubits.Comment: 10 pages, 10 figures, 1 table. Added references and new data. Erratum
added as appendix. 1 Figure and 1 Table added. Research is available at
http://www.quantware.ups-tlse.fr
Managing diversity in organisations: practitioner and academic perspectives: report from a gender in management special interest group research event
Purpose - This report aims to provide a brief summary of the presentations made by researchers and practitioners at the Gender in Management Special Interest Group’s research event, Managing Diversity in Organisations: Practitioner and Academic Perspectives.
Design/methodology/approach - The research seminar was chaired by Dr. Adelina Broadbridge (University of Stirling) and Dr. Gillian Maxwell (Glasgow Caledonian University), and featured five presentations related to diversity in organisations, with a focus on gender issues. Twenty-five delegates were in attendance.
Findings - The academic research presented provided empirical evidence that women continue to face barriers to career progress in a number of industry sectors. The industry presentations provided examples of organisational efforts to improve diversity both among staff and customers.
Research limitations/implications - More needs to be done to ensure that women enjoy career opportunities equal to those of men in a variety of industry sectors. Even in organisations where women are comparatively well represented, such as
professional services firms, research indicates that they are disadvantaged in terms of career development and progress.
Originality/value - This session provided a valuable opportunity for practitioners and academics to meet and share information regarding the state of diversity in today’s workplace
Fast Quantum Modular Exponentiation
We present a detailed analysis of the impact on modular exponentiation of
architectural features and possible concurrent gate execution. Various
arithmetic algorithms are evaluated for execution time, potential concurrency,
and space tradeoffs. We find that, to exponentiate an n-bit number, for storage
space 100n (twenty times the minimum 5n), we can execute modular exponentiation
two hundred to seven hundred times faster than optimized versions of the basic
algorithms, depending on architecture, for n=128. Addition on a neighbor-only
architecture is limited to O(n) time when non-neighbor architectures can reach
O(log n), demonstrating that physical characteristics of a computing device
have an important impact on both real-world running time and asymptotic
behavior. Our results will help guide experimental implementations of quantum
algorithms and devices.Comment: to appear in PRA 71(5); RevTeX, 12 pages, 12 figures; v2 revision is
substantial, with new algorithmic variants, much shorter and clearer text,
and revised equation formattin
Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
We estimate the resource requirements, the total number of physical qubits
and computational time, required to compute the ground state energy of a 1-D
quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of
the system size and the numerical precision. This estimate is based on
analyzing the impact of fault-tolerant quantum error correction in the context
of the Quantum Logic Array (QLA) architecture. Our results show that due to the
exponential scaling of the computational time with the desired precision of the
energy, significant amount of error correciton is required to implement the TIM
problem. Comparison of our results to the resource requirements for a
fault-tolerant implementation of Shor's quantum factoring algorithm reveals
that the required logical qubit reliability is similar for both the TIM problem
and the factoring problem.Comment: 19 pages, 8 figure
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