112,428 research outputs found
Resources Required for Preparing Graph States
International audienceGraph states have become a key class of states within quantum computation. They form a basis for universal quantum computation, capture key properties of entanglement, are related to quantum error correction , establish links to graph theory, violate Bell inequalities, and have elegant and short graph-theoretical descriptions. We give here a rigorous analysis of the resources required for producing graphs states. Using a novel graph-contraction procedure, we show that any graph state can be prepared by a linear-size constant-depth quantum circuits, and we establish trade-offs between depth and width. We show that any minimal-width quantum circuit requires gates that acts on several qubits, regardless of the depth. We relate the complexity of preparing graph states to a new graph-theoretical concept, the local minimum degree, and show that it captures basic properties of graph states
Resource costs for fault-tolerant linear optical quantum computing
Linear optical quantum computing (LOQC) seems attractively simple:
information is borne entirely by light and processed by components such as beam
splitters, phase shifters and detectors. However this very simplicity leads to
limitations, such as the lack of deterministic entangling operations, which are
compensated for by using substantial hardware overheads. Here we quantify the
resource costs for full scale LOQC by proposing a specific protocol based on
the surface code. With the caveat that our protocol can be further optimised,
we report that the required number of physical components is at least five
orders of magnitude greater than in comparable matter-based systems. Moreover
the resource requirements grow higher if the per-component photon loss rate is
worse than one in a thousand, or the per-component noise rate is worse than
. We identify the performance of switches in the network as the single
most influential factor influencing resource scaling
Graph States, Pivot Minor, and Universality of (X,Z)-measurements
The graph state formalism offers strong connections between quantum
information processing and graph theory. Exploring these connections, first we
show that any graph is a pivot-minor of a planar graph, and even a pivot minor
of a triangular grid. Then, we prove that the application of measurements in
the (X,Z)-plane over graph states represented by triangular grids is a
universal measurement-based model of quantum computation. These two results are
in fact two sides of the same coin, the proof of which is a combination of
graph theoretical and quantum information techniques
Quantum Computing with Very Noisy Devices
In theory, quantum computers can efficiently simulate quantum physics, factor
large numbers and estimate integrals, thus solving otherwise intractable
computational problems. In practice, quantum computers must operate with noisy
devices called ``gates'' that tend to destroy the fragile quantum states needed
for computation. The goal of fault-tolerant quantum computing is to compute
accurately even when gates have a high probability of error each time they are
used. Here we give evidence that accurate quantum computing is possible with
error probabilities above 3% per gate, which is significantly higher than what
was previously thought possible. However, the resources required for computing
at such high error probabilities are excessive. Fortunately, they decrease
rapidly with decreasing error probabilities. If we had quantum resources
comparable to the considerable resources available in today's digital
computers, we could implement non-trivial quantum computations at error
probabilities as high as 1% per gate.Comment: 47 page
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