77,360 research outputs found
Surface code compilation via edge-disjoint paths
We provide an efficient algorithm to compile quantum circuits for
fault-tolerant execution. We target surface codes, which form a 2D grid of
logical qubits with nearest-neighbor logical operations. Embedding an input
circuit's qubits in surface codes can result in long-range two-qubit operations
across the grid. We show how to prepare many long-range Bell pairs on qubits
connected by edge-disjoint paths of ancillas in constant depth that can be used
to perform these long-range operations. This forms one core part of our
Edge-Disjoint Paths Compilation (EDPC) algorithm, by easily performing many
parallel long-range Clifford operations in constant depth. It also allows us to
establish a connection between surface code compilation and several
well-studied edge-disjoint paths problems. Similar techniques allow us to
perform non-Clifford single-qubit rotations far from magic state distillation
factories. In this case, we can easily find the maximum set of paths by a
max-flow reduction, which forms the other major part of EDPC. EDPC has the best
asymptotic worst-case performance guarantees on the circuit depth for compiling
parallel operations when compared to related compilation methods based on swaps
and network coding. EDPC also shows a quadratic depth improvement over
sequential Pauli-based compilation for parallel rotations requiring magic
resources. We implement EDPC and find significantly improved performance for
circuits built from parallel cnots, and for circuits which implement the
multi-controlled gate.Comment: 48 pages, 20 figures. Published version in PRX Quantum. Includes new
comparison table, tightened Theorem 3.3/3.4, and source cod
Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
We show how macroscopically distinct quantum superposition states
(Schroedinger cat states) may be used as logical qubit encodings for the
correction of spontaneous emission errors. Spontaneous emission causes a bit
flip error which is easily corrected by a standard error correction circuit.
The method works arbitrarily well as the distance between the amplitudes of the
superposed coherent states increases.Comment: 4 pages, 2 postscript figures, LaTeX2e, RevTeX, minor changes, 1
reference adde
Active Topology Inference using Network Coding
Our goal is to infer the topology of a network when (i) we can send probes
between sources and receivers at the edge of the network and (ii) intermediate
nodes can perform simple network coding operations, i.e., additions. Our key
intuition is that network coding introduces topology-dependent correlation in
the observations at the receivers, which can be exploited to infer the
topology. For undirected tree topologies, we design hierarchical clustering
algorithms, building on our prior work. For directed acyclic graphs (DAGs),
first we decompose the topology into a number of two-source, two-receiver
(2-by-2) subnetwork components and then we merge these components to
reconstruct the topology. Our approach for DAGs builds on prior work on
tomography, and improves upon it by employing network coding to accurately
distinguish among all different 2-by-2 components. We evaluate our algorithms
through simulation of a number of realistic topologies and compare them to
active tomographic techniques without network coding. We also make connections
between our approach and alternatives, including passive inference, traceroute,
and packet marking
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