6 research outputs found
Distributing Quantum Circuits Using Teleportations
Scalability is currently one of the most sought-after objectives in the field
of quantum computing. Distributing a quantum circuit across a quantum network
is one way to facilitate large computations using current quantum computers. In
this paper, we consider the problem of distributing a quantum circuit across a
network of heterogeneous quantum computers, while minimizing the number of
teleportations (the communication cost) needed to implement gates spanning
multiple computers. We design two algorithms for this problem. The first,
called Local- Best, initially distributes the qubits across the network, then
tries to teleport qubits only when necessary, with teleportations being
influenced by gates in the near future. The second, called Zero- Stitching,
divides the given circuit into sub-circuits such that each sub-circuit can be
executed using zero teleportations and the teleportation cost incurred at the
borders of the sub-circuits is minimal. We evaluate our algorithms over a wide
range of randomly-generated circuits as well as known benchmarks, and compare
their performance to prior work. We observe that our techniques outperform the
prior approach by a significant margin (up to 50%)
Tight Approximation Algorithms for p-Mean Welfare Under Subadditive Valuations
We develop polynomial-time algorithms for the fair and efficient allocation of indivisible goods among n agents that have subadditive valuations over the goods. We first consider the Nash social welfare as our objective and design a polynomial-time algorithm that, in the value oracle model, finds an 8n-approximation to the Nash optimal allocation. Subadditive valuations include XOS (fractionally subadditive) and submodular valuations as special cases. Our result, even for the special case of submodular valuations, improves upon the previously best known O(n log n)-approximation ratio of Garg et al. (2020).
More generally, we study maximization of p-mean welfare. The p-mean welfare is parameterized by an exponent term p ? (-?, 1] and encompasses a range of welfare functions, such as social welfare (p = 1), Nash social welfare (p ? 0), and egalitarian welfare (p ? -?). We give an algorithm that, for subadditive valuations and any given p ? (-?, 1], computes (in the value oracle model and in polynomial time) an allocation with p-mean welfare at least 1/(8n) times the optimal.
Further, we show that our approximation guarantees are essentially tight for XOS and, hence, subadditive valuations. We adapt a result of Dobzinski et al. (2010) to show that, under XOS valuations, an O (n^{1-?}) approximation for the p-mean welfare for any p ? (-?,1] (including the Nash social welfare) requires exponentially many value queries; here, ? > 0 is any fixed constant
Distribution of Quantum Circuits Over General Quantum Networks
Near-term quantum computers can hold only a small number of qubits. One way
to facilitate large-scale quantum computations is through a distributed network
of quantum computers. In this work, we consider the problem of distributing
quantum programs represented as quantum circuits across a quantum network of
heterogeneous quantum computers, in a way that minimizes the overall
communication cost required to execute the distributed circuit. We consider two
ways of communicating: cat-entanglement that creates linked copies of qubits
across pairs of computers, and teleportation. The heterogeneous computers
impose constraints on cat-entanglement and teleportation operations that can be
chosen by an algorithm. We first focus on a special case that only allows
cat-entanglements and not teleportations for communication. We provide a
two-step heuristic for solving this specialized setting: (i) finding an
assignment of qubits to computers using Tabu search, and (ii) using an
iterative greedy algorithm designed for a constrained version of the set cover
problem to determine cat-entanglement operations required to execute gates
locally.
For the general case, which allows both forms of communication, we propose
two algorithms that subdivide the quantum circuit into several portions and
apply the heuristic for the specialized setting on each portion. Teleportations
are then used to stitch together the solutions for each portion. Finally, we
simulate our algorithms on a wide range of randomly generated quantum networks
and circuits, and study the properties of their results with respect to several
varying parameters