# Optimal qubit assignment and routing via integer programming

@inproceedings{Nannicini2021OptimalQA, title={Optimal qubit assignment and routing via integer programming}, author={Giacomo Nannicini and Lev Bishop and Oktay Gunluk and Petar Jurcevic}, year={2021} }

We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes the initial allocation of qubits and their routing. We consider several cost functions: an approximation of the fidelity of the circuit, its total depth, and a measure of cross-talk, all of which can be incorporated in the model. Numerical experiments on… Expand

#### Figures and Tables from this paper

#### 2 Citations

Best Approximate Quantum Compiling Problems

- Physics, Mathematics
- 2021

We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate… Expand

Optimal Qubit Mapping with Simultaneous Gate Absorption

- Computer Science, Physics
- ArXiv
- 2021

Before quantum error correction (QEC) is achieved, quantum computers focus on noisy intermediate-scale quantum (NISQ) applications. Compared to the well-known quantum algorithms requiring QEC, like… Expand

#### References

SHOWING 1-10 OF 24 REFERENCES

A polynomial size model with implicit SWAP gate counting for exact qubit reordering

- Physics, Computer Science
- ArXiv
- 2020

An Integer Linear Programming model is introduced of the problem of which the size scales polynomially in the number of qubits and gates, and this formulation seems to be suitable for developing heuristic methods since (near) optimal solutions are discovered quickly in the search process. Expand

Depth-Optimal Quantum Circuit Placement for Arbitrary Topologies

- Computer Science, Physics
- ArXiv
- 2017

This work considers an arbitrary qubit topology and presents an Integer Linear Programming (ILP) formulation for achieving minimal logical depth while guaranteeing the nearest neighbor arrangement between the interacting qubits. Expand

An exact qubit allocation approach for NISQ architectures

- Computer Science
- Quantum Inf. Process.
- 2020

An exact approach for qubit allocation is proposed, which takes advantage of the branch and bound algorithm as the basic framework, and can serve as a evaluation baseline of any heuristic approach. Expand

Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices

- Computer Science, Physics
- ASPLOS
- 2019

A SWAP-based Bidirectional heuristic search algorithm (SABRE) is proposed, applicable to NISQ devices with arbitrary connections between qubits, which outperforms the best known algorithm with exponential speedup and comparable or better results on various benchmarks. Expand

Qubit allocation

- Computer Science
- CGO
- 2018

This paper formally introduces the qubit allocation problem and provides an exact solution to it, and provides a heuristic solution to qu bit allocation, which is faster than the current solutions already implemented to deal with this problem. Expand

Mathematical formulation of quantum circuit design problems in networks of quantum computers

- Computer Science
- Quantum Inf. Process.
- 2020

This work defines the global and local reordering problems for distributed quantum computing, and formalises the mathematical problems and model them as integer linear programming problems, to minimise the number of SWAP gates or theNumber of interactions between different quantum computers. Expand

Quantum Circuit Placement

- Computer Science, Physics
- IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
- 2008

This work studies the theoretical aspects of the problem of the practical realization of an abstract quantum circuit when executed on a quantum hardware and presents empirical results that match the best known solutions that have been developed by experimentalists. Expand

Validating quantum computers using randomized model circuits

- Physics
- 2019

We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\ensuremath{\lesssim}50$), and measure it on… Expand

Nearly optimal time-independent reversal of a spin chain

- Physics
- 2020

We propose a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of $N$ spins. Our protocol has an easily implementable nearest-neighbor, transverse-field Ising model… Expand

Complexity-Theoretic Foundations of Quantum Supremacy Experiments

- Computer Science, Physics
- Computational Complexity Conference
- 2016

General theoretical foundations are laid for how to use special-purpose quantum computers with 40--50 high-quality qubits to demonstrate "quantum supremacy": that is, a clear quantum speedup for some task, motivated by the goal of overturning the Extended Church-Turing Thesis as confidently as possible. Expand