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Qubit Allocation

Marcos Yukio Siraichi, Fernando Magno Quintão Pereira, Vinicius Dos Santos, Caroline Collange

Published Jun 30, 2020• 51 citations
Publisher

Abstract

The availability of the first prototypes of quantum computers, in 2016, with free access through the cloud, brought much enthusiasm to the research community. Yet, programming said computers is difficult. One core challenge is the so called qubit allocation problem. This problem consists in mapping the virtual qubits that make up a logical quantum program onto the physical qubits that exist in the target quantum architecture. To deal with this challenge, we have proposed one of the first algorithms to solve qubit allocation. This algorithm, together with its ensuing formulations, is today available in the Enfield compilera concrete product of this work. Our first paper in this field, titled Qubit Allocation, has inspired much research, and our latest qubit allocation design, called Bounded Mapping Tree, stands out today as one of the most effective qubit allocators in the world.

DOI
10.5753/ctd.2020.11368

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The availability of the first prototypes of quantum computers, in 2016, with free access through the cloud, brought much enthusiasm to the research community. Yet, programming said computers is difficult. One core challenge is the so called qubit allocation problem. This problem consists in mapping the virtual qubits that make up a logical quantum program onto the physical qubits that exist in the target quantum architecture. To deal with this challenge, we have proposed one of the first algorithms to solve qubit allocation. This algorithm, together with its ensuing formulations, is today available in the Enfield compilera concrete product of this work. Our first paper in this field, titled Qubit Allocation, has inspired much research, and our latest qubit allocation design, called Bounded Mapping Tree, stands out today as one of the most effective qubit allocators in the world.
In May of 2016, IBM Research has made a quantum processor available in the cloud to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, quantum programming still lacks the compiler support that modern programming languages enjoy today. To use universal quantum computers like IBM's, programmers must design low-level circuits. In particular, they must map logical qubits into physical qubits that need to obey connectivity constraints. In this work, we shall formally introduce the qubit allocation problem and provide an exact solution to it. This optimal algorithm deals with the simple quantum machinery available today; however, it cannot scale up to the more complex architectures scheduled to appear. Thus, we will also provide heuristics to solve qubit allocation, one of which is faster, and another one that performs better than the current solutions already implemented to deal with this problem.
In May of 2016, IBM Research has made a quantum processor available in the cloud to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, quantum programming still lacks the compiler support that modern programming languages enjoy today. To use universal quantum computers like IBM's, programmers must design low-level circuits. In particular, they must map logical qubits into physical qubits that need to obey connectivity constraints. This task resembles the early days of programming, in which software was built in machine languages. In this paper, we formally introduce the qubit allocation problem and provide an exact solution to it. This optimal algorithm deals with the simple quantum machinery available today; however, it cannot scale up to the more complex architectures scheduled to appear. Thus, we also provide a heuristic solution to qubit allocation, which is faster than the current solutions already implemented to deal with this problem.
In May of 2016, IBM Research has made a quantum processor available in the cloud to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, quantum programming still lacks the compiler support that modern programming languages enjoy today. To use universal quantum computers like IBM's, programmers must design low-level circuits. In particular, they must map logical qubits into physical qubits that need to obey connectivity constraints. This task resembles the early days of programming, in which software was built in machine languages. In this paper, we formally introduce the qubit allocation problem and provide an exact solution to it. This optimal algorithm deals with the simple quantum machinery available today; however, it cannot scale up to the more complex architectures scheduled to appear. Thus, we also provide a heuristic solution to qubit allocation, which is faster than the current solutions already implemented to deal with this problem.
In 2016, the first quantum processors have been made available to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, such possibility also brought challenges. One challenge is the so called Qubit Allocation problem: the mapping of a virtual quantum circuit into an actual quantum architecture. There exist solutions to this problem; however, in our opinion, they fail to capitalize on decades of improvements on graph theory. In contrast, this paper shows how to model qubit allocation as the combination of Subgraph Isomorphism and Token Swapping. This idea has been made possible by the publication of an approximative solution to the latter problem in 2016. We have compared our algorithm against five other qubit allocators, all independently designed in the last two years, including the winner of the IBM Challenge. When evaluated in "Tokyo", a quantum architecture with 20 qubits, our technique outperforms these state-of-the-art approaches in terms of the quality of the solutions that it finds and the amount of memory that it uses, while showing practical runtime.
To run an algorithm on a quantum computer, one must choose an assignment from logical qubits in a circuit to physical qubits on quantum hardware. This task of initial qubit placement, or qubit allocation, is especially important on present-day quantum computers which have a limited number of qubits, connectivity constraints, and varying gate fidelities. In this work we formulate and implement the qubit placement problem as a quadratic, unconstrained binary optimization (QUBO) problem and solve it using simulated annealing to obtain a spectrum of initial placements. Compared to contemporary allocation methods available in t|ket$\rangle $ and Qiskit, the QUBO method yields allocations with improved circuit depth for $>$50% of a large set of benchmark circuits, with many also requiring fewer CX gates.
The qubit mapping problem is a challenge in quantum computing that is related to mapping logical qubits to the physical ones on the quantum computer. Due to the diversity of quantum computer topologies and circuits, numerous approaches solving this problem exist. Finding the best solution for specific combination of topology and circuit remains difficult and no unified framework currently exists for systematically evaluating and comparing qubit mapping algorithms across different cases. We present QuMeld, an open-source framework that is designed for solving this issue. The framework currently supports six qubit mapping algorithms, sixteen quantum computer topologies and multiple evaluation metrics. The modular design of the framework allows integration of new mapping algorithms, quantum circuits, hardware topologies, and evaluation metrics, ensuring extensibility and adaptability to future developments.