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Quantum Information Processing

An exact qubit allocation approach for NISQ architectures

Pengcheng Zhu, Xueyun Cheng, Zhijin Guan

Published Nov 1, 2020• 27 citations
Publisher
DOI
10.1007/s11128-020-02901-4

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Quantum Science and Technology / NISQ circuit compilation is the travelling salesman problem on a torus

Alexandru Paler, Alwin Zulehner, Robert Wille

Noisy, intermediate-scale quantum (NISQ) computers are expected to execute quantum circuits of up to a few hundred qubits. The circuits have to conform to NISQ architectural constraints regarding qubit allocation and the execution of multi-qubit gates. Quantum circuit compilation (QCC) takes a nonconforming circuit and outputs a compatible circuit. Can classical optimisation methods be used for QCC? Compilation is a known combinatorial problem shown to be solvable by two types of operations: (1) qubit allocation, and (2) gate scheduling. We show informally that the two operations form a discrete ring. The search landscape of QCC is a two dimensional discrete torus where vertices represent configurations of how circuit qubits are allocated to NISQ registers. Torus edges are weighted by the cost of scheduling circuit gates. The novelty of our approach uses the fact that a circuit's gate list is circular: compilation can start from any gate as long as all the gates will be processed, and the compiled circuit has the correct gate order. Our work bridges a theoretical and practical gap between classical circuit design automation and the emerging field of quantum circuit optimisation.

•Jan 1, 2021•19 citations
In recent years, the advancement of quantum computers has been improving, with its use increasing in practical applications, including noisy intermediate-scale quantum (NISQ) technology. However, an obstacle that limits quantum computer usage is the connectivity restriction between logical and physical qubits. For performing quantum entanglement on NISQ machines, two logical qubits must be mapped to physical qubit pairs that much up to the connectivity constraint. This mapping process must insert additional operations into an initial quantum circuit. Many powerful algorithms have been proposed to solve the mapping problem, which also mitigate circuit size or depth and improve the fidelity of the quantum state. In this review paper, we present various studies for solving qubit mapping or allocation problems and analyze their time complexity and methods.
Abstract Noisy, intermediate-scale quantum (NISQ) computers are expected to execute quantum circuits of up to a few hundred qubits. The circuits have to conform to NISQ architectural constraints regarding qubit allocation and the execution of multi-qubit gates. Quantum circuit compilation (QCC) takes a nonconforming circuit and outputs a compatible circuit. Can classical optimisation methods be used for QCC? Compilation is a known combinatorial problem shown to be solvable by two types of operations: (1) qubit allocation, and (2) gate scheduling. We show informally that the two operations form a discrete ring. The search landscape of QCC is a two dimensional discrete torus where vertices represent configurations of how circuit qubits are allocated to NISQ registers. Torus edges are weighted by the cost of scheduling circuit gates. The novelty of our approach uses the fact that a circuit’s gate list is circular: compilation can start from any gate as long as all the gates will be processed, and the compiled circuit has the correct gate order. Our work bridges a theoretical and practical gap between classical circuit design automation and the emerging field of quantum circuit optimisation.
Noisy, intermediate-scale quantum (NISQ) computers are expected to execute quantum circuits of up to a few hundred qubits. The circuits have to conform to NISQ architectural constraints regarding qubit allocation and the execution of multi-qubit gates. Quantum circuit compilation (QCC) takes a nonconforming circuit and outputs a compatible circuit. Can classical optimisation methods be used for QCC? Compilation is a known combinatorial problem shown to be solvable by two types of operations: (1) qubit allocation, and (2) gate scheduling. We show informally that the two operations form a discrete ring. The search landscape of QCC is a two dimensional discrete torus where vertices represent configurations of how circuit qubits are allocated to NISQ registers. Torus edges are weighted by the cost of scheduling circuit gates. The novelty of our approach uses the fact that a circuit's gate list is circular: compilation can start from any gate as long as all the gates will be processed, and the compiled circuit has the correct gate order. Our work bridges a theoretical and practical gap between classical circuit design automation and the emerging field of quantum circuit optimisation.