An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures

Abstract

In the past years, quantum computers more and more have evolved from an academic idea to an upcoming reality. IBM's project IBM Q can be seen as evidence of this progress. Launched in March 2017 with the goal to provide access to quantum computers for a broad audience, this allowed users to conduct quantum experiments on a 5-qubit and, since June 2017, also on a 16-qubit quantum computer (called IBM QX2 and IBM QX3, respectively). Revised versions of these 5-qubit and 16-qubit quantum computers (named IBM QX4 and IBM QX5, respectively) are available since September 2017. In order to use these, the desired quantum functionality (e.g. provided in terms of a quantum circuit) has to be properly mapped so that the underlying physical constraints are satisfied -a complex task. This demands solutions to automatically and efficiently conduct this mapping process.In this paper, we propose a methodology which addresses this problem, i.e. maps the given quantum functionality to a realization which satisfies all constraints given by the architecture and, at the same time, keeps the overhead in terms of additionally required quantum gates minimal. The proposed methodology is generic, can easily be configured for similar future architectures, and is fully integrated into IBM's SDK. Experimental evaluations show that the proposed approach clearly outperforms IBM's own mapping solution. In fact, for many quantum circuits, the proposed approach determines a mapping to the IBM architecture within minutes, while IBM's solution suffers from long runtimes and runs into a timeout of 1 hour in several cases. As an additional benefit, the proposed approach yields mapped circuits with smaller costs (i.e. fewer additional gates are required). All implementations of the proposed methodology is publicly available at http://iic.

Quantum Circuit Transformation Based on Simulated Annealing and Heuristic Search

“…Thanks to this novel idea, the proposed algorithm is able to find a better solution with less circuit size within acceptable running time. Experimental results on extensive realistic circuits show that our algorithm is efficient and, when compared with the state-of-the-art algorithms [25,13], can reduce on average the size of the output circuits by above 10% on IBM QX5 and above 55% on IBM Q20.…”

“…A cost function which assigns decreasing weights to gates in later layers is used to select the state of the next step. Note that the above procedure is standard for circuit transformation, and has been adopted in [25]. Our algorithm distinguishes itself from the previous ones in the ways of choosing the initial mapping (Sec 4.2), the definition of the cost function, and the strategy of updating step states (Sec 4.3).…”

“…3 (bottom)). Otherwise, we have dist cnot (v, v ) = 7 × (d − 1) + 4, as we need to add 2 Hadamard gates before and after to change the direction of the target CNOT [25]. Take QX5 as an example.…”

“…Note that the look-ahead mechanism has already been introduced in the heuristic cost function during the search process in existing works like [25,13]. However, we adopt in this paper a double look-ahead mechanism: in addition to looking ahead at subsequent layers when defining the cost function, we also look ahead (at grandchild states) in finding the state with minimal cost in order to make the best transformation.…”

t|ket⟩: a retargetable compiler for NISQ devices

“…If there is a subgraph monomorphism p : t|ket solves the problem in two steps: finding an initial placement of logical qubits to physical qubits and subsequent addition of SWAP operations to the circuit. We consider this to be a dynamic approach, in contrast to static approaches [78,79,80], that partition circuits into parallelised slices of two-qubit interactions, and then use SWAP networks to permute logical qubits between placements that satisfy these slices.…”