CODAR: A Contextual Duration-Aware Qubit Mapping for Various NISQ Devices Haowei Deng, Yu Zhang∗ and Quanxi Li School of Computer Science and Technology, University of Science and Technology of China, Hefei, China Email: [email protected], [email protected]∗, [email protected] Abstract—Quantum computing devices in the NISQ era share In this paper, we focus on solving the qubit mapping problem by common features and challenges like limited connectivity between heuristic search with the consideration of gate duration difference qubits. Since two-qubit gates are allowed on limited qubit pairs, and program context to explore more program’s parallelism. To quantum compilers must transform original quantum programs address the challenges of qubit mapping problem and adapt to to fit the hardware constraints. Previous works on qubit mapping different quantum technologies, we first give several examples to assume different gates have the same execution duration, which explain our motivation, then propose a Multi-architecture Adaptive limits them to explore the parallelism from the program. To Quantum Abstract Machine (maQAM) for studying the qubit map- address this drawback, we propose a Multi-architecture Adaptive ping problem. The maQAM is modeled as a coupling graph with Quantum Abstract Machine (maQAM) and a COntext-sensitive limited qubit connectivity and configurable durations of different and Duration-Aware Remapping algorithm (CODAR). The CO- kinds of quantum gates. Based on the maQAM, we further propose DAR remapper is aware of gate duration difference and program two mechanisms that enable COntext-sensitive and Duration-Aware context, enabling it to extract more parallelism from programs Remapping algorithm (CODAR) to solve the qubit mapping problem and speed up the quantum programs by 1.23 in simulation on with the awareness of gate duration difference and program context. average in different architectures and maintain the fidelity of The main contributions of this paper are as follows: circuits when running on OriginQ quantum noisy simulator. • We summarize the features of different QC technologies in- cluding their available gates, operation fidelity and execution I. INTRODUCTION duration, and establish the quantum architecture abstraction with Quantum Computing (QC) has attracted huge attention in recent a configurable parameters – maQAM. decade due to its ability to exponentially accelerate some important • We propose a SWAP-based heuristic algorithm for qubit remap- algorithms [22]. Both QC algorithm designers and programmers work ping, CODAR, which considers the gate duration difference and at a very high level, and know little about (future) NISQ devices program context and can further speed up the quantum program. that (will) execute quantum programs. There exists a gap, however, • We evaluate CODAR with various benchmarks on several latest between NISQ devices and the hardware requirements (e.g., size hardware models such as Google’s 54-qubit Sycamore proces- and reliability) of QC algorithms. To bridge the gap, QC requires sor [3]. Experimental results show that CODAR speeds up quan- abstraction layer and toolchain to translate and optimize quantum tum programs by 1.212∼1.258 at the average in comparison programs [8]. QC compilers typically translate high-level QC code with the best-known algorithm, and maintains the fidelity of into (optimized) circuit-level assembly code in multiple stages. circuits when running on OriginQ quantum noisy simulator [24]. In order to use NISQ hardware, quantum circuit programs have to be compiled to the target device, which includes mapping logical II. PROBLEM ANALYSIS qubits to physical ones of the device. The mapping step, which we focus on in this paper, faces a tough challenge because further A. Recent Work on Qubit Mapping physical constraints have to be considered. In fact, 2-qubit gates can only be applied to certain physical qubit pairs. A common method to There are a lot of research on the qubit mapping problem. Here we solve this problem is to insert additional SWAP operations in order to focus on analyzing some valuable solutions in recent two years [4, “move” the logical qubits to positions where they can interact with 18, 21, 26, 28, 32, 35]. All of them are proposed for some IBM QX each other. This qubit mapping problem has been proved to be a architectures, and none of them consider the gate duration difference. NP-Complete problem [26]. a) Solutions only considering qubit coupling: [26, 32] Previous solutions to this problem can be classified into two provide solutions for 5-qubit IBM QX architectures with directed arXiv:2002.10915v1 [quant-ph] 24 Feb 2020 types. One of them is to formulate the problem into an equivalent coupling. Siraichi et al. [26] propose an optimal algorithm based on mathematical problem and apply a solver [6, 7, 23, 29, 30, 32] and dynamic programming, which only fits for small circuits; then they the other type is to use heuristic search to obtain approximate results propose a heuristic one which is fast but oversimplified with results [5, 15, 16, 18, 33, 35]. The former suffers from a very long runtime worse than IBM’s solution. Wille et al. [32] present a solution with a and can only apply to small-size cases. The latter is better in runtime, minimal number of additional SWAP and H operations, in which qubit especially when the circuit is large scale. All these algorithms assume mapping problem is formulated as a symbolic optimization problem that different gates have the same execution duration. with high complexity. They utilize powerful reasoning engines to On NISQ hardware, however, different gates have different du- solve the computationally task. rations (see Table I). Ignoring the gate duration difference may [18, 35] use heuristic search to provide good solutions in accept- cause these algorithms to find the shortest depth but not the shortest able time for large scale circuits. Zulehner et al. [35] divide the two- execution time. The real execution time of the circuit is associated qubit gates into independent layers, then use A∗ search plus heuristic with the weighted depth, in which different gates have different cost function to determine compliant mappings for each layer. Li et al. duration weights. Considering gate duration difference will help the [18] propose a SWAP-based bidirectional heuristic search algorithm compiler make better use of the parallelism of quantum circuits and – SABRE, which can produce comparable results with exponential generate circuits with shorter execution time. speedup against previous solutions such as [35]. TABLE I: Parameter information of several quantum computing devices. Ion Trap Superconducting Neutral Atom [25] Ion Q5 [19] Ion Q11 [34] IBM Q5 [19] IBM Q16 [21] IBM Q20 [18] θ θ Available 1-qubit gate Rα X, Y, Z, H, S, T Rα Available 2-qubit gate XX CNOT (CX) CNOT (CX)[27] 1-qubit gate 99.1(5)% 99.5% 99.7% ∼99.8% ∼99.56% 99.995% [25] 2-qubit gate 97(1)% 97.5%[95.1%,98.9%] 96.5% ∼96% ∼97% 82%[20] Fidelity 1-qubit readout j0i:99.7(1)%, j1i:99.1(1)% 99.3% ∼ 96% ∼93% ∼91.2% 98.6% [12] average readout 95.7(1)% – ∼ 80% – – ≥97.4(3)% [17] 1-qubit gate 20µ s 130 ns 80 ns – 1µ ∼20µ s Time 2-qubit gate 250µ s – 250-450 ns 170-391 ns – ∼10µ s Depolarization (T1) ∼ 1 – ∼ 60µ s ∼ 70µ s 87.29µ s >10s Spin dephasing (T2) ∼ 0.5s – ∼ 60µ s ∼ 70µ s 54.43µ s ∼ 1s b) Solutions further considering error rates: [4, 21, 28] provide another type of perspective for solving the qubit mapping problem. They consider the variation in the error rates of different qubits and connections to generate directly executable circuits that improve reliability rather than minimize circuit depth and number of gates. Based on the error rate data from real IBM Q16 and Q20 (a) (c) respectively, [21, 28] use a SMT solver to schedule gate operations to qubits with lower error probabilities. Ash-Saki et al. propose two approaches, Sub-graph Search and Greedy approach, to optimize gate-errors [4]. Circuits generated by them may suffer from long execution time due to no consideration of the minimal circuit depth. c) What we consider in the qubit mapping: We want to produce solutions for the qubit mapping problem with speedup (b) (d) against previous works and maintain the fidelity meanwhile. Besides Fig. 2: A 4-qubit QFT example reflecting the impact of gate duration the coupling map, what we further concern includes the program difference:“SWAP q[3],q[1]” is the best candidate since it can context and the gate duration difference, which affect the design of start immediately after “T q[1]” while “CX q[0],q[2]” has not qubit mapping. Considering these factors will help to find remapping finished yet, increasing the parallelism of the circuit. solution with approximate optimal execution close to reality. B. Motivating Examples We use several examples written in OpenQASM [10] to explain our motivation for considering program context and gate duration performing the CX operation. In this case, there are four candidate difference in the qubit remapping process. The two examples base on SWAP pairs, i.e., (Q0, Q1), (Q0, Q2), (Q3, Q1) and (Q3, Q2). If the the coupling map of four physical qubits Q0 ∼ Q3 and the assumed program context, i.e., the predecessor instruction “T q[2];”, is not gate durations defined in Fig. 1 (a) and (b). We directly map the considered, there are no differences among the four candidates when logical qubits q[0]∼q[3] initially to physical qubits Q0 ∼ Q3 for selecting. However, SWAP operation on pair (Q3, Q2) or (Q0, Q2) easier explanation. conflicts with the context instruction “T q[2];” due to operating the same Q2, and has to be executed serially after T operation as shown in Fig.1 (c).