Due to little considerations in the hardware constraints, eg, limited connections between physical qubits to enable two-qubit gates, most quantum algorithms cannot be directly executed on the Noisy Intermediate-Scale Quantum (NISQ) devices Dynamically remapping logical qubits to physical qubits in the compiler is needed to enable the two-qubit gates in the algorithm, which introduces additional operations and inevitably reduces the fidelity of the algorithm Previous solutions in finding such remapping suffer from high complexity, poor initial mapping quality, and limited flexibility and control To address these drawbacks mentioned above, this paper proposes a SWAP-based Bidirectional heuristic search algorithm (SABRE), which is applicable to NISQ devices with arbitrary connections between qubits By optimizing every search attempt, globally optimizing the initial mapping using a novel reverse traversal technique, introducing the decay effect to enable the trade-off between the depth and the number of gates of the entire algorithm, SABRE outperforms the best known algorithm with exponential speedup and comparable or better results on various benchmarks

https://dl.acm.org/doi/pdf/10.1145/3297858.3304023

Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices

Existing and near-term quantum computers are not yet large enough to support fault-tolerance. Such systems with few tens to few hundreds of qubits are termed as Noisy Intermediate Scale Quantum computers (NISQ), and these systems can provide benefits for a class of quantum algorithms. In this paper, we study the problems of Qubit-Allocation (mapping of program qubits to machine qubits) and Qubit-Movement (routing qubits from one location to another for entanglement). We observe that there can be variation in the error rates of different qubits and links, which can impact the decisions for qubit movement and qubit allocation. We analyze publicly available characterization data for the IBM-Q20 to quantify the variation and show that there is indeed significant variability in the error rates of the qubits and the links connecting them. We show that the device variability has a significant impact on the overall system reliability. To exploit the variability in error rate, we propose Variation-Aware Qubit Movement (VQM) and Variation-Aware Qubit Allocation (VQA), policies that optimize the movement and allocation of qubits to avoid the weaker qubits and links, and guide more operations towards the stronger qubits and links. Our evaluations, with a simulation-based model of IBM-Q20, show that Variation-Aware policies can improve the system reliability by up to 1.7x. We also evaluate our policies on the IBM-Q5 machine and demonstrate that our proposal significantly improves the reliability of real systems (up to 1.9X).

Not All Qubits Are Created Equal: A Case for Variability-Aware Policies for NISQ-Era Quantum Computers

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.

Qubit allocation

A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet with less than 80 quantum bits (qubits) total, they are too resource-constrained to implement error correction. The term Noisy Intermediate-Scale Quantum (NISQ) refers to these current and near-term systems of 1000 qubits or less. Given NISQ's severe resource constraints, low reliability, and high variability in physical characteristics such as coherence time or error rates, it is of pressing importance to map computations onto them in ways that use resources efficiently and maximize the likelihood of successful runs. 
This paper proposes and evaluates backend compiler approaches to map and optimize high-level QC programs to execute with high reliability on NISQ systems with diverse hardware characteristics. Our techniques all start from an LLVM intermediate representation of the quantum program (such as would be generated from high-level QC languages like Scaffold) and generate QC executables runnable on the IBM Q public QC machine. We then use this framework to implement and evaluate several optimal and heuristic mapping methods. These methods vary in how they account for the availability of dynamic machine calibration data, the relative importance of various noise parameters, the different possible routing strategies, and the relative importance of compile-time scalability versus runtime success. Using real-system measurements, we show that fine grained spatial and temporal variations in hardware parameters can be exploited to obtain an average $2.9$x (and up to $18$x) improvement in program success rate over the industry standard IBM Qiskit compiler.

Noise-Adaptive Compiler Mappings for Noisy Intermediate-Scale Quantum Computers

Crosstalk is a major source of noise in Noisy Intermediate-Scale Quantum (NISQ) systems and is a fundamental challenge for hardware design. When multiple instructions are executed in parallel, crosstalk between the instructions can corrupt the quantum state and lead to incorrect program execution. Our goal is to mitigate the application impact of crosstalk noise through software techniques. This requires (i) accurate characterization of hardware crosstalk, and (ii) intelligent instruction scheduling to serialize the affected operations. Since crosstalk characterization is computationally expensive, we develop optimizations which reduce the characterization overhead. On 3 20-qubit IBMQ systems, we demonstrate two orders of magnitude reduction in characterization time (compute time on the QC device) compared to all-pairs crosstalk measurements. Informed by these characterization, we develop a scheduler that judiciously serializes high crosstalk instructions balancing the need to mitigate crosstalk and exponential decoherence errors from serialization. On real-system runs on 3 IBMQ systems, our scheduler improves the error rate of application circuits by up to 5.6x, compared to the IBM instruction scheduler and offers near-optimal crosstalk mitigation in practice. In a broader picture, the difficulty of mitigating crosstalk has recently driven QC vendors to move towards sparser qubit connectivity or disabling nearby operations entirely in hardware, which can be detrimental to performance. Our work makes the case for software mitigation of crosstalk errors.

/pdf/software-mitigation-of-crosstalk-on-noisy-intermediate-scale-3zaogynohs.pdf

Software Mitigation of Crosstalk on Noisy Intermediate-Scale Quantum Computers

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.

https://dl.acm.org/doi/pdf/10.1145/3360546

Marcos Yukio Siraichi

Papers

Qubit allocation

Qubit allocation as a combination of subgraph isomorphism and token swapping