http://user.it.uu.se/~jarst116/slides/week4.pdf

Graph-Based Algorithms for Boolean Function Manipulation

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

Noisy quantum computers can in principle perform reliable quantum computations, but truly scalable systems require noise levels lower than are presently achieved. Still, moderate-complexity computations can be performed. This review discusses what is possible in this ``noisy intermediate scale'' quantum (NISQ) era. Topic areas include the simulation of many-body physics and chemistry, combinatorial optimization, and machine learning. It is evident that the NISQ era has produced new paradigms for programming that will be built upon as quantum computers are further perfected. 

/pdf/noisy-intermediate-scale-quantum-algorithms-204m0vt3.pdf

Noisy intermediate-scale quantum algorithms

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 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- 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 h 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 are publicly available at http://iic.jku.at/eda/research/ibm_qx_mapping .

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

The recent progress in the physical realization of quantum computers (the first publicly available ones---IBM's QX architectures---have been launched in 2017) has motivated research on automatic methods that aid users in running quantum circuits on them. Here, certain physical constraints given by the architectures which restrict the allowed interactions of the involved qubits have to be satisfied. Thus far, this has been addressed by inserting SWAP and H operations. However, it remains unknown whether existing methods add a minimum number of SWAP and H operations or, if not, how far they are away from that minimum---an NP-complete problem. In this work, weaddress this by formulating the mapping task as a symbolic optimization problem that is solved using reasoning engines like Boolean satisfiability solvers. By this, we do not only provide a method that maps quantum circuits to IBM's QX architectures with a minimal number of SWAP and H operations, but also show by experimental evaluation that the number of operations added by IBM's heuristic solution exceeds the lower bound by more than 100% on average. An implementation of the proposed methodology is publicly available at http://iic.jku.at/eda/research/ibm_qx_mapping.

Mapping Quantum Circuits to IBM QX Architectures Using the Minimal Number of SWAP and H Operations

Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups, e.g., for integer factorization or database search. However, since physical realizations of quantum computers are in their infancy, a significant amount of research in this domain still relies on simulations of quantum computations on conventional machines. This causes a significant complexity which current state-of-the-art simulators try to tackle with a rather straight forward array-based representation and by applying massive hardware power. There also exist solutions based on decision diagrams (i.e., graph-based approaches) that try to tackle the exponential complexity by exploiting redundancies in quantum states and operations. However, these existing approaches do not fully exploit redundancies that are actually present. In this paper, we revisit the basics of quantum computation, investigate how corresponding quantum states and quantum operations can be represented even more compactly, and, eventually, simulated in a more efficient fashion. This leads to a new graph-based simulation approach which outperforms state-of-the-art simulators (array-based as well as graph-based). Experimental evaluations show that the proposed solution is capable of simulating quantum computations for more qubits than before, and in significantly less run-time (several magnitudes faster compared to previously proposed simulators). An implementation of the proposed simulator is publicly available online at http://iic.jku.at/eda/research/quantum_simulation .

Advanced Simulation of Quantum Computations

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 (eg 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, ie 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 (ie fewer additional gates are required) All implementations of the proposed methodology is publicly available at this http URL

In March 2017, IBM launched the project IBM Q 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). In order to use these, the desired quantum functionality (e.g. provided in terms of a quantum circuit) has to properly be mapped so that the underlying physical constraints are satisfied — a complex task. This demands for solutions to automatically and efficiently conduct this mapping process. In this paper, we propose such an approach which satisfies all constraints given by the architecture and, at the same time, aims to keep the overhead in terms of additionally required quantum gates minimal. The proposed approach is generic and can easily be configured for future architectures. Experimental evaluations show that the proposed approach clearly outperforms IBM's own mapping solution with respect to runtime as well as resulting costs.

Alwin Zulehner

Papers

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

Mapping Quantum Circuits to IBM QX Architectures Using the Minimal Number of SWAP and H Operations

Advanced Simulation of Quantum Computations

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

Efficient mapping of quantum circuits to the IBM QX architectures