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arXiv:2109.06445 · International Conference on Computer Aided Design

Optimal qubit mapping with simultaneous gate absorption

Daniel Bochen Tan, Jason Cong

Published Nov 1, 2021• 34 citations
arXivHTMLPDF

Abstract

Before quantum error correction (QEC) is achieved, quantum computers focus on noisy intermediate-scale quantum (NISQ) applications. Compared to the well-known quantum algorithms requiring QEC, like Shor's or Grover's algorithm, NISQ applications have different structures and properties to exploit in compilation. A key step in compilation is mapping the qubits in the program to physical qubits on a given quantum computer, which has been shown to be an NP-hard problem. In this paper, we present OLSQ-GA, an optimal qubit mapper with a key feature of simultaneous SWAP gate absorption during qubit mapping, which we show to be a very effective optimization technique for NISQ applications. For the class of quantum approximate optimization algorithm (QAOA), an important NISQ application, OLSQ-GA reduces depth by up to 50.0% and SWAP count by 100% compared to other state-of-the-art methods, which translates to 55.9% fidelity improvement. The solution optimality of OLSQ-GA is achieved by the exact SMT formulation. For better scalability, we augment our approach with additional constraints in the form of initial mapping or alternating matching, which speeds up OLSQ-GA by up to 272X with no or little loss of optimality.

DOI
10.1109/iccad51958.2021.9643554

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Before quantum error correction (QEC) is achieved, quantum computers focus on noisy intermediate-scale quantum (NISQ) applications. Compared to the well-known quantum algorithms requiring QEC, like Shor's or Grover's algorithm, NISQ applications have different structures and properties to exploit in compilation. A key step in compilation is mapping the qubits in the program to physical qubits on a given quantum computer, which has been shown to be an NP-hard problem. In this paper, we present OLSQ-GA, an optimal qubit mapper with a key feature of simultaneous SWAP gate absorption during qubit mapping, which we show to be a very effective optimization technique for NISQ applications. For the class of quantum approximate optimization algorithm (QAOA), an important NISQ application, OLSQ-GA reduces depth by up to 50.0% and SWAP count by 100% compared to other state-of-the-art methods, which translates to 55.9% fidelity improvement. The solution optimality of OLSQ-GA is achieved by the exact SMT formulation. For better scalability, we augment our approach with additional constraints in the form of initial mapping or alternating matching, which speeds up OLSQ-GA by up to 272X with no or little loss of optimality.
The physical qubits in current quantum computers do not all interact with each other. Therefore, in executing a quantum algorithm on an actual quantum computer, layout synthesis is a crucial step that ensures that the synthesized circuit of the quantum algorithm can run smoothly on the quantum computer. In this paper, we focus on a layout synthesis problem for quantum circuits and improve a prior work, TB-OLSQ, which adopts a transition-based satisfiability modulo theories (SMT) formulation. We present how to modify TB-OLSQ to obtain an accelerated version for runtime reduction. In addition, we extend the accelerated version by considering gate absorption for better solution quality. Our experimental results show that compared with TB-OLSQ, the accelerated version achieves 121X speedup for a set of SWAP-free circuits and 6X speedup for the other set of circuits with no increase in SWAP gates. In addition, the accelerated version with gate absorption helps reduce the number of SWAP gates by 38.9% for the circuits requiring SWAP gates, while it is also 3X faster.
Quantum computing has already demonstrated great computational potential across multiple domains and has received more and more attention. However, due to the connectivity limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, most of the quantum algorithms cannot be directly executed without the help of inserting SWAP gates. Nevertheless, more SWAP gates lead to a longer execution time and, inevitably, lower fidelity of the algorithm. To this end, this paper proposes an optimized qubit mapping algorithm based on a dynamic look-ahead strategy to minimize the number of SWAP gates inserted. Firstly, a heuristic algorithm is proposed based on maximizing physical qubit connectivity to generate the optimal initial qubit mapping, which reduces the need for logical qubit shifts during subsequent SWAP gate insertion. Secondly, in the form of directed acyclic graphs, we identify quantum gates that violate the constraints of physical coupling and insert SWAP gates to remap qubits, thereby overcoming the limitations of qubit interactions. Finally, the optimal SWAP gate insertion strategy is built by comparing the cost of different SWAP gate insertion strategies through a multi-window look-ahead strategy to reduce the number of SWAP gates inserted. The experimental results show that the strategy in this paper decreases the number of SWAP gate insertions and significantly reduces the depth of quantum circuits when performing qubit mapping compared with state-of-the-art methods.
The performance of the Quantum Approximate Optimization Algorithm (QAOA) on noisy intermediate-scale quantum (NISQ) devices is strongly limited by sparse qubit connectivity. When interactions required by QAOA Hamiltonians are not aligned to the hardware topology, transpilation introduces SWAP gates, increasing circuit depth and noise. We propose a SWAP-free QAOA framework based on modifying the cost Hamiltonian so that it can be implemented natively on the hardware. We formulate this as a mixed-integer semidefinite program (MISDP) that selects a hardware-compatible approximation of the original cost matrix and optimizes the allocation of logical variables to physical qubits. We prove that the associated decision problem is NP-complete and derive theoretical guarantees relating the MISDP objective to the loss in the original optimization problem through the Lovász number of the hardware graph. Since solving MISDPs is practical only for small instances, we introduce heuristics based on spectral properties of the problem matrix and hardware graph. Our experiments on a cardinality-constrained quadratic optimization model for index tracking show competitive performance against a baseline representing ideal QAOA under SWAP-induced noise. These results indicate that, on sparse NISQ architectures, a hardware-aware approximation of the objective may be more effective than an exact but heavily transpiled Hamiltonian implementation.
Quantum computing, leveraging the principles of superposition and entanglement, holds the potential to revolutionize computational problem-solving across a wide array of fields, from cryptography to complex system simulations. However, unlocking the full power of quantum computing requires the development of advanced quantum compilation techniques that can efficiently map high-level algorithms onto physical quantum hardware. This paper delves into state-of-the-art optimization strategies within quantum compilers, with a particular focus on methods such as Relaxed Peephole Optimization (RPO), gate reordering techniques for the Quantum Approximate Optimization Algorithm (QAOA), and reinforcement learning (RL)-driven frameworks. It also explores innovative approaches like distributed quantum compilation, parity quantum optimization, and the Paulihedral framework, all designed to minimize gate counts, reduce circuit depth, and optimize overall resource utilization. A key contribution of this work is the introduction of error mitigation techniques that enhance the fidelity and scalability of quantum circuits, particularly on noisy intermediate-scale quantum (NISQ) devices. Through comprehensive empirical evaluations across a variety of quantum algorithms, the paper demonstrates significant improvements in critical performance metrics such as circuit depth, gate count, and execution efficiency, providing a promising direction for optimizing quantum circuit design tailored to diverse quantum hardware platforms.
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA), an approach to solve combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from QAOA critically relies on the mitigation of errors during the execution of the algorithm, which for coherence-limited operations is achievable by reducing the gate count. Here, we demonstrate an improvement of up to a factor of 3 in algorithmic performance as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two CZZZ-gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to 9 layers. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
Variational quantum algorithms are believed to be promising for solving computationally hard problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from these algorithms critically relies on the mitigation of errors during their execution, which for coherence-limited operations is achievable by reducing the gate count. Here, we demonstrate an improvement of up to a factor of 3 in algorithmic performance for the quantum approximate optimization algorithm (QAOA) as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two CZ gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to nine layers. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.