**Related Publication:**

*IEEE Transactions on Computers*(2021) - Optimality Study of Existing Quantum Computing Layout Synthesis Tools- ICCAD'20 - Optimal Layout Synthesis for Quantum Computing
- ICCAD'21 - Optimal Qubit Mapping with Simultaneous Gate Absorption
*IEEE Journal on Emering and Selected Topics in Circuits and Systems*(2022) - Domain-Specific Quantum Architecture Optimization- ICCAD'22 - Qubit Mapping for Reconfigurable Atom Arrays
- Chapter in
*Design Automation of Quantum Computers*- Layout Synthesis for Near-Term Quantum Computing: Gap Analysis and Optimal Solution - DAC'23 - Scalable Optimal Layout Synthesis for NISQ Quantum Processors
- DAC'23 - Lightning Talk: Scaling Up Quantum Compilation – Challenges and Opportunities
*Quantum*(2024) - Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors- DATE'24 (Spotlight on UCLA CQSE website) - Depth-Optimal Addressing of 2D Qubit Array with 1D Controls Based on Exact Binary Matrix Factorization

**Software Release:**

## Description:

- Compilation in quantum computing (QC)
- Benchmarks - what quantum algorithm we compile?
- Optimality study - how far are we from optimal?
- Optimal quantum layout synthesis
- Exploring architecture design with layout synthesis
- Layout synthesis for reconfigruable QC architectures

## Compilation in quantum computing (QC)

Quantum computing (QC) has been shown, in theory, to hold huge advantages over classical computing. However, there remains many engineering challenges in the implementation of real-world QC applications. In order to divide-and-conquer, we can split the task as below.

The topics that we are particularly interested in are those concerning QC architecture and compilation, which connects algorithms and devices. One of them, is layout synthesis for quantum computing (QLS), also named qubit mapping or allocation. A quantum program usually assumes all-to-all connectivity of the qubits, but this is not the case for some QC technologies. QLS aims to transform the programs so that they are executable on actual quantum hardware and, at the same time, overcome some limitations of these near-term devices, e.g. volatile qubits and error-prone quantum gates.

## Benchmarks - what quantum algorithm we compile?

The tools we have developed so far are for physical quantum circuits. If the results of these circuits are interpreted directly, the formalism of quantum computing is what we call noisy intermediate scale quantum computing (NISQ). In the long run, we may construct logical quantum circuits based on quantum error correcting codes which will translate to a huge amount of physical circuits. This formalism is called fault-tolerant quantum computing (FTQC). Introducing the middle layer of abstraction for error correction changes the compilation fundamentally. FTQC compilation is a future direction of ours while we focus on physical circuits on this page.

Our compilers are general purpose. We have used the following four benchmark sets so far.

- Arithematic circuits. These are small components for larger quantum circuits requiring arithematic manipulations. This set includes a few versions of Toffoli gate, the "NAND" for quantum computing. These circuits are results from a quantum circuit optimizer by Y. Nam, N.J. Ross, Y. Su, A.M. Childs, and D. Maslov. Automated optimization of large quantum circuits with continuous parameters. October 2017.
- 3-Regular MaxCut QAOA. QAOA, one of the most well-known NISQ quantum algorithms, is a quantum-classical hybrid iterative method for solving combinatorial optimization problems. An example is QAOA for the MaxCut problem where the earlist work in QAOA projects a potential quantum advantage on 3-regular graphs. We find these circuits particularly useful to benchmark compilers because 1) the graphs can be generated at quantity and with randomness, and 2) the gates are commutable, i.e., can be executed at any order, resulting in a larger solution space for the compiler.
- QUEKO as specified in the next section. This benchmark set consists of synthetic quantum circuits to measure the performance of a compiler against the theoretical optimal depth/gate count.
- QASMBench is a low-level, easy-to-use benchmark suite. It consolidates commonly used quantum routines and kernels from a variety of domains including chemistry, simulation, linear algebra, searching, optimization, arithmetic, machine learning, fault tolerance, cryptography, etc., trading-off between generality and usability.

## Optimality study - how far are we from optimal?

We published QUEKO, a set of QLS benchmarks with known optimal depths and gate counts on given architectures, which can be used to evaluate existing QLS tools, and direct future development of such tools. Previously, QLS benchmarks do not provide optimal solutions, so researchers can only compare with each other, but how far are they from theoretical optimum? This is an NP-hard problem to answer in general but, specifically, the optimal solutions for QUEKO benchmarks on the given architectures are known, so we can measure the optimality gaps with QUEKO. In our study, large gaps were found, even up to 45x on some near-term feasible QUEKO circuits.

## Optimal quantum layout synthesis

After we revealed the optimality gaps, we went on to develop an optimal/exact QLS tool, OLSQ. We represented the solution space in a more compact way, resulting in orders-of-magnitubes reductions in time and memory. By eliminating some redundant variables between mapping transformations, we arrived at a more scalable, nearly-optimal solution, transition-based (TB-) OLSQ. It can reduce 70% SWAP cost in geomean and increase fidelity by 1.3x in geomean compared to leading related works. We also applied some domain-specific knowledge to adjust TB-OLSQ in the LSQC of QAOA circuits, resulting in further reductions in depth and SWAP cost. A microgrant for open-source OLSQ has been granted by Unitary Fund.

By analyzing the properties of NISQ applications, we developed three techniques improving qubit mapping quality and efficiency: SWAP absorption, commutation, and alternating matchings, which leads to OLSQ-GA, a qubit mapper that formulates the generalized NISQ mapping problem (with SWAP absorption) using SMT optimization and solves it optimally. Comparing to state-of-the-art optimal method (TB-OLSQ), we reduce depth by up to 50.0%, SWAP count by 100%. We improve fidelity by 9.45% for a single iteration, and 55.9% for 5 iterations on a set of QAOA instances. Compared to heuristic methods, the gaps are even larger.

## Exploring architecture design with layout synthesis

Current quantum processors are designed manually and not targeted on a specific quantum application. In classical computing, customized architectures have demonstrated significant performance and energy efficiency gains over general-purpose counterparts. For quantum computing, the qubit connectivity of quantum processors is an important factor that effects the circuit fidelity as additional computation overhead will be introduced in the QLS stage. Therefore, we focused on customizing qubit connectivity to improve fidelity for a given quantum circuit. We proposed a framework that integrates the optimal QLS tool into architecture optimization procedure in order to make the QLS tool search the architecture leading to the optimal compilation results. We demonstrate up to 59% fidelity improvement in simulation by optimizing the heavy-hexagon architecture for QAOA MAXCUT circuits, and up to 14% improvement on the grid architecture. For the QCNN circuit, architecture optimization improves fidelity by 11% on the heavy-hexagon architecture and 605% on the grid architecture.

## Layout synthesis for reconfigruable QC architectures

Because of the largest number of qubits available, and the massive parallel execution of entangling two-qubit gates, atom arrays is a promising platform for quantum computing. The qubits are selectively loaded into arrays of optical traps, some of which can be moved *during the computation itself*. By adjusting the locations of the traps and shining a specific global laser, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. In comparison, previous QC architectures only generate entanglement on *a fixed set* of quantum register pairs. Thus, *reconfigurable atom arrays* (RAA) present a new challenge for QC compilation, especially the QLS which decides the qubit placement and gate scheduling.

To further scale up our compiler, we learn from our previous experience in VLSI, an approach named *iterative peeling*. Specifically, we relax our SMT formulation so that each invocation of the solver handles as many gates as possible *for one two-qubit gate stage*, and the solver is called iteratively until all gates are compiled. As a result, our tool, OLSQ-DPQA, manages to compile larger circuit, e.g., the 90-qubit QAOA MaxCut shown below. This link provide a high-resolution version of the video.