Optimal Layout-Aware CNOT Circuit Synthesis with Qubit Permutation

CNOT optimization plays a significant role in noise reduction for Quantum Circuits. Several heuristic and exact approaches exist for CNOT optimization. In this paper, we investigate more complicated variations of optimal synthesis by allowing qubit permutations and handling layout restrictions. We encode such problems into Planning, SAT, and QBF. We provide optimization for both CNOT gate count and circuit depth. For experimental evaluation, we consider standard T-gate optimized benchmarks and optimize CNOT sub-circuits. We show that allowing qubit permutations can further reduce up to 56% in CNOT count and 46% in circuit depth. In the case of optimally mapped circuits under layout restrictions, we observe a reduction up to 17% CNOT count and 19% CNOT depth.

Optimal Layout Synthesis for Deep Quantum Circuits on NISQ Processors with 100+ Qubits

Layout synthesis is mapping a quantum circuit to a quantum processor. SWAP gate insertions are needed for scheduling 2-qubit gates only on connected physical qubits. With the ever-increasing number of qubits in NISQ processors, scalable layout synthesis is of utmost importance. With large optimality gaps observed in heuristic approaches, scalable exact methods are needed. While recent exact and near-optimal approaches scale to moderate circuits, large deep circuits are still out of scope. In this work, we propose a SAT encoding based on parallel plans that apply 1 SWAP and a group of CNOTs at each time step. Using domain-specific information, we maintain optimality in parallel plans while scaling to large and deep circuits. From our results, we show the scalability of our approach which significantly outperforms leading exact and near-optimal approaches (up to 100x). For the first time, we can optimally map several 8, 14, and 16 qubit circuits onto 54, 80, and 127 qubit platforms with up to 17 SWAPs. While adding optimal SWAPs, we also report near-optimal depth in our mapped circuits.

Optimal Layout Synthesis for Quantum Circuits as Classical Planning

In Layout Synthesis, the logical qubits of a quantum circuit are mapped to the physical qubits of a given quantum hardware platform, taking into account the connectivity of physical qubits. This involves inserting SWAP gates before an operation is applied on distant qubits. Optimal Layout Synthesis is crucial for practical Quantum Computing on current error-prone hardware: Minimizing the number of SWAP gates directly mitigates the error rates when running quantum circuits. In recent years, several approaches have been proposed for minimizing the required SWAP insertions. The proposed exact approaches can only scale to a small number of qubits. Proving that a number of swap insertions is optimal is much harder than producing near optimal mappings. In this paper, we provide two encodings for Optimal Layout Synthesis as a classical planning problem. We use optimal classical planners to synthesize the optimal layout for a standard set of benchmarks. Our results show the scalability of our approach compared to previous leading approaches. We can optimally map circuits with 7 qubits onto a 16 qubit platform, which could not be handled before by exact methods.

Concise QBF Encodings for Games on a Grid

Encoding 2-player games in QBF correctly and efficiently is challenging and error-prone. To enable concise specifications and uniform encodings of games played on grid boards, like Tic-Tac-Toe, Connect-4, Domineering, Pursuer-Evader and Breakthrough, we introduce Board-game Domain Definition Language (BDDL), inspired by the success of PDDL in the planning domain. We provide an efficient translation from BDDL into QBF, encoding the existence of a winning strategy of bounded depth. Our lifted encoding treats board positions symbolically and allows concise definitions of conditions, effects and winning configurations, relative to symbolic board positions. The size of the encoding grows linearly in the input model and the considered depth. To show the feasibility of such a generic approach, we use QBF solvers to compute the critical depths of winning strategies for instances of several known games. For several games, our work provides the first QBF encoding. Unlike plan validation in SAT-based planning, validating QBF-based winning strategies is difficult. We show how to validate winning strategies using QBF certificates and interactive game play.

Implicit State and Goals in QBF Encodings for Positional Games

We address two bottlenecks for concise QBF encodings of maker-breaker positional games, like Hex and Tic-Tac-Toe. Our baseline is a QBF encoding with explicit variables for board positions and an explicit representation of winning configurations. The first improvement is inspired by lifted planning and avoids variables for explicit board positions, introducing a universal quantifier representing a symbolic board state. The second improvement represents the winning configurations implicitly, exploiting their structure. The paper evaluates the size of several encodings, depending on board size and game depth. It also reports the performance of QBF solvers on these encodings. We evaluate the techniques on Hex instances and also apply them to Harary's Tic-Tac-Toe. In particular, we study scalability to 19$\times$19 boards, played in human Hex tournaments.

Classical Planning as QBF without Grounding (extended version)

Most classical planners use grounding as a preprocessing step, reducing planning to propositional logic. However, grounding comes with a severe cost in memory, resulting in large encodings for SAT/QBF based planners. Despite the optimisations in SAT/QBF encodings such as action splitting, compact encodings and using parallel plans, the memory usage due to grounding remains a bottleneck when actions have many parameters, such as in the Organic Synthesis problems from the IPC 2018 planning competition (in its original non-split form). In this paper, we provide a compact QBF encoding that is logarithmic in the number of objects and avoids grounding completely by using universal quantification for object combinations. We compare the ungrounded QBF encoding with the simple SAT encoding and also show that we can solve some of the Organic Synthesis problems, which could not be handled before by any SAT/QBF based planners due to grounding.