Scaling Quantum Programs with Smarter Qubit Management

Classiq’s latest white paper, Scalable Memory Recycling for Large Quantum Programs, explores a practical way to optimize quantum computing resources: qubit reuse.

Quantum computing holds the promise of solving complex problems exponentially faster than classical computers. However, scaling it for real-world applications isn’t just about adding more qubits. Efficient resource management—memory optimization in particular—is key to handling larger, more complex quantum programs.

This blog takes you through the main highlights of the latest white paper from Classiq, Scalable Memory Recycling for Large Quantum Programs. By analyzing the structure of the circuit, our approach identifies opportunities to significantly reduce the number of qubits required for large-scale quantum circuits and improves execution efficiency—without sacrificing circuit quality.

A High-Level Abstraction that Addresses Reuse Challenges

The workflow proposed in our paper begins with the high-level quantum code. High-level code expresses the quantum program intuitively in terms of functions and variables, similar to classical programming. Classiq is a software platform for writing such quantum code, allowing the programmer to focus on the functional intent and leaving the low-level implementation details to the compiler.

Next, the platform transforms the high-level description into a control flow graph, applies uncomputation operations according to schemes based on existing scientific work, and then systematically analyzes uncomputation operations to maximize qubit reuse. The result is a circuit with lower qubit requirements and improved runtime, addressing one of the fundamental limitations of quantum programming.

The Heart of the Method: Control Flow Graphs and Topological Sorting

At the core of our approach lies the control flow graph (CFG), an intermediate representation of a quantum program that abstracts away low-level gate implementation. This structured representation enables a deeper analysis of the dependency relations between the quantum operations. An analysis pass serves to topologically sort the control flow graph, making it easier to identify qubit reuse opportunities following uncomputation operations.

We form the operation control flow by translating the high-level description of variables into an intermediate representation that illustrates the flow of quantum data between the operations. Essentially, the result is a directed acyclic graph (DAG) where each node is a quantum operation. These operations can be either atomic (e.g., native gates or qubit allocation) or compound, having a sequence of atomic operations.

The resulting CFG resembles a quantum circuit, but it abstracts away the individual qubits associated with the quantum variables and low-level implementation details of the quantum operations. More importantly, it inherently does not include edges to or from zero-state variables. Such edges are treated as degrees of freedom for the qubit reuse optimization to follow.

To maximize qubit reuse, we use topological sorting—a process that determines an execution order for the operations, while prioritizing qubit-releasing nodes. By scheduling these nodes before applying qubit-requiring ones, the approach ensures that freed qubits are reused efficiently, preventing allocation nodes (qubit-requiring ) from having to draw qubits from the device pool instead of recycling.

Each node in the graph has one of the following roles:

• Allocation nodes - represent points where new qubits are drawn from the pool of available qubits in the |0} state.
• Deallocation nodes - mark points where qubits are released to the pool and available for reuse.
• Neutral nodes - include operations that neither allocate nor deallocate qubits.

The problem description includes the total number of qubits required or released per node. The nodes themselves can include input/output functional qubits or auxiliary qubits. The I/O function’s arguments remain unchanged, while the result variable uses qubits drawn from the pool. Auxiliary qubits are both allocated and released by the node and are similar to classical temporary variables that store intermediate quantum results instead of recomputing them.

Essentially, different control flow graphs for the same problem correspond to different quantum circuits that exhibit different tradeoffs between total qubit count and the circuit’s execution time—depending on whether more or less qubits are reused.

Qubit Reuse Analysis and Trade-offs

Once the topological sorting is complete, the platform converts the intermediate representation of the control flow graph into a circuit-level description that explicitly connects qubit-releasing nodes with qubit-requiring ones. The reuse analysis pass then traverses this graph, deciding whether a qubit should be recycled or allocated from the device pool.

The decision to reuse qubits is influenced by optimization priorities. We use several heuristic strategies to determine how qubits are reused. These strategies are customized according to width/depth trade-offs –-- whether reducing memory requirements or preferring execution speed.

In cases where more sophisticated decision-making is needed, backtracking techniques can be applied to explore multiple reuse configurations before settling on an optimal one. You can find more information on our backtracking strategy in the blog The Classiq Engine II: Electric Boogaloo (or, How to Look for a Needle in a Haystack).

Tackling Scalability: From Theory to Practice

Our topological sorting algorithm scales quadratically with the number of nodes. This poses a major challenge in large-scale quantum circuits, and it can lead to compilation bottlenecks.

To counteract this, we can take a divide-and-conquer approach: We can apply the algorithm to disjoint clusters of atomic nodes, merge each cluster into a composite node, and apply the algorithm again.

How to choose the right node partitioning? Our paper explores how to reduce the process's complexity so that it scales asymptotically linearly with the number of nodes. But in practice, the solution is much simpler: we can leverage the code's high-level structure. Clustering the nodes based on their functional role in the high-level description makes clustering more intuitive and efficient. Note that this requires retaining the high-level information during the transformation into the CFG’s intermediate representation.

Our workflow highlights the advantages of writing a quantum program using a high-level description. This is exactly where Classiq technologies shine. Classiq is a software platform that helps quantum teams automate the process of converting high-level functional models into optimized quantum circuits.

Bringing the Future of Quantum Closer

The Classiq approach stands out from existing tools by helping you:

• Speed quantum algorithm development using an intuitive programming language and automation tool.
• Create applications that provide state of the art results, while balancing tradeoffs based on your priorities.
• Execute your custom algorithms on any quantum hardware or simulator.

Optimizing memory management and qubit reuse is a critical step toward making large-scale quantum computing feasible. By significantly reducing qubit overhead, it brings us closer to realizing a practical quantum future.

For a deeper dive into the technical details and methodologies behind this approach, read the full white paper on arXiv: Scalable Memory Recycling for Large Quantum Programs.