Quantum computation has shown significant advantages over classical computation, but the practical implementation of quantum algorithms and quantum circuits faces challenges, including the qubit connectivity constraint. This constraint can increase the depth overhead, which impacts the execution time of quantum algorithms. In a new study, researchers present a unified algorithm for qubit routing that fully characterizes the depth overhead. This could provide valuable insights into the layout of qubits to ensure their connectivity facilitates a small circuit depth overhead, potentially leading to more efficient quantum computing systems.
What is the Depth Overhead in Quantum Circuit Compilation?
Quantum computation has demonstrated significant advantages over classical computation in solving problems such as integer factorization, search, and various others through structurally designed algorithms. Quantum hardware technologies have seen considerable advancements in recent years, enabling the execution of quantum algorithms. A crucial aspect of this execution involves the compilation of quantum algorithms into quantum circuits, typically composed of 1 and 2-qubit gates.
However, the practical implementation of quantum algorithms and quantum circuits faces numerous challenges, one of which is the qubit connectivity constraint. On certain hardware platforms, 2-qubit gates can only act on certain pairs of qubits, while operations on two distant qubits are usually achieved by a sequence of SWAP operations. This qubit connectivity constraint can be naturally modeled by a connected constraint graph, where the vertex set represents the qubits and the edge set specifies the pairs of qubits on which 2-qubit gates can act.
How is the Depth Overhead Measured?
The depth overhead is measured by the ratio of the depth of the compiled circuit that respects the constraint graph to the depth of the original circuit. The aim is to compile any circuit with a small overhead. The depth increase ratio is controlled for any possible input circuit. While there are a few compilation algorithms working for a few specific graph constraints, no algorithm for a general graph is known.
What is the Impact of the Depth Overhead?
The depth overhead significantly impacts the execution time of quantum algorithms. In the NISQ era, the execution time is particularly relevant as most variational quantum algorithms require executing the same circuit thousands of times and use the sample average to estimate the expectation of an observable on the circuit’s final state.
How Can the Depth Overhead be Minimized?
In this paper, the authors present a unified algorithm for qubit routing for any given constraint graph, with the depth overhead fully characterized by the routing number, a well-studied graph theoretic measure. They provide an algorithm to compile an arbitrarily given circuit with no connectivity constraint into another circuit with the depth increase ratio bounded from above. Furthermore, they show that this is the best possible outcome, one cannot compile a generic circuit with a depth increase factor asymptotically better than the routing number.
What are the Implications of this Study?
This study has significant implications for the design of quantum chips. By fully characterizing the depth overhead for any given graph, the authors provide valuable insights into how to layout the qubits to ensure their connectivity facilitates a small circuit depth overhead. This could potentially lead to more efficient quantum computing systems.
On February 4, 2024, authors Pei Yuan and Shengyu Zhang published an article titled “Full Characterization of the Depth Overhead for Quantum Circuit Compilation with Arbitrary Qubit Connectivity Constraint” in arXiv (Cornell University). The paper provides a comprehensive analysis of the depth overhead for quantum circuit compilation with arbitrary qubit connectivity constraint.
