Quantinuum scientists find new approach for optimizing and automating qubit reuse
Advanced technique enables larger algorithms in NISQ era and beyond
By Matthew DeCross, Eli Chertkov, Megan K., Michael Foss-Feig
Quantinuum scientists have found a new way to reuse qubits that maximizes the size of programs that can be run on quantum computers with limited numbers of qubits. While this approach will benefit algorithms in the NISQ era, company researchers also expect it to scale as quantum computers gain additional qubits and become less error prone.
The paper, Qubit-reuse compilation with mid-circuit measurement and reset, was authored by Quantinuum scientists Matthew DeCross, Eli Chertkov, Megan Kohagen, and Michael Foss-Feig. The research was recently published on arXiv.
Many current quantum computers are limited by the number of qubits available for computation. To achieve computational advantage of quantum computers over their classical counterparts on a variety of practical applications, researchers will need to make efficient use of qubits.
“We were mainly motivated by increasing the utility of the relatively small quantum computers we have today. But looking ahead to the early days of fault-tolerant quantum computing, there will be a point in time where we’re trying to run circuits with 50 logical qubits and very low error rates,” Foss-Feig said. “At that point, we’ll be starved for logical qubits to solve a lot of problems, and so this approach will also be useful in that intermediate timeframe.”
The new technique offers an automated framework for compiling circuits to run on fewer qubits by mapping a circuit to a compressed version of itself using mid-circuit measurement and reset. According to the scientists, this technique will still be viable when quantum systems have achieved several thousand qubits. It is also device agnostic and can work with any circuits on any machine.
Qubit reuse is an essential ingredient of scalable quantum error correction protocols, which require repeated mid-circuit measurements and resets of ancilla qubits to measure error syndromes. Recently, reuse techniques have been used to experimentally prepare and time-evolve large tensor network states on trapped ion quantum computers and to study a nonequilibrium phase transition.
Automation of Qubit Reuse
Compiling programs with qubit reuse is a difficult combinatorial optimization problem and an underexplored area of quantum circuit design. The key principle underlying this approach is that in many cases only partial execution of a circuit is required to measure a given output qubit. In order to measure a given output qubit, only the gates that causally influence that output in the future need to be executed, a set of operations called the “causal cone” of the output. After executing only part of the original circuit, that output qubit can potentially be reset and recycled as an input qubit elsewhere in the circuit.
Once the causal structure of a circuit has been identified, there is still a lot of freedom related to the order in which output qubits are measured. Previous efforts to exploit causal structure involved a laborious manual process for each new application, and required circuits to be simple enough for causal cones to be determined visually and optimal measurement orders to be identified. DeCross, the lead author of the study, said their new technique automatically generates an exact logical rewriting of the circuit using fewest possible qubits, but the exact same number of gates.
In previous studies, Quantinuum researchers have used this old labor-intensive approach to build compressed circuits for quantum tensor network simulations of materials.
“In a lot of cases, it would be really difficult to imagine scaling those techniques up by inspection,” Foss-Feig said. “You would need an automated tool to implement this analysis and our algorithms let you do that.”
The team used two algorithms for performing qubit-reuse compilation: an exact constraint programming optimization model and a greedy heuristic that runs quickly up to large numbers of qubits and scales polynomially with qubit number.
The team numerically benchmarked these algorithms on the QAOA applied to the MaxCut problem on random three-regular graphs. They also investigated several examples of highly structured circuits with near-term relevance, including 1D and 2D time evolution circuits and certain quantum tensor networks, and solved the qubit-reuse compilation problem analytically for these cases.
Qubit Reuse in Practice
The research team demonstrated the practical benefit of these qubit-reuse compilation algorithms by experimentally solving an 80-qubit MaxCut quantum adiabatic optimization algorithm (QAOA) problem on the 20-qubit Quantinuum H1–1 quantum processor. Variational algorithms like QAOA and the variational quantum eigensolver (VQE) are natural use cases for this compilation because their circuits are wide, shallow, and designed to be run on NISQ devices.
During the experiment, the team performed the full QAOA optimization protocol on the quantum computer, as opposed to some previous experiments which sometimes performed the optimization on classical computers and only executed one calculation on the quantum computer at the optimal parameters.
“Our results show the application of qubit-reuse compilation to an important benchmark problem, and demonstrate that the resulting circuits are feasible to run and optimize at realistic levels of noise” DeCross said.
