QCrank Encoding Optimises Algorithm Deployment on Dynamically Programmable Qubit Arrays

Efficiently translating complex calculations into instructions for quantum computers remains a significant challenge, and recent work by Jan Balewski from the National Energy Research Scientific Computing Center, Wan-Hsuan Lin from the University of California, Los Angeles, and Anupam Mitra from Lawrence Berkeley National Laboratory, along with several colleagues, addresses this problem by focusing on a specific encoding algorithm called QCrank. The team investigates how QCrank can effectively store and retrieve classical data using dynamically programmable qubit arrays, a promising architecture for near-term quantum processors. This research demonstrates how the unique features of these arrays, including a high qubit count and reconfigurable connectivity, can be leveraged to optimise algorithm deployment and improve performance. By developing a realistic noise model and comparing results with existing quantum hardware, the study highlights the potential for these arrays to achieve promising accuracy when handling increasingly complex datasets.

Neutral Atom Qubit Systems and Parallel Control

Neutral-atom technologies are emerging as a promising platform for building quantum computers, with experimental systems now reaching hundreds of qubits and achieving competitive two-qubit gate fidelities of approximately 99.5%. These devices, known as dynamically programmable qubit arrays (DPQAs), offer key features including reconfigurable qubit connections, distinct functional zones, and simultaneous operation on multiple qubits using global laser beams. This functionality stems from the ability to physically move atoms without losing their quantum information. Unlike fixed-configuration arrays, DPQAs allow real-time adjustments to qubit connectivity and operations during computation.

By physically transporting atoms while preserving their quantum state, and applying two-qubit gates only between atoms brought close together, the system selectively operates on specific qubit subsets using a single optical pulse. Individual qubit addressing is also possible, providing further control over the quantum processor. Researchers are investigating how to optimize quantum circuit compilation and execution for DPQAs, focusing on maximizing gate application while minimizing atom movement, determining the optimal number of functional zones, and designing the best qubit layout for these zones. This work assumes plausible hardware constraints and illustrates the optimization process with a QCrank implementation for sequenced data encoding, comparing its projected accuracy on a simulated DPQA with results from Quantinuum’s H1-1E trapped-ion emulator and IBM Heron superconducting devices.

The neutral-atom DPQA model adopts an architecture inspired by Rb atom-based devices at Harvard and related Gemini-class quantum computers by QuEra. Contemporary neutral-atom quantum computers deterministically load atoms into laser traps created by spatial light modulators (SLMs), forming static trapping configurations that can be segmented into distinct zones. One zone might consist of a dense, regular square lattice for qubit storage, while another features closely paired trapping sites dedicated to entangling operations. Single-qubit gates can be applied globally or locally using laser beams. Site-selected atoms can be transported between zones and rearranged using acousto-optical deflectors (AODs), which can move several atoms in parallel. While research explores mid-circuit atom-selective measurements, this model assumes global destructive measurement of all qubits.

Photonic Quantum Noise and Atom Movement Errors

The research involves modeling noise channels for a digital photonic quantum computing architecture. The chosen noise values represent a current state-of-the-art baseline, with analyses also performed with noise levels adjusted by ±30% to explore potential improvements. Atom shuttling introduces a movement-related error, modeled as a Pauli channel error dependent on the number of atom movements, and contributes to circuit execution time. However, given long relaxation and decoherence times, movement-related delays have a negligible impact on result fidelity compared to channel errors. The QCrank encoding algorithm was selected to benchmark performance on a practically relevant quantum computing task.

QCrank encodes real-valued data sequences onto data qubits using uniformly controlled rotation gates and entangling gates, leveraging the exponential capacity of the Hilbert space. A QCrank circuit with na address qubits and nd data qubits can store L = nd × 2^na real-valued numbers, requiring L single-qubit rotations and L two-qubit entangling gates. Transpiling the circuit to a neutral-atom native gate-set, consisting of arbitrary angle rotations and CZ entangling gates, reveals features well-suited for this architecture. The resulting quantum circuit exhibits high execution parallelism, with identical single-qubit gates acting on all qubits or entangling gates applied in parallel layers.

The bipartite connectivity between address and data qubits is also well-suited for the architecture’s reconfigurable connectivity. Accuracy is quantified using the root mean square error (RMSE), reflecting errors introduced by the noisy execution of a QCrank circuit. A compilation optimization strategy was analyzed using a QCrank configuration with na = 4 address qubits and nd = 8 data qubits, encoding 128 real values onto 12 qubits. The data qubits are partitioned into two subsets of size na. CZ gates are applied between address qubits and one subset of data qubits, requiring dynamic movement of address qubits.

The strategy involves moving only address qubits, using horizontal moves for cyclic permutations, and vertical moves for addressing different data qubit sets. The performance of QCrank circuits was evaluated using the Qiskit simulator with a density matrix backend, across various input sizes. Results indicate that longer input sequences require more entangling gates, which are the dominant source of inaccuracy. Simulations were also performed using the Quantinuum noisy simulator and on IBM Fez with Pauli Twirling, providing a comparison across different hardware platforms. The findings suggest comparable QCrank accuracy for digital neutral atom and trapped-ion QPUs, with performance dependent on the ratio of address to data qubits.

Dynamic Qubit Arrays Show Promising Accuracy Scaling

Results demonstrate promising accuracy scaling for dynamically programmable qubit arrays, using simulations with Quantinuum’s H1-1E and experimental results from IBM Fez. These findings indicate potential advancements in the performance and scalability of quantum computations utilising dynamically programmable qubit architectures.

Scaling Simulations for Materials Discovery

Future work will focus on extending these methods to larger systems and more complex geometries, with the ultimate goal of simulating realistic materials with unprecedented accuracy. Investigations into alternative numerical schemes and parallelisation strategies are also planned to further improve computational efficiency and scalability. The research team intends to explore the application of these techniques to a wider range of scientific problems, including the study of high-temperature superconductivity and the design of novel energy materials.