Asymptotic Improvements to Quantum Circuits via Qutrits (1905.10481v1)

Abstract: Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$ binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla--a significant improvement over linear depth for the best qubit-only equivalent. Our circuit construction also features a 70x improvement in two-qudit gate count over the qubit-only equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search. We develop an open-source circuit simulator for qutrits, along with realistic near-term noise models which account for the cost of operating qutrits. Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation.

• The paper introduces a novel qutrit-based circuit achieving logarithmic depth in decomposing the Generalized Toffoli gate while reducing the two-qudit gate count by 70-fold.
• It leverages qutrits for temporary data storage to eliminate ancillary qubits, streamlining circuit design and ensuring compatibility with existing qubit I/O systems.
• Benchmarking with realistic noise models demonstrates over 90% fidelity on superconducting and trapped ion platforms, pointing to scalable improvements in quantum computation.

Asymptotic Improvements to Quantum Circuits via Qutrits

The paper entitled "Asymptotic Improvements to Quantum Circuits via Qutrits" presents a significant advancement in quantum computation by exploring the use of qutrits, a three-level quantum system, to enhance quantum circuit efficiencies. This work specifically addresses the decomposition of the Generalized Toffoli gate, an essential element in many quantum algorithms.

The authors introduce a novel circuit construction using qutrits that results in a logarithmic depth decomposition of the Generalized Toffoli gate, a marked improvement over the best qubit-only equivalent which has linear depth. Furthermore, this qutrit-based approach achieves a 70-fold reduction in the two-qudit gate count compared to the qubit-based equivalent. Such reductions in circuit complexity have substantial implications for the implementation and reliability of quantum algorithms, particularly in the constrained environments of NISQ (Noisy Intermediate Scale Quantum) computation.

A key insight of the paper is leveraging the additional quantum state offered by qutrits for temporary data storage, which eliminates the need for ancillary qubits—thereby operating efficiently within the ancilla-free frontier zone defined by utilizing every machine qubit for data storage. The design ensures communication between qubits while maintaining input and output states as binary, facilitating compatibility with current quantum devices focused on initialization and measurement in the qubit framework.

The implications of these findings are multifaceted. First, the reduction of circuit depth and gate count directly translates to enhanced fidelity and less susceptibility to errors—a critical consideration given current quantum hardware limitations. The circuit designs were benchmarked using realistic noise models for both superconducting and trapped ion quantum systems and demonstrated superior fidelity, over 90% reliability, compared to equivalent qubit circuits.

The paper's development of an open-source circuit simulator for qutrits offers a valuable tool for further exploration and validation of ternary quantum logic in practical applications such as quantum search algorithms like Grover's, artificial quantum neurons, and broader arithmetic circuits needed in Shor's algorithm. These algorithms can now potentially operate with fewer resources, expanding the achievable scope of quantum computation in the near term.

Notably, while the focus remains on qutrits, future research could explore further potential efficiency gains by extending to qudits with more than three levels in well-chosen contexts. Such work holds promise for optimizing specific quantum algorithms or adapting to hardware with more complex connectivity constraints.

This research indicates promising directions for quantum circuit design, where utilizing higher-dimensional quantum systems could pave the way for scalable quantum computing by bringing traditionally resource-intensive algorithms within reach without necessitating significant advancements in hardware. The approach outlined in this paper not only extends the computational frontier of current devices but also strengthens theoretical understanding and operational reliability of ternary logic in quantum computation.