Quantum-assisted quantum compiling (1807.00800v5)

Abstract: Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitary $U$ and a trainable unitary $V$ as the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost involves not only the global overlap ${\rm Tr} (V^\dagger U)$ but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we prove that our cost cannot be efficiently approximated with a classical algorithm under reasonable complexity assumptions. We present both gradient-free and gradient-based approaches to minimizing this cost. As a demonstration of QAQC, we compile various one-qubit gates on IBM's and Rigetti's quantum computers into their respective native gate alphabets. Furthermore, we successfully simulate QAQC up to a problem size of 9 qubits, and these simulations highlight both the scalability of our cost function as well as the noise resilience of QAQC. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking.

• The paper presents a novel variational quantum-classical approach (QAQC) that compiles target unitaries by using a quantum cost function evaluation.
• It shows that evaluating the cost function is -hard, underscoring a decisive quantum advantage over classical methods.
• Implementations on IBM and Rigetti hardware confirm the feasibility of one-qubit gate compilation, with simulations demonstrating scalability up to nine qubits.

Quantum-Assisted Quantum Compiling: A Technical Overview

This paper, "Quantum-assisted quantum compiling," by Sumeet Khatri et al., addresses the challenge of compiling quantum algorithms for near-term quantum computers while considering device-specific constraints. Quantum compiling is crucial for optimizing the performance of noisy intermediate-scale quantum (NISQ) computers, bridging the gap between high-level quantum algorithms and their execution on quantum hardware. The authors introduce a variational hybrid quantum-classical algorithm, called quantum-assisted quantum compiling (QAQC), which leverages a quantum computer to evaluate the cost function that measures the closeness between a target unitary $U$ and a trainable unitary $V$.

Key Contributions

1. Cost Function Design: The paper presents a cost function based on the overlap between the target unitary $U$ and the trainable unitary $V$, which is calculated on a quantum computer. Importantly, this includes not only the global overlap but also local overlaps concerning individual qubits, facilitating scalability with problem size.
2. Hardness of Classical Approximation: The authors establish that evaluating their proposed cost function is -hard, indicating that no classical algorithm can efficiently simulate it under reasonable complexity assumptions. This result underscores the advantage of using a quantum approach for specific computational tasks.
3. Implementation and Results: The paper demonstrates small-scale implementations of QAQC on actual quantum hardware from IBM and Rigetti, successfully compiling one-qubit gates into the respective native gate alphabets. Further, the method's scalability is evidenced by simulations up to nine qubits, highlighting both scalability of the cost function and noise resilience.
4. Potential Applications: The authors outline potential applications of QAQC, including algorithm depth compression, black-box compiling, noise mitigation, and benchmarking. The flexibility in compiling shorter-depth gate sequences or mitigating noise impacts marks QAQC's utility in the NISQ era.

Theoretical and Practical Implications

Theoretically, the paper provides a framework for using quantum resources to perform tasks inherently difficult for classical systems. Practically, the advances in quantum compiling have implications for enhancing the performance of NISQ devices, allowing more efficient utilization of limited resources. The proposed QAQC algorithm aligns with the current trajectory of quantum hardware capabilities and offers a pathway for quantum software to evolve in tandem with hardware advancements.

Future Directions

Looking forward, QAQC can be refined and expanded to accommodate larger and more complex quantum systems. Exploration into more sophisticated cost functions, specific ansatz structures that consider Hamiltonian dynamics, and the integration of error correction techniques can further enhance the algorithm's efficacy and applicability. Moreover, comprehensive studies on the impact of noise within quantum circuits, along with strategies for robust QAQC implementations on diverse quantum platforms, would be beneficial.

In conclusion, this paper contributes a pivotal methodology to the field of quantum compiling while addressing the practical challenges of executing quantum algorithms on contemporary quantum devices. The intersection of theoretical insights and experimental validations positions QAQC as an essential tool in the quantum computing landscape.