Pareto-Efficient Quantum Circuit Simulation Using Tensor Contraction Deferral (1710.05867v4)

Abstract: With the current rate of progress in quantum computing technologies, systems with more than 50 qubits will soon become reality. Computing ideal quantum state amplitudes for circuits of such and larger sizes is a fundamental step to assess both the correctness, performance, and scaling behavior of quantum algorithms and the fidelities of quantum devices. However, resource requirements for such calculations on classical computers grow exponentially. We show that deferring tensor contractions can extend the boundaries of what can be computed on classical systems. To demonstrate this technique, we present results obtained from a calculation of the complete set of output amplitudes of a universal random circuit with depth 27 in a 2D lattice of $7 \times 7$ qubits, and an arbitrarily selected slice of $2^{37}$ amplitudes of a universal random circuit with depth 23 in a 2D lattice of $8 \times 7$ qubits. Combining our methodology with other decomposition approaches found in the literature, we show that we can simulate $7 \times 7$-qubit random circuits to arbitrary depth by leveraging secondary storage. These calculations were thought to be impossible due to resource requirements.

• The paper introduces tensor contraction deferral to extend classical simulation capabilities for quantum circuits.
• It employs hypergraph representations and tensor slicing to optimize memory and computation, reducing simulation complexity.
• Results include simulating a 49-qubit, depth-27 circuit using only 64 TB, marking a breakthrough in overcoming traditional resource limits.

Pareto-Efficient Quantum Circuit Simulation Using Tensor Contraction Deferral

In the paper titled Pareto-Efficient Quantum Circuit Simulation Using Tensor Contraction Deferral, the authors present a novel simulation methodology that aims to push the computational boundaries of simulating quantum circuits on classical computers. The essential problem tackled is the exponential growth in resource requirements when simulating quantum circuits, which limits our ability to verify quantum algorithms and device fidelities, especially in systems exceeding 50 qubits. Here, they introduce tensor contraction deferral as a key technique to extend the capabilities of classical simulations, effectively challenging prior assumptions about computational limits.

The authors conducted simulations of universal random circuits with notable configurations: a complete set of output amplitudes for a 49-qubit circuit with depth 27 arranged in a 2D lattice, and a slice of amplitudes from a 56-qubit circuit with depth 23. The results showcase that the deferral of tensor contractions, combined with optimized secondary storage techniques, enables vastly larger circuits to be simulated than previously thought possible.

Methodology

The paper elaborates on an advanced simulation strategy employing tensor networks as graphical models for quantum circuits. By introducing a hypergraph representation, the method particularly focuses on handling diagonal and separable gates efficiently, significantly reducing the complexity in tensor contractions. The computational approach is divided into a sequence of contractions that incorporates tensor slicing for parallel processing, thus optimizing memory usage.

Utilizing a comprehensive graph-Theoretical framework, the authors outline how non-adjacent contractions can be leveraged alongside traditional adjacent contractions, creating opportunities to defer these operations. This allows breaking down the simulation into subcircuits, each of which can be independently calculated prior to merging, reducing intermediate data size and computational load.

Numerical Results and Impact

On the Vulcan supercomputer, the research demonstrated the feasibility of simulating a 49-qubit circuit, a task thought to require multiple petabytes of memory with earlier methods. The authors achieved this with efficient use of approximately 64 terabytes, attributed to the reduction in computational overhead enabled by tensor contraction deferral and strategic organization across primary and secondary storage.

Such results provoke reconsideration of the computational hurdles in quantum simulation, suggesting a tangible pathway towards more practically assessing quantum algorithms and devices. The outcomes resonate with ongoing discussions in quantum supremacy, showcasing the practical significance of nuanced methodologies in extending what classical simulations can achieve.

Future Directions

Given the dramatic efficiency improvements alluded to in this paper, future research directions could investigate deeper integration of contraction deferral with novel quantum hardware adaptations, as well as further exploration into quantum circuit designs with exotic connectivity or gate sets. As these methods gain traction, there's potential for dynamic feedback connections between classical simulations and quantum circuit optimization.

The broader implications touch upon various domains, such as chemical modeling and complex system analysis, due to the versatility and adaptiveness of tensor networks beyond quantum circuits. Moreover, tackling larger and deeper circuits might also unlock new insights in quantum algorithm development, directly impacting quantum programming paradigms.

Ultimately, the paper stands as a testament to the ingenuity and creativity in addressing computational obstacles in quantum studies, ensuring that classical tools can remain robust and relevant amidst the rapid advancements in quantum technologies.