Classical Simulation of Intermediate-Size Quantum Circuits (1805.01450v2)

Abstract: We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater depth than previously reported using the cluster supported by the Data Infrastructure and Search Technology Division of the Alibaba Group. For example, computing a single amplitude of an $8\times 8$ qubit circuit with depth $40$ was previously beyond the reach of supercomputers. Our algorithm can compute this within $2$ minutes using a small portion ($\approx$ 14% of the nodes) of the cluster. Furthermore, by successfully simulating quantum supremacy circuits of size $9\times 9\times 40$, $10\times 10\times 35 $, $11\times 11\times 31$, and $12\times 12\times 27 $, we give evidence that noisy random circuits with realistic physical parameters may be simulated classically. This suggests that either harder circuits or error-correction may be vital for achieving quantum supremacy from random circuit sampling.

• The paper demonstrates a novel distributed algorithm using tensor network contractions to simulate circuits up to sizes of 12x12x27.
• It achieves efficient simulation of an 8x8 circuit at depth 40 using modest cluster resources, significantly reducing computational time.
• The work challenges quantum supremacy claims by showing classical methods can replicate noisy random circuits, prompting further error-correction research.

Essay on "Classical Simulation of Intermediate-Size Quantum Circuits"

The paper "Classical Simulation of Intermediate-Size Quantum Circuits" contributes to the ongoing efforts in the classical simulation of quantum systems, with particular emphasis on circuits that approach the boundaries of what's considered feasible using classical computational resources. The authors present a novel distributed algorithm designed for the classical simulation of general quantum circuits—specifically, for calculating output probabilities from universal random circuits.

Overview of Contributions

The innovative aspect of this work lies in its ability to simulate what were previously considered unfeasible quantum circuit configurations. The authors demonstrate this with numerical results, highlighting computations like the output amplitude of an $8 \times 8$ qubit circuit at a depth of $40$ within a remarkably short time using only a modest fraction of a computational cluster. This represents a significant leap over previous capabilities, which often required substantial supercomputing resources.

Their approach uses a distributed technique that leverages tensor network contractions, informed by insights from Markov and Shi. By optimizing tensors through preprocessing and exploiting the temporal sequence of gate operations, the authors achieve performance improvements that permit simulations of circuits up to sizes of $12 \times 12 \times 27$. This approach also incorporates an undirected graphical model, utilizing parallelization to overcome limits imposed by classical memory in simulating high-depth circuits.

Implications and Results

The simulation of quantum supremacy circuits of sizes up to $12 \times 12 \times 27$ provides compelling evidence regarding the classical tractability of noisy random circuits. The results suggest that classical simulation can feasibly mirror the behavior of such circuits, which were initially posited to be exclusive in their computational capability to quantum devices demonstrating supremacy.

This research underscores the necessity of either increasing the complexity of circuits or adopting error-corrective methodologies to legitimately claim supremacy through random circuit sampling. The findings imply that without such enhancements, achieving quantum supremacy in this domain might require additional computational depths or novel computing paradigms.

Future Developments

Looking ahead, the work highlights potential directions for future research. Enhanced classical simulation techniques could be developed by exploring alternative heuristics for node elimination in the tensor network. Moreover, refining the efficacy of parallelization strategies and optimizing memory usage within and across clusters could yield further advancements in simulating ever-larger quantum circuits.

On the quantum end, the paper suggests a pivot towards constructing fundamentally more challenging quantum circuits or implementing robust error-corrective mechanisms to ensure quantum supremacy's demonstrability against classical simulators.

Conclusion

In conclusion, this paper makes noteworthy strides in the field of classical simulation of quantum circuits. It challenges the conventional limits and opens the door for further exploration into both the potential and limitations of classical computing in simulating quantum dynamics. The practical and theoretical insights provided have the potential to significantly influence future developments in quantum simulation and the ongoing discourse surrounding quantum supremacy.