Characterizing Quantum Supremacy in Near-Term Devices (1608.00263v3)

Abstract: A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers, achieving so-called quantum supremacy. We study the task of sampling from the output distributions of (pseudo-)random quantum circuits, a natural task for benchmarking quantum computers. Crucially, sampling this distribution classically requires a direct numerical simulation of the circuit, with computational cost exponential in the number of qubits. This requirement is typical of chaotic systems. We extend previous results in computational complexity to argue more formally that this sampling task must take exponential time in a classical computer. We study the convergence to the chaotic regime using extensive supercomputer simulations, modeling circuits with up to 42 qubits - the largest quantum circuits simulated to date for a computational task that approaches quantum supremacy. We argue that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.

• The paper demonstrates that random quantum circuits serve as effective benchmarks for quantum supremacy, as classical simulation scales exponentially with qubit number.
• It employs cross entropy as a fidelity measure, with simulations up to 42 qubits showing convergence to the Porter-Thomas distribution indicative of quantum chaos.
• The study grounds its findings in quantum chaos and computational complexity theory, suggesting that around 50 superconducting qubits may be sufficient to achieve supremacy.

Characterizing Quantum Supremacy in Near-Term Devices

The paper "Characterizing Quantum Supremacy in Near-Term Devices" provides a comprehensive paper on the capabilities of quantum computers in executing specific computational tasks that are infeasible for classical computers. The paper particularly focuses on the concept of quantum supremacy—a state where quantum devices can outperform the most advanced classical systems in a well-defined computational activity without error correction. The work employs random quantum circuits as a benchmarking tool for achieving this milestone.

Random quantum circuits serve as a natural testbed for evaluating quantum supremacy since simulating these circuits classically necessitates performing tasks that scale exponentially with the number of qubits involved. The authors leverage the complexity of sampling from these circuits to demonstrate the computational difficulty for classical simulators, highlighting the exponential time requirement for classical simulation tasks, extending similar arguments from quantum chaos literature.

Through extensive simulations up to 42 qubits—the largest simulated thus far—this paper evaluates the transition towards the chaotic regime of quantum circuits, emphasizing that around 50 superconducting qubits may suffice for observing quantum supremacy. The authors introduce cross entropy as a pivotal measure for gauging the fidelity of quantum circuits in reaching this regime, suggesting it as a practical benchmark for contrasting experimental outputs against ideal distributions.

Theoretically, the paper grounds its arguments on the principles of computational complexity and quantum chaos, connecting them to quantum physics through extrapolations to the chaotic nature of quantum systems. The findings suggest that, owing to chaotic evolutions, only a high-fidelity classical simulation that scales exponentially with resources can achieve comparable results, implying the inherent computational power of quantum circuits in such scenarios.

Numerically, the research shows that simulated circuits remarkably align with the Porter-Thomas distribution, indicative of quantum chaotic behavior, and hence hard for classical systems. Strong numerical results demonstrate that the simulations can achieve Porter-Thomas distributions at depth 25, showing promising convergence even across entropies and moments up to the tenth order.

The implementation of quantum chaos metrics and computational complexity arguments stands out theoretically, as they bolster the author's stance on the likely intractability for classical systems to replicate quantum sampling processes. The implications stretch beyond immediate computational tasks, shedding light on future endeavors in quantum computing, where quantum supremacy could redefine computational limits, optimization problems, and complex simulations.

However, the authors emphasize that achieving and confirming quantum supremacy not only hinges on improving quantum hardware but also on validating these results through benchmarks that correlate with theoretical predictions, presenting a robust framework for routinely asserting such capabilities. Future visions in AI and computing could certainly leverage quantum supremacy for advanced problem-solving abilities and operational efficiency, unearthing prospects that remain speculative with current classical resources.

In conclusion, while the approach designed by the authors doesn't make bold assertions outside the scope, it meticulously lays the groundwork for pursuing quantum computational superiority. The paper implies that as computational requirements escalate across domains, the practical demonstration and acceptance of quantum supremacy could herald transformative impacts across scientific and artificial intelligence landscapes.