Quantum computing and the entanglement frontier (1203.5813v3)

Abstract: Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly entangled quantum systems efficiently, and we hope to hasten the day when well controlled quantum systems can perform tasks surpassing what can be done in the classical world. One way to achieve such "quantum supremacy" would be to run an algorithm on a quantum computer which solves a problem with a super-polynomial speedup relative to classical computers, but there may be other ways that can be achieved sooner, such as simulating exotic quantum states of strongly correlated matter. To operate a large scale quantum computer reliably we will need to overcome the debilitating effects of decoherence, which might be done using "standard" quantum hardware protected by quantum error-correcting codes, or by exploiting the nonabelian quantum statistics of anyons realized in solid state systems, or by combining both methods. Only by challenging the entanglement frontier will we learn whether Nature provides extravagant resources far beyond what the classical world would allow.

• The paper demonstrates that exploiting quantum entanglement can break classical simulation limits, paving the way for quantum supremacy.
• It details various quantum computing models and emphasizes error correction and decoherence management as key to advancing system reliability.
• The findings underscore significant theoretical and practical challenges in developing scalable quantum computers to simulate complex quantum states.

Overview of "Quantum Computing and the Entanglement Frontier"

In "Quantum Computing and the Entanglement Frontier," John Preskill examines the potential and challenges of quantum information science, particularly focusing on the concept of the "entanglement frontier." The primary motivation behind this exploration is the belief that classical systems cannot efficiently simulate highly entangled quantum systems, prompting the pursuit of what is termed "quantum supremacy." Preskill discusses various approaches to achieving quantum supremacy, the complexities of managing quantum states, and the implications of this work on both theoretical and practical levels.

Achieving Quantum Supremacy

Preskill identifies several potential pathways toward achieving quantum supremacy, wherein quantum systems perform tasks beyond the capabilities of classical computers. A central route is through the development of quantum algorithms that offer super-polynomial speedups over classical counterparts, such as Shor's algorithm for factorization. Other strategies include using quantum systems for simulating exotic states of matter that are strongly correlated. A notable bottleneck in these efforts is mitigating the effects of decoherence, a process that often renders quantum systems effectively classical.

The Role of Quantum Entanglement

At the heart of quantum information science is entanglement, a distinctly quantum phenomenon with no classical counterpart. Preskill uses the metaphor of a "quantum book" to highlight the distributed nature of information in entangled systems. He explores the challenge of capturing information embedded in quantum states, noting that the classical description of a quantum state taxed by entanglement demands 'astronomical' classical resources.

Current and Potential Models of Quantum Computation

Preskill explores various models of quantum computation, from universal quantum computers to more specialized configurations like linear quantum optics and topological quantum computers. He highlights how some systems, albeit not fully universal, point towards classical intractability, shedding light on the threshold of quantum-classical distinctions in computation.

Quantum Error Correction and Scalability

The reliability of quantum computing inherently depends on effective quantum error correction to combat noise and errors—phenomena that accumulate in complex quantum circuits. Preskill distinguishes key methods for encoding quantum information in redundancies that protect against these errors. He marks the development of scalable quantum computing as contingent upon reducing error rates below a critical threshold and employing quantum error-correcting codes efficiently.

Future Directions

Preskill provocatively raises questions about the future of quantum computing, including the feasibility of adiabatic approaches, the bridging of topology and non-abelian anyon structures, and the broader application of quantum simulation in understanding strongly correlated materials. These issues and questions underscore the quantum-classical boundary and the enigmatic regime of highly entangled states.

Conclusion

In conclusion, Preskill's paper underscores both the extraordinary opportunities and challenges faced in advancing quantum information science. The exploration of the entanglement frontier holds profound implications not just for computation but for our understanding of complex quantum systems. As quantum technologies evolve, they promise to expand our scientific toolkit significantly, unraveling new phenomena and enabling computation that vastly exceeds classical limits. However, achieving these promises hinges on overcoming the substantial theoretical, practical, and engineering challenges outlined in this discourse on quantum supremacy and its prospects.