[Paper Review] Quantum computing and the entanglement frontier

John Preskill|arXiv (Cornell University)|Mar 26, 2012

Quantum Computing Algorithms and ArchitectureComputer Science31 references149 citations

TL;DR

This paper proposes that quantum computing can achieve 'quantum supremacy' by harnessing highly entangled quantum states—beyond classical simulation—through fault-tolerant quantum error correction or topological quantum computation. It argues that controlling large-scale quantum systems will reveal new quantum phenomena and surpass classical capabilities, marking a transformative frontier in physics and computation.

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.

Motivation & Objective

• To investigate whether large-scale, highly entangled quantum systems can be controlled and whether they can outperform classical computers.
• To determine if quantum systems with exponential Hilbert space complexity can be simulated efficiently by classical systems, given current understanding.
• To assess the feasibility of achieving quantum supremacy through quantum error correction or topological quantum computation.
• To explore whether quantum simulators and universal quantum computers can probe exotic quantum phenomena inaccessible to classical methods.
• To evaluate whether near-term quantum devices with ~100 qubits can demonstrate super-classical behavior without full fault tolerance.

Proposed method

• Model feasible quantum states as those preparable via polynomial-sized quantum circuits acting on product states, restricting the Hilbert space to physically relevant, non-typical states.
• Use quantum circuits with polynomially bounded gate counts to define physically realizable quantum states and measurements.
• Propose quantum error-correcting codes as a mechanism to protect quantum information from decoherence, enabling scalable quantum computation.
• Explore topological quantum computation using non-Abelian anyons as an alternative path to fault tolerance, leveraging exotic quantum statistics.
• Compare analog quantum simulators (with limited fault tolerance) to universal quantum computers in simulating strongly correlated quantum systems.
• Use the concept of 'entanglement frontier' to frame the exploration of quantum systems with increasing complexity and entanglement.

Experimental results

Research questions

• RQ1 Can quantum systems with high entanglement surpass the capabilities of classical computers, and if so, under what conditions?
• RQ2 Is the classical simulation of highly entangled quantum states fundamentally intractable, and what evidence supports this claim?
• RQ3 Can quantum error correction based on standard qubits or topological anyons make scalable quantum computing feasible?
• RQ4 What experimental signatures would confirm the existence of robust quantum error-correcting codes in physical systems?
• RQ5 Can analog quantum simulators with imperfect control still demonstrate super-classical behavior in simulating exotic quantum phases?

Key findings

• Quantum systems with high entanglement occupy an exponentially small portion of Hilbert space, but these states are physically relevant and potentially hard to simulate classically.
• Theoretical evidence suggests that classical systems cannot efficiently simulate highly entangled quantum states, implying a fundamental quantum advantage.
• Quantum error correction offers a viable path to fault-tolerant quantum computation, though scalability depends on overcoming physical and engineering challenges.
• Topological quantum computation using non-Abelian anyons may provide inherently robust quantum information protection, offering an alternative to standard error correction.
• Analog quantum simulators can probe universal quantum phenomena even without full fault tolerance, especially when results are consistent across different experimental platforms.
• Systems with around 100 qubits may already demonstrate quantum supremacy in specific tasks, even without full error correction, suggesting near-term experimental feasibility.