Quantum computing and the entanglement frontier

TL;DR

The paper surveys the entanglement frontier as the core motivation for pursuing quantum supremacy, framing the challenge around controlling highly entangled quantum states under decoherence. It analyzes the landscape of quantum hardness versus classical simulability, highlighting both universal fault-tolerant schemes and topological approaches, as well as the role of local Hamiltonians and quantum simulation. It discusses error correction, scalable architectures, and the potential of topological quantum computing, while contrasting digital quantum computing with analog quantum simulators as near-term routes to gaining quantum advantage. The work articulates key open questions and the practical considerations for achieving large-scale, reliable quantum devices, and underscores the potential transformative impact of mastering highly entangled quantum systems.

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.

Figures (6)

• Figure 1: For a typical quantum state with many parts, a measurement acting on just one part collects a negligible amount of information about the state.
• Figure 2: (a) Hilbert space is vast, but the quantum states that can be prepared with reasonable resources occupy only a small part of it. (b) We believe that quantum computers can solve some problems that are hard for classical computers, but even quantum computers have limitations.
• Figure 3: The trace of a large matrix can be computed in the "one-clean-qubit" model of quantum computation, for which the input is one pure qubit and many maximally mixed qubits.
• Figure 4: Two quantum systems that may be hard to simulate classically. (a) A quantum circuit with commuting gates. (b) Nonadaptive linear optics with photon sources and photon detectors.
• Figure 5: The energy of a system governed by a local Hamiltonian can be measured efficiently by a quantum computer, using a procedure called "phase estimation."