[Paper Review] Exact sampling and entanglement-free resources for measurement-based quantum computation

Matty J. Hoban, Joel J. Wallman+4 more|arXiv (Cornell University)|Apr 9, 2013

Quantum Information and Cryptography4 citations

TL;DR

This paper introduces a classical analog of measurement-based quantum computation (MBQC) using quantum-generated resource states that violate no Bell inequalities yet exhibit non-classical computational power. It identifies uniform families of quantum circuits whose exact classical simulation is likely intractable, and shows these can be efficiently implemented in MBQC without adaptive measurements, demonstrating quantum non-classicality in resource states without entanglement-based nonlocality.

ABSTRACT

Measurement-based quantum computation (MBQC) is a model of quantum computation, in which computation proceeds via adaptive single qubit measurements on a multi-qubit quantum state. It is computationally equivalent to the circuit model. Unlike the circuit model, however, its classical analog is little studied. Here we present a classical analog of MBQC whose computational complexity presents a rich structure. To do so, we identify uniform families of quantum computations (refining the circuits introduced by Bremner, Jozsa and Shepherd in Proc. R. Soc. A 467, 459 (2011)) whose output is likely hard to exactly simulate (sample) classically. We demonstrate that these circuit families can be efficiently implemented in the MBQC model without adaptive measurement, and thus can be achieved in a classical analog of MBQC whose resource state is a probability distribution which has been created quantum mechanically. Such states (by definition) violate no Bell inequality, but nevertheless exhibit non-classicality when used as a computational resource - an imprint of their quantum origin.

Motivation & Objective

• To develop a classical analog of measurement-based quantum computation (MBQC) that retains computational power despite lacking quantum nonlocality.
• To identify uniform families of quantum circuits whose exact classical simulation is likely intractable, establishing computational hardness.
• To demonstrate that such hard-to-simulate computations can be efficiently realized in MBQC using resource states that do not violate Bell inequalities.
• To show that non-classicality in computational resources can emerge from quantum origin even without entanglement-based nonlocality.

Proposed method

• Identifies uniform families of quantum circuits refined from Bremner, Jozsa, and Shepherd (2011), which are likely hard to exactly simulate classically.
• Constructs a classical analog of MBQC where the resource state is a probability distribution prepared via quantum means but not exhibiting quantum nonlocality.
• Demonstrates that these quantum-generated resource states can implement the hard-to-simulate circuits in MBQC without requiring adaptive single-qubit measurements.
• Analyzes the computational complexity of the classical analog, revealing a rich structure in classical simulation difficulty.
• Establishes that the non-classicality of the resource states arises from their quantum origin rather than from Bell inequality violations or entanglement-based nonlocality.

Experimental results

Research questions

• RQ1 Can a classical analog of MBQC be constructed that retains computational power despite the absence of quantum nonlocality?
• RQ2 Which families of quantum circuits are likely hard to exactly simulate classically, and can they be efficiently realized in MBQC?
• RQ3 Can resource states that do not violate Bell inequalities still serve as non-classical computational resources in MBQC?
• RQ4 What is the role of quantum origin in generating non-classicality in computational resources, independent of entanglement or nonlocality?

Key findings

• The paper identifies uniform families of quantum circuits whose exact classical simulation is likely intractable, establishing a computational hardness threshold.
• These hard-to-simulate circuits can be efficiently implemented in the MBQC model without adaptive measurements, using quantum-generated resource states.
• The resource states used are probability distributions created quantum mechanically but do not violate any Bell inequality, indicating no quantum nonlocality.
• Despite the absence of Bell inequality violations, these resource states still exhibit non-classicality when used as computational resources, a signature of their quantum origin.
• The results demonstrate that non-classical computational power can emerge from quantum resource states without entanglement-based nonlocality, highlighting a new form of quantum advantage.