Demonstrating an unconditional separation between quantum and classical information resources

TL;DR

This work demonstrates an unconditional quantum advantage in information resources required for a computational task, realized on Quantinuum's H1-1 trapped-ion quantum computer operating at a median two-qubit partial-entangler fidelity of 99.941(7)%.

Abstract

A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum systems and are prerequisites for useful quantum computation. To date, quantum advantage has been demonstrated, for example, through violations of Bell inequalities and sampling-based quantum supremacy experiments. However, both forms of advantage come with important caveats: Bell tests are not computationally difficult tasks, and the classical hardness of sampling experiments relies on unproven complexity-theoretic assumptions. Here we demonstrate an unconditional quantum advantage in information resources required for a computational task, realized on Quantinuum's H1-1 trapped-ion quantum computer operating at a median two-qubit partial-entangler fidelity of 99.941(7)%. We construct a task for which the most space-efficient classical algorithm provably requires between 62 and 382 bits of memory, and solve it using only 12 qubits. Our result provides the most direct evidence yet that currently existing quantum processors can generate and manipulate entangled states of sufficient complexity to access the exponentiality of Hilbert space. This form of quantum advantage -- which we call quantum information supremacy -- represents a new benchmark in quantum computing, one that does not rely on unproven conjectures.

Figures (8)

• Figure 1: One-way communication between two parties (a) is reinterpreted as a time-separated process on a single quantum device (b).
• Figure 2: Comparison of classical one-way communication lower bounds for our problem (green, from \ref{['thm:classical-lb']}) and Hidden Matching (purple, from BRSW12-bell), assuming implementation on a noiseless $n$-qubit quantum device (i.e., $\varepsilon = 1$). Points above the gray curve ($m = n$) indicate quantum advantage.
• Figure 3: $4$-qubit example circuits for implementing our protocol. The full implementation consists of concatenating the parameterized ansatz circuit (a) with the measurement circuit (b).
• Figure 4: Classical communication bounds as a function of $\mathcal{F}_{\mathsf{XEB}}$ for the $n=12$ task. The lower shaded region (purple) indicates infeasibility, meaning that no $m$-bit classical protocol achieves the given $\mathcal{F}_{\mathsf{XEB}}$. Conversely, the upper shaded region (green) indicates feasibility, meaning that there exists an $m$-bit classical protocol to achieve the given $\mathcal{F}_{\mathsf{XEB}}$. The vertical line marks the sample mean $\widehat{\mathcal{F}}_{\mathsf{XEB}} = 0.427$ achieved by our experiment, and the vertical shaded region (gray) marks $\widehat{\mathcal{F}}_{\mathsf{XEB}} \pm 5\sigma$.
• Figure S1: Comparison of upper bounds on $\mathcal{F}_{\mathsf{XEB}}$ derived from \ref{['thm:XEB_bound_from_norms']} with $n = 12$ and three different measurement ensembles: random Clifford (purple), exact $t$-design (red), and the Haar measure (gray). For the $t$-design ensemble, $t = 10$ optimizes the bound from \ref{['lem:design_op_norm']}. Also shown is the lower bound on $\mathcal{F}_{\mathsf{XEB}}$ known to be achievable by classical protocols (green), due to \ref{['cor:classical_upper_bound']}. Although $\varepsilon$ is the dependent variable (i.e., it is computed as a function of $m$), the figure is transposed to indicate the bounds on communication complexity as a function of the average linear cross-entropy benchmark.

Theorems & Definitions (51)

• Theorem 1
• Definition 1: $\varepsilon$-DXHOG, or Distributed Linear Cross-Entropy Heavy Output Generation
• Theorem 2
• Definition 2: BHH16-designs
• Theorem 3
• Lemma 1
• Lemma 2
• proof
• Lemma 3: Pin22-subexp
• Lemma 4