Efficiently verifiable quantum advantage on near-term analog quantum simulators

TL;DR

The paper tackles the challenge of verifiably demonstrating quantum advantage on near-term analog quantum simulators. It introduces a protocol that couples a single-step Feynman-Kitaev encoding with a commuting $ZZ+Z$ Hamiltonian to certify classically hard sampling tasks, while requiring only $O(\lambda^2)$ classical time and $O(1)$ history-state samples from the prover. A measurement scheme estimates three key parameters—input fidelity $F_{in}$, sampling probability $p_{samp}$, and $|\operatorname{Tr}[\rho O_{10}]|^2$—to bound the output fidelity $F_{out}$ and the total variation distance to the ideal distribution, all via constant-shot, single-qubit measurements. The authors provide a near-term honest-prover strategy based on an echo-based history-state preparation and discuss realistic experimental pathways leveraging mostly analog computation with a global CZ gate. Overall, the work delivers a resource-efficient route to verified quantum advantage on analog devices, with concrete thresholds and robustness analyses that guide practical implementations.

Abstract

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an $O(λ^2)$-time classical computation, and the prover need only prepare $O(1)$ samples of a history state and perform $O(λ^2)$ single-qubit measurements, for a security parameter $λ$. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

Figures (6)

• Figure 1: [protocol]prot:protocol_draft_1 Our protocol for demonstrating quantum advantage.
• Figure 1: The square lattice can be divided into two parts such that every $ZZ$ operator acts on qubits from both parts.
• Figure 1: The final quantum circuit for a (4+1)-qubit example system, where the initial state has been prepared as $\ket{\psi_\mathrm{initial}} = \frac{1}{\sqrt{2}}(\ket{0} + \ket{1}) \ket{\phi_\mathrm{in}})$. Here the first qubit is the clock qubit, and part $B$ consists qubits 1 and 4, while part $A$ consists of qubits 2 and 3. The initial state $\ket{\psi_\mathrm{initial}}$ can be prepared by single-qubit rotations. By applying Hadamard gates before and after the globally controlled-$ZZZZ$ gate for qubits in part $B$, a controlled-$XZZX$ is implemented. As single-qubit $Z$ commutes with $e^{-\mathrm{i} H T}$, the $Z$ operations cancel out for qubits in block $A$.
• Figure 1: The "bus" scheme for realizing a global $CZ$ gate. All simulation qubits are only coupled with the central "bus" cavity mode, which behaves effectively as the clock qubit. Both the global $CZ$ gate and the $ZZ+Z$ interaction between simulation qubits can be mediated via the bus mode.
• Figure 1: The quantum switch scheme. Here the simulation qubits are assigned in the square lattice as usual. A photon source gives signals that implement $Z$ operations for each simulation qubit. A high-performance quantum switch, controlled by the clock qubit which could be in superposition, determines whether the signal can be received by simulation qubits or not, which realizes a global $CZ$ gate.

Theorems & Definitions (24)

• Definition 1: $\mathsf{QPIP}_k$ protocol (simplified)
• Definition 2: Mostly analog quantum computation
• Definition 3: Mostly analog commuting quantum computation
• Definition 4: Mostly analog + $\mathrm{GCZ}$ commuting quantum computation
• Theorem 1: Main result---state-transmission version
• Theorem 2: Main result---trusted-measurement version
• Theorem 3: Lower bound on the output fidelity
• Lemma 1: Sufficiency of single-qubit measurements for $F_\mathrm{in}$ and $p_\mathrm{samp}$
• proof
• Lemma 2: Sufficiency of single-qubit Pauli measurements for $|\langle O_{10}\rangle|^2$