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Fast classical simulation of Harvard/QuEra IQP circuits

Dmitri Maslov, Sergey Bravyi, Felix Tripier, Andrii Maksymov, Joe Latone

TL;DR

This work targets the question of when structured IQP circuits become classically intractable by presenting a fast strong-simulation algorithm for the Harvard/QuEra $HQ_k$ circuit family. The authors recast $HQ_k$ as $H D'_k H$ and reduce amplitude computation to a sum over $2^{n/3}$ Clifford subcircuits, each on $2n/3$ qubits, with overall time $O((n/3)^3 2^{n/3})$. They implement a public tool achieving a 48-qubit amplitude in $\approx 2.6\times10^{-3}$ s and a 96-qubit amplitude in about $4.17$ s, substantially faster than previous reports, and provide estimates suggesting 192-qubit simulations could be feasible on TPU-based clusters in days. These results imply that, for this structured IQP instance, increasing depth or modestly expanding qubit count does not immediately yield a quantum advantage, guiding future experimental design toward different, more challenging regimes or fault-tolerant architectures. The study advances understanding of the boundary between classical simulability and quantum advantage for IQP-type circuits and informs the design of scalable demonstrations.

Abstract

Establishing an advantage for (white-box) computations by a quantum computer against its classical counterpart is currently a key goal for the quantum computation community. A quantum advantage is achieved once a certain computational capability of a quantum computer is so complex that it can no longer be reproduced by classical means, and as such, the quantum advantage can be seen as a continued negotiation between classical simulations and quantum computational experiments. A recent publication (Bluvstein et al., Nature 626:58-65, 2024) introduces a type of Instantaneous Quantum Polynomial-Time (IQP) computation complemented by a $48$-qubit (logical) experimental demonstration using quantum hardware. The authors state that the ``simulation of such logical circuits is challenging'' and project the simulation time to grow rapidly with the number of CNOT layers added, see Figure 5d/bottom therein. However, we report a classical simulation algorithm that takes only $0.00257947$ seconds to compute an amplitude for the $48$-qubit computation, which is roughly $10^3$ times faster than that reported by the original authors. Our algorithm is furthermore not subject to a significant decline in performance due to the additional CNOT layers. We simulated these types of IQP computations for up to $96$ qubits, taking an average of $4.16629$ seconds to compute a single amplitude, and estimated that a $192$-qubit simulation should be tractable for computations relying on Tensor Processing Units.

Fast classical simulation of Harvard/QuEra IQP circuits

TL;DR

This work targets the question of when structured IQP circuits become classically intractable by presenting a fast strong-simulation algorithm for the Harvard/QuEra circuit family. The authors recast as and reduce amplitude computation to a sum over Clifford subcircuits, each on qubits, with overall time . They implement a public tool achieving a 48-qubit amplitude in s and a 96-qubit amplitude in about s, substantially faster than previous reports, and provide estimates suggesting 192-qubit simulations could be feasible on TPU-based clusters in days. These results imply that, for this structured IQP instance, increasing depth or modestly expanding qubit count does not immediately yield a quantum advantage, guiding future experimental design toward different, more challenging regimes or fault-tolerant architectures. The study advances understanding of the boundary between classical simulability and quantum advantage for IQP-type circuits and informs the design of scalable demonstrations.

Abstract

Establishing an advantage for (white-box) computations by a quantum computer against its classical counterpart is currently a key goal for the quantum computation community. A quantum advantage is achieved once a certain computational capability of a quantum computer is so complex that it can no longer be reproduced by classical means, and as such, the quantum advantage can be seen as a continued negotiation between classical simulations and quantum computational experiments. A recent publication (Bluvstein et al., Nature 626:58-65, 2024) introduces a type of Instantaneous Quantum Polynomial-Time (IQP) computation complemented by a -qubit (logical) experimental demonstration using quantum hardware. The authors state that the ``simulation of such logical circuits is challenging'' and project the simulation time to grow rapidly with the number of CNOT layers added, see Figure 5d/bottom therein. However, we report a classical simulation algorithm that takes only seconds to compute an amplitude for the -qubit computation, which is roughly times faster than that reported by the original authors. Our algorithm is furthermore not subject to a significant decline in performance due to the additional CNOT layers. We simulated these types of IQP computations for up to qubits, taking an average of seconds to compute a single amplitude, and estimated that a -qubit simulation should be tractable for computations relying on Tensor Processing Units.
Paper Structure (8 sections, 2 theorems, 13 equations, 2 figures, 1 table)

This paper contains 8 sections, 2 theorems, 13 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. IQP circuits
  3. Structure of Harvard/QuEra circuit
  4. Types of simulation
  5. Our simulation
  6. Details of the implementation
  7. Runtime and resource estimate
  8. Discussion

Key Result

Lemma 1

For the $HQ_k$ circuit, the minimal covering set contains exactly $n/3$ qubits.

Figures (2)

  • Figure 1: Illustration of the $HQ_4$ circuit. Each block of three qubits is numbered $1..16$. The $\textsc{CNOT}$ gate colors match the colors of edges in the Boolean 4-dimensional cube illustrated on the right. The arrows point in the direction of targets of the respective $\textsc{CNOT}$ gates. The diagonal operators are applied in stages marked "Z". Not shown are two layers of Hadamard gates---one at the beginning and the other at the end of the computation.
  • Figure 2: Comparison of simulation runtimes with the number of additional layers added between bluvstein2023logical (teal, redrawn), and our simulation (blue).

Theorems & Definitions (3)

  • Lemma 1
  • proof
  • Lemma 2