Big cats: entanglement in 120 qubits and beyond

TL;DR

The work addresses scalable preparation and certification of genuine multipartite entanglement in large GHZ states on superconducting qubits. It introduces an adaptive compiler that grows GHZ circuits on the hardware graph, leverages $ZZ$ back-propagation to maximize error-detection regions, and uses temporary uncomputation to mitigate dephasing, enabling a $120$-qubit GHZ state with a post-selection rate of $0.28$ and fidelity $F = 0.56(3)$. Fidelity is established through two complementary methods—parity oscillations and Direct Fidelity Estimation (DFE)—which are shown to be equivalent in this regime, with readout-mitigation integrated. The results are demonstrated across multiple IBM processors, illustrating reproducibility and the practical viability of large-scale entanglement benchmarks; code and data are publicly available for transparency and reuse.

Abstract

Entanglement is the quintessential quantum phenomenon and a key enabler of quantum algorithms. The ability to faithfully entangle many distinct particles is often used as a benchmark for the quality of hardware and control in a quantum computer. Greenberger-Horne-Zeilinger (GHZ) states, also known as Schrödinger cat states, are useful for this task. They are easy to verify, but difficult to prepare due to their high sensitivity to noise. In this Letter we report on the largest GHZ state prepared to date consisting of 120 superconducting qubits. We do this via a combination of optimized compilation, low-overhead error detection and temporary uncomputation. We use an automated compiler to maximize error-detection in state preparation circuits subject to arbitrary qubit connectivity constraints and variations in error rates. We measure a GHZ fidelity of 0.56(3) with a post-selection rate of 28%. We certify the fidelity of our GHZ states using multiple methods and show that they are all equivalent, albeit with different practical considerations.

Figures (3)

• Figure 1: Preparation of a 120-qubit GHZ state on the $ibm\_aachen$ processor. (a) The circuit has a CNOT depth of 18, with a final layer of parity checks consisting of 8 ancilla qubits. The spacetime detecting region of one of the ancilla qubits is highlighted in red, consisting of all edges that lie in the subtree spanning from the checked qubits to their lowest common ancestor. (b) The same region is highlighted spatially on the layout of qubits, where the GHZ state begins from the root qubit highlighted in green and spreads outwards in blue in a breadth-first-search manner. Missing nodes and edges signify dropouts due to high gate or measurement error. The position of ancillas are highlighted in pink. The root qubit is uncomputed early in the circuit, and only recomputed in the final layer, resulting in a long timespan highlighted in green where the qubit is relaxed and in the ground state. (c) To certify the state fidelity, we use DFE and measure seven diagonal and seven non-diagonal stabilizers, with their average fidelities and error bars shown for various cases of parity check or readout error mitigation.
• Figure 2: Demonstrating the equivalence of state certification using either (a-b) measurement of parity oscillations and population or (c) direct fidelity estimation. Identical circuits are used to prepare a 100-qubit GHZ state on $ibm\_kingston$, and three different quantities are measured. The first method gives a fidelity estimate of $F = 0.536(8)$ (average of (a) coherence=$0.539(5)$ and (b) population=$0.54(1)$). The second method gives a direct fidelity estimate of (c) $F=0.55(3)$. The two estimates are within error bars of each other. Due to the linearly increasing number of circuits in the first method, state certification takes a longer time. Different colors in the stacked bars in panels (b) and (c) indicate how parity checks and readout mitigation improve the fidelity and its estimate, respectively.
• Figure 3: Effect of dynamical decoupling. The off-diagonal stabilizers are made worse by dephasing (left), unless we perform dynamical decoupling (right). The timeline view shows the exact timing of DD pulses (green) in relation to the single-qubit gates (red) and two-qubit gates (blue). The experiment prepares a 20-qubit GHZ state on $ibm\_kingston$.

Theorems & Definitions (2)

• Lemma 1: Detecting region of a GHZ parity check
• proof : Proof