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arXiv:2501.16335 · Physical Review Research

Experimental simulation of postselected closed timelike curves for decoding scrambled quantum information

Yi-Te Huang, Hsiang-Wei Huang, Jhen-Dong Lin, Adam Miranowicz, Neill Lambert, Guang-Yin Chen, Franco Nori, Yueh-Nan Chen

Published Mar 30, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum information scrambling (QIS) describes the rapid spread of initially localized information across an entire quantum many-body system through entanglement generation. Once scrambled, the original local information becomes encoded globally, inaccessible from any single subsystem. In this work, we introduce a circuit-based decoding protocol. By utilizing the concept of postselected closed timelike curves (PCTCs), we demonstrate how postselection allows us to interpret an ordinary quantum experiment as an example of a paradox-free trajectory, simulating a consistent time loop and reliable information recovery. Specifically, when conditioned on a final postselected outcome, this experiment can be interpreted as decoding the scrambled information even before the original information is generated. Furthermore, the success probability of the PCTC is governed by out-of-time-ordered correlations, which is a standard measure of QIS. We experimentally implement our protocol on cloud-based Quantinuum and IBM quantum processors. Our approach illuminates a unique quantum task under postselection: the causally consistent simulation of future-to-past scrambled information retrieval.

DOI
10.1103/tm83-sxpm

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Quantum information scrambling (QIS) describes the rapid spread of initially localized information across an entire quantum many-body system through entanglement generation. Once scrambled, the original local information becomes encoded globally, inaccessible from any single subsystem. In this work, we introduce a circuit-based decoding protocol. By utilizing the concept of postselected closed timelike curves (PCTCs), we demonstrate how postselection allows us to interpret an ordinary quantum experiment as an example of a paradox-free trajectory, simulating a consistent time loop and reliable information recovery. Specifically, when conditioned on a final postselected outcome, this experiment can be interpreted as decoding the scrambled information even before the original information is generated. Furthermore, the success probability of the PCTC is governed by out-of-time-ordered correlations, which is a standard measure of QIS. We experimentally implement our protocol on cloud-based Quantinuum and IBM quantum processors. Our approach illuminates a unique quantum task under postselection: the causally consistent simulation of future-to-past scrambled information retrieval.
Closed timelike curves (CTCs) are a theoretical testbed for how quantum mechanics behaves when causal order breaks down. Two major quantum models exist: Deutsch CTCs, which impose a fixed-point self-consistency condition on the state inside the loop, and postselected CTCs, which model time travel via teleportation and postselection. Although both avoid logical paradoxes, they generally produce different quantum evolutions for the same circuit. This paper compares the two models directly at the circuit level using a small density-matrix and statevector simulator. The Deutsch model is implemented by solving for self-consistent fixed points; the postselected model by applying the corresponding nonlinear postselection map. Identical test circuits, including grandfather-paradox circuits, CNOT, SWAP, controlled-unitary families, and Haar-random unitaries, are run through both models, and the outputs compared using trace distance. The two models are found to disagree generically, not just numerically. The disagreement stems from a structural difference: Deutsch CTCs enforce consistency with mixed fixed-point states, while postselected CTCs renormalize only successful histories. For example, the X-gate "grandfather" circuit yields a well-defined mixed state under the Deutsch rule but an undefined (null-projection) output under postselection. Across 200 random unitaries, the two prescriptions never agree. All simulation code is included for full reproducibility.
Deutsch closed timelike curves (D-CTCs) are described by a fixed-point condition for a chronology-violating register. We study a finite-dimensional circuit model that places a Hayden--Preskill/Yoshida--Kitaev recovery map inside such a consistency loop. A register-routing construction makes the Deutsch map explicit: an initial SWAP moves the incoming CTC state to an idle dump register, the scrambler and decoder act on the remaining active registers, and a final SWAP writes the recovered message back to the CTC register. When the active branch recovers the message, the induced map on the CTC register is the replacement channel σ↦ρMσ\mapsto ρ_Mσ↦ρM​, with the unique fixed point ρMρ_MρM​. We implement the associated Lloyd-type post-selected decoder circuits on quantum hardware and formulate a classical-feedback iteration for the experimentally estimated map. Qiskit simulations and IBM-hardware data for single-qubit instances quantify decoder fidelity, post-selection overhead, routing-dependent noise, and quantum-geometric susceptibility.
Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we analyze an alternative quantum formulation of CTCs based on teleportation and postselection, and show that it is inequivalent to Deutsch's. The predictions or retrodictions of our theory can be simulated experimentally: we report the results of an experiment illustrating how in our particular theory the "grandfather paradox" is resolved.
Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.
Complex quantum many-body dynamics spread initially localized quantum information across the entire system. Information scrambling refers to such a process whose simulation is one of the promising applications of quantum computing. We demonstrate the Hayden-Preskill recovery protocol and the interferometric protocol for calculating out-of-time-ordered correlators to study the scrambling property of a one-dimensional kicked-Ising model on 20-qubit trapped-ion quantum processors. The simulated quantum circuits have a geometrically local structure that exhibits the ballistic growth of entanglement, resulting in the circuit depth being linear in the number of qubits for the entire state to be scrambled. We experimentally confirm the growth of signals in the Hayden-Preskill recovery protocol and the decay of out-of-time-ordered correlators at late times. As an application of the created scrambling circuits, we also experimentally demonstrate the calculation of the microcanonical expectation values of local operators adopting the idea of thermal pure quantum states. Our experiments are made possible by extensively utilizing one of the highest-fidelity quantum processors currently available and, thus, should be considered as a benchmark for the current status of the most advanced quantum computers.
In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a deep understanding of many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring Rényi entanglement entropies.