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arXiv:2605.27211 · Quantum Science and Technology

Time Crystals on Quantum Devices

Gonzalo Camacho, Benedikt Fauseweh

quant-phcond-mat.str-elSubmitted May 26, 2026• Announced May 27, 2026• 0 citations• Revised Oct 29, 2026 (v2)
v1 · May 26, 2026v2 · Oct 29, 2026
arXivHTMLPDF

Abstract

Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.

Journal reference
Quantum Sci. Technol. 11 043004 (2026)
DOI
10.1088/2058-9565/aeb255
Comments
30 pages, 5 figures. Close to published version. Licenses for adopted figures in the source files

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Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.
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Traditional condensed matter physics relies heavily on spatial periodicity to classify states of matter using crystal lattices and momentum space. In recent years, the paradigm has expanded to include temporal dimensions, notably through the theoretical and experimental exploration of discrete time crystals. However, searching strictly for discrete time crystals imposes rigid constraints on phase rigidity and symmetry breaking. In this paper, we propose a broader and more fundamental paradigm: Quantum Material Temporal Lattice Spectroscopy (QMTLS). Rather than seeking an isolated time crystal phase, QMTLS focuses on identifying internal temporal structures characterized by periodic sequences t_n = nT formed spontaneously or under driving within quantum materials. We formalize the theoretical foundation of temporal lattices in condensed matter, define the spectral density function S(omega) containing discrete temporal lattice peaks, and outline the microscopic mechanisms driving these phenomena. By avoiding traditional experimental validation sections and focusing on rigorous theoretical foundations, this framework opens a promising pathway toward discovering novel non-equilibrium states of matter with potential profound implications for fundamental physics.
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The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization. Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics --- that of an intrinsically out-of-equilibrium many-body phase of matter. We include a compendium of necessary background, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. We formalize the notion of a time-crystal as a stable, macroscopic, conservative clock --- explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. We also cover a range of related phenomena, including various types of long-lived prethermal time-crystals, and expose the roles played by symmetries -- exact and (emergent) approximate -- and their breaking. We clarify the distinctions between many-body time-crystals and other ostensibly similar phenomena dating as far back as the works of Faraday and Mathieu. En route, we encounter Wilczek's suggestion that macroscopic systems should exhibit TTSB in their ground states, together with a theorem ruling this out. We also analyze pioneering recent experiments detecting signatures of time crystallinity in a variety of different platforms, and provide a detailed theoretical explanation of the physics in each case. In all existing experiments, the system does not realize a `true' time-crystal phase, and we identify necessary ingredients for improvements in future experiments.
We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that break discrete time translation symmetry in driven quantum many-body systems undergoing nonequilibrium dynamics. They are stabilized by many-body localization arising from disorder. We directly target the thermodynamic limit using instances of infinite tensor network states, and we implement disorder in a translationally invariant setting by introducing auxiliary systems at each site. We discuss how such disorder can be realized in programmable quantum simulators: This gives rise to the interesting situation in which a classical tensor network simulation can contribute to devising a blueprint of a quantum simulator featuring prethermal time crystalline dynamics, one that will ultimately have to be built in order to explore the stability of this phase of matter for long times.