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Abstract Trapped matter-wave interferometry offers the promise of compact high-precision local force sensing. However, noise in the trap itself can introduce new systematic errors which are absent in traditional free-fall interferometers. We describe and demonstrate an intrinsically noise-tolerant Floquet-engineered platform for continuously trapped atom interferometry. A non-interacting degenerate quantum gas undergoes position-space Bloch oscillations through an amplitude-modulated optical lattice, whose resulting Floquet-Bloch band structure includes Landau-Zener beamsplitters and Bragg mirrors, forming the components of a Mach-Zehnder interferometric force sensor. We identify, realize, and experimentally characterize magic band structures, analogous to the magic wavelengths employed in optical lattice clocks, for which the interferometric phase is insensitive to lattice intensity noise. We leverage the intrinsic programmability of the Floquet band synthesis approach to demonstrate a variety of interferometer structures, highlighting the potential of this technique for quantum force sensors which are tunable, compact, simple, and robust. 

Abstract The development of superconducting quantum processors relies on understanding and mitigating decoherence in superconducting qubits. Piezoelectric coupling contributes to decoherence by mediating energy exchange between microwave photons and acoustic phonons. Although bulk centrosymmetric materials like silicon and sapphire are non-piezoelectric and commonly used as qubit substrates, the lack of centrosymmetry at interfaces may induce piezoelectric losses. This effect was predicted decades ago but never experimentally observed in superconducting devices. Here, we report interface piezoelectricity at aluminum-silicon junctions and demonstrate it as a significant loss channel in superconducting devices. Using aluminum interdigital transducers on silicon, we observe piezoelectric transduction from room to millikelvin temperatures, with an effective electromechanical coupling factorK² ≈ (3 ± 0.4) × 10⁻⁵%, comparable to weakly piezoelectric substrates. Modeling shows this mechanism limits qubit quality factors toQ ~ 10⁴ − 10⁸, depending on surface participation and mode matching. These findings reveal interface piezoelectricity as a major dissipation channel and highlight the need for heterostructure and phononic engineering in next-generation superconducting qubits. 

Abstract We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters. 

Abstract We provide a complete solution to the problem of infinite quantum signal processing (QSP) for the class of Szegő functions, which are functions that satisfy a logarithmic integrability condition and include almost any function that allows for a QSP representation. We do so by introducing a new algorithm called the Riemann–Hilbert–Weiss algorithm, which can compute any individual phase factor independent of all other phase factors. Our algorithm is also the first provably stable numerical algorithm for computing phase factors of any arbitrary Szegő function. The proof of stability involves solving a Riemann–Hilbert factorization problem in nonlinear Fourier analysis using elements of spectral theory. 

Abstract Quantum computers promise to tackle quantum simulation problems that are classically intractable¹. Although a lot of quantum algorithms^2–4have been developed for simulating quantum dynamics, a general-purpose method for simulating low-temperature quantum phenomena remains unknown. In classical settings, the analogous task of sampling from thermal distributions has been largely addressed by Markov Chain Monte Carlo (MCMC) methods^5,6. Here we propose an efficient quantum algorithm for thermal simulation that—akin to MCMC methods—exhibits detailed balance, respects locality and serves as a toy model for thermalization in open quantum systems. The enduring impact of MCMC methods suggests that our new construction may play an equally important part in quantum computing and applications in the physical sciences and beyond. 

Abstract The exceptionally low-energy²²⁹Th nuclear isomeric state is expected to provide several new and powerful applications^1,2, including the construction of a robust and portable solid-state nuclear clock³, perhaps contributing to a redefinition of the second⁴, exploration of nuclear superradiance^5,6and tests of fundamental physics^7–10. Further, analogous to the capabilities of traditional Mössbauer spectroscopy, the sensitivity of the nucleus to its environment can be used to realize laser Mössbauer spectroscopy and, with it, new types of strain and temperature sensors^3,11and a new probe of the solid-state environment^12,13, all with excellent sensitivity. However, current models for examining the nuclear transition in a solid require the use of a high-bandgap, vacuum ultraviolet (VUV) transmissive host, severely limiting the applicability of these techniques. Here we report the first, to the authors’ knowledge, demonstration of laser-induced conversion electron Mössbauer spectroscopy (CEMS) of the²²⁹Th isomer in a thin ThO₂sample whose bandgap (approximately 6 eV) is considerably smaller than the nuclear isomeric state energy (8.4 eV). Unlike fluorescence spectroscopy of the²²⁹Th isomeric transition, this technique is compatible with materials whose bandgap is less than the nuclear transition energy, opening a wider class of systems to study and the potential of a conversion-electron-based nuclear clock. 

Abstract There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman. We show how to generalize this to a large class of hierarchical graphs in which the vertices are grouped into “supervertices” which are arranged according to ad-dimensional lattice. Supervertices can have different sizes, and edges between supervertices correspond to random connections between their constituent vertices. The hitting times of quantum walks on these graphs are related to the localization properties of zero modes in certain disordered tight binding Hamiltonians. The speedups range from superpolynomial to exponential, depending on the underlying dimension and the random graph model. We also provide concrete realizations of these hierarchical graphs, and introduce a general method for constructing graphs with efficient quantum traversal times using graph sparsification. 

Abstract We develop and analyze a fault-tolerant quantum algorithm for non-linear response properties of molecular and condensed phase systems. We consider a semi-classical description in which the electronic degrees of freedom are treated quantum mechanically and the light is treated as a classical field interacting via the electric dipole approximation. We use the technique of eigenstate filtering, to efficiently resolve excitation energies for dominant dipole transitions. When applied to the electronic structure Hamiltonian with double factorized representation, each significant spectral line can be approximated to a width of ±γ, and to a height of ±ϵwith$$O\left({N}^{6}{\eta }^{2}{\gamma }^{-1}{\epsilon }^{-1}\log (1/\epsilon )\right)$$ $O\left(N^6{\eta }^2{\gamma }^{-1}{ϵ}^{-1}\log \left(1/ϵ\right)\right)$queries to the block encoding of the unperturbed electronic structure Hamiltonian forηelectrons overNbasis functions. These quantities can be used to compute thenth order response functions for non-linear spectroscopies under limited assumptions using$$\widetilde{O}\left({N}^{5n+1}{\eta }^{n+1}/{\gamma }^{n}\epsilon \right)$$ $\tilde{O}\left(N^{5n+1}{\eta }^{n+1}/{\gamma }^nϵ\right)$queries to the block encoding of the Hamiltonian. 

Abstract Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial thermostat in classical Monte Carlo or molecular dynamics methods, rather than being treated as an approximation to weakly coupled system-bath unitary dynamics. Recently, Chen, Kastoryano, and Gilyén (arXiv:2311.09207) introduced the first efficiently implementable Lindbladian satisfying the Kubo–Martin–Schwinger (KMS) detailed balance condition, which ensures that the Gibbs state is a fixed point of the dynamics and is applicable to non-commuting Hamiltonians. This Gibbs sampler uses a continuously parameterized set of jump operators, and the energy resolution required for implementing each jump operator depends only logarithmically on the precision and the mixing time. In this work, we build upon the structural characterization of KMS detailed balanced Lindbladians by Fagnola and Umanità, and develop a family of efficient quantum Gibbs samplers using a finite set of jump operators (the number can be as few as one), akin to the classical Markov chain-based sampling algorithm. Compared to the existing works, our quantum Gibbs samplers have a comparable quantum simulation cost but with greater design flexibility and a much simpler implementation and error analysis. Moreover, it encompasses the construction of Chen, Kastoryano, and Gilyén as a special instance. 

Abstract A Floquet quantum system is governed by a Hamiltonian that is periodic in time. Consider the space of piecewise time-independent Floquet systems with (geometrically) local interactions. We prove that for all but a measure zero set of systems in this space, starting from a random product state, many properties (including expectation values of observables and the entanglement entropy of a macroscopically large subsystem) at long times are approximately periodic with the same period as the Hamiltonian. Thus, in almost every Floquet system of arbitrarily large but finite size, discrete time-crystalline behavior does not persist to strictly infinite time.