The RQS Institute Workshop poster session will be on Thursday, June 22, 2023 from 4 to 6 pm on the ground floor of the Physical Sciences Complex (296 Stadium Dr, College Park, MD 20742). Join us in the lobby to meet our researchers and view the following posters.

  1. Quantum Back-action Limits in Dispersively Measured Bose-Einstein Condensates

    Emine Altuntas
    UMD/NIST & JQI
    Abstract
    A fundamental tenet of quantum mechanics is that measurements change a system's wavefunction to that most consistent with the measurement outcome, even if no observer is present. Weak measurements---termed partial or non-destructive in different settings---produce only limited information about the system, and as a result only minimally change the system's state. We theoretically and experimentally characterize quantum back-action in atomic Bose-Einstein condensates (BECs), weakly measured by the light scattered from a far-from resonant, i.e., dispersively interacting, probe laser beam. We theoretically describe this process using a quantum trajectories approach and present a measurement model based on an ideal photodetection mechanism. We experimentally quantify the resulting wave function change with three observations: the change in total atom number, the contrast of a Ramsey interferometer, and the deposited energy. Finally, we use phase contrast imaging technique to obtain multiple successive weak measurements of the same BEC. We directly observe the dispersion of excitations from the correlation function of time-separated weak measurements. These results are necessary precursors for achieving true quantum back-action limited measurements of quantum gases and open the door to quantum feedback control of ultracold atoms. Emine Altuntas, I. B. Spielman; Joint Quantum Institute, NIST and UMD

  2. Linear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost

    Dong An
    UMD
    Abstract
    We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

  3. QisDAX: An Open-Source Bridge from Qiskit to Trapped-Ion Quantum Devices

    Kaustubh Badrike
    North Carolina State University
    Abstract
    QisDAX presents a bridge between IBMs Qiskit and Duke Artiq extensions (DAX) that attempts to resolve the disconnect between the wealth of open-source quantum abstractions and low-level control systems. QisDAX provides interfaces for Python programs written using IBM's Qiskit and transpiles them to the DAX abstraction. This allows users to generically interface to the ARTIQ control systems accessing trapped-ion quantum devices. Consequently, the algorithms expressed in Qiskit become available to an open-source quantum software stack. This provides the first open-source, end-to-end, full-stack modular pipeline for remote submission of quantum programs for trapped-ion quantum systems in a non-commercial setting.

  4. Enhanced Photon Routing Beyond the Blockade Limit Via Linear Optics

    Jasvith Basani
    UMD
    Abstract
    Directing indistinguishable photons from one input port into separate output ports is a fundamental operation in quantum information processing. The simplest scheme for achieving routing beyond random chance uses the photon blockade effect of a two-level emitter. But this approach is limited by a time-energy uncertainty relation. We show that a linear optical unitary transformation applied after the atom enables splitting efficiencies that exceed this time-energy limit. We show that the linear optical unitary improves the splitting efficiency from 67% to 82% for unentangled photon inputs, and from 77% to 90% for entangled photon inputs. We then optimize the temporal mode profile of the entangled photon wavefunction to attain the optimal splitting efficiency of 92%, a significant improvement over previous limits derived using a two-level atom alone. These results provide a path towards optimizing single photon nonlinearities and engineering programmable and robust photon-photon interactions for practical, high-fidelity quantum operations.

  5. Next-generation ion-trap quantum computer – pathway to long ion chains

    Debopriyo Biswas
    Duke Quantum Center
    Abstract
    Robust trapped ion quantum computers can be used to simulate numerous quantum phenomena and many-body physics systems, explore quantum error correction codes and noise models, and investigate challenges regarding scaling. Here, we present progress on building a state-of-the-art machine with full control of up to 32 171Yb+ ion qubits. We control sources of electric field noise that affect the heating of motion and thereby our gate fidelity. We also report on efforts to reduce magnetic field noise. We discuss the electrical and magnetic field noise effect on the system performance leading to improved T2 time and lower heating rates. Finally, we report on operations with a few qubits using counter-propagating Raman beams, and on work towards scaling to long ion chains in the same system. The aforementioned performance upgrades should lead to better fidelity gates and expand the complexity of physics that we can simulate with our quantum processor.

  6. Gate Operations in Sympathetically cooled Yb+ Chains

    Marko Cetina
    Duke University
    Abstract
    Preserving high gate fidelity while maintaining qubit connectivity is a major goal in scaling up quantum computers and simulators. In systems based on long chains of trapped ions, this is challenging due to heating via the coupling of ions to noisy electric fields, especially in the weakly-confined axial direction. In systems based on 171Yb+, this challenge can be countered by sympathetic cooling using 172Yb+ coolants [1]. We present progress towards an algorithmically useful implementation of this scheme in a room-temperature Yb+ system based on the Sandia HOA-2.1.1 trap. We demonstrate isotope-selective loading of long mixed-species 171Yb+ - 172Yb+ ion chains, protocols for reordering these chains to counter background-gas collisions and radial sympathetic narrow-line cooling of short mixed-species chains. This work is supported by the NSF QLCI RQS program, ARO with funding from the IARPA LogiQ Capstone program, and the DOE QSA program. References [1] M. Cetina et.al., PRX QUANTUM 3, 010334 (2022).

  7. Quantum computation for predicting electron and phonon properties of solids

    Kamal Choudhary
    NIST
    Abstract
    Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE–VQD calculations for 307 spin–orbit coupling based electronic WTBHs and 933 finite-difference based phonon WTBHs. Also, we discuss a workflow for using VQD with lattice Green's function that can be used for solving dynamical mean-field theory problems. The WTBH model solvers can be used for testing other quantum algorithms and models also.

  8. A Trapped Ion Computing Platform with Software-Tailored Architecture for Quantum co-Design

    Marissa D'Onofrio
    Duke University
    Abstract
    A full-stack approach to quantum computing requires collaborative design and integration between layers, from the algorithms and programming language to the qubit-specific hardware. Our team on the Software-Tailored Architecture for Quantum co-design (STAQ) project focuses on demonstrating quantum advantage on an ion trap platform developed at Duke University. This poster outlines progress toward our goals of realizing a 32-qubit, fully-connected quantum computer, using the system in-house to address computer engineering and software challenges, and making the system available to collaborating universities through an easily programmable software interface.

  9. Programmable quantum simulation of many-body systems

    Arinjoy De
    UMD
    Abstract
    Trapped-ion quantum simulators with native long-range interactions are well suited for studying quantum many-body systems as the flexibility of such platform allows us to probe dynamics over a broad range of both spatial and temporal resolution. In the presence of long-range interactions, one-dimensional systems can exhibit a host of quantum phases of matter which can be probed either through a quench across a phase boundary or a via an adiabatic ramp. We show that by performing a series of quenches to the critical Hamiltonian of a long-range Ising model one can observe truly non-equilibrium universal critical scaling exponents. We can also utilize the simultaneous control over all the spin-spin interactions to ramp a staggered field Hamiltonian to an effective XY Hamiltonian in order to prepare a state with long-range spin order, which is a characteristic of the continuous symmetry breaking phase of matter. In addition to the native Hamiltonian, trapped-ion simulators can also implement Floquet Hamiltonian engineering to realize non-native models. We use this to demonstrate a dynamical decoupling method where a periodic flip of the spins mitigating the decoherence effects in quantum simulation. Furthermore, the Floquet drive can also realize an effective Haldane-Shastry and Su-Schrieffer-Heeger type hamiltonian which allows us to explore novel phases of quantum matter.

  10. Unearthing Quantum States from their Euclidean Shadows

    Navya Gupta
    UMD
    Abstract
    Quantum simulators offer great potential for investigating the dynamical properties of quantum field theories. However, a significant challenge lies in preparing the initial state required for simulations. In our ongoing research, we delve into extracting ground state preparation recipes starting from classical Euclidean path integral Monte Carlo samples. With the scalar field theory in mind, we develop a range of ansatze for the ground states of single and multimode bosonic systems which could be implemented efficiently on digital, continuous, and hybrid quantum simulation platforms. These anstaze are constrained by fitting to the Monte Carlo samples. Taking inspiration from the scalar field theory, our ultimate vision is to leverage pre-existing lattice quantum chromodynamics (QCD) data to prepare the QCD ground state on quantum simulators. This poster is based on ongoing work with Prof. Zohreh Davoudi and Dr. Christopher White.

  11. Thermally driven quantum refrigerator autonomously resets superconducting qubit

    Jose Antonio Marin Guzman
    UMD
    Abstract
    The first thermal machines steered the industrial revolution, but their quantum analogs have yet to prove useful. Here, we demonstrate a useful quantum absorption refrigerator formed from superconducting circuits. We use it to reset a transmon qubit to a temperature lower than that achievable with any one available bath. The process is driven by a thermal gradient and is autonomous -- requires no external control. The refrigerator exploits an engineered three-body interaction between the target qubit and two auxiliary qudits coupled to thermal environments. The environments consist of microwave waveguides populated with synthesized thermal photons. The target qubit, if initially fully excited, reaches a steady-state excited-level population of 5×10−4±5×10−4 (an effective temperature of 23.5~mK) in about 1.6~μs. Our results epitomize how quantum thermal machines can be leveraged for quantum information-processing tasks. They also initiate a path toward experimental studies of quantum thermodynamics with superconducting circuits coupled to propagating thermal microwave fields.

  12. Random Pulse Sequences for Qubit Noise Spectroscopy

    Kaixin Huang
    UMD
    Abstract
    Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for implementing noise spectroscopy are time-consuming, because they require multiple measurements of the noise spectral density at different frequencies. Here we describe an alternative method for quickly characterizing the spectral density. Our method utilizes random pulse sequences, with carefully-controlled correlations among the pulses, to measure arbitrary linear functionals of the noise spectrum. Such measurements allow us to estimate k'th-order moments of the noise spectrum, as well as to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum compared to conventional dynamical decoupling approaches.

  13. Noise in Quantum Rigid Rotors: a QEC perspective

    Shubham Jain
    UMD
    Abstract
    Robust encodings for quantum bits using continuous degrees of freedom can furnish qubits with resilience to common sources of decoherence. Molecular codes are designed to encode quantum information in the orientation of a rigid rotor, such as a molecule, in such a way as to allow error correction from torques. Here, we build a qualitative characterisation of noise in such systems to better structure the construction of codes. We present a no-go theorem giving an example of an uncorrectable noise model and present a code which works for setups relevant to experiments.

  14. Trapped-ion quantum simulations for condensed-phase chemical dynamics: seeking a quantum advantage

    Mingyu Kang
    Duke
    Abstract
    Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a "quantum advantage" for these simulations, performance analysis of both classical-digital algorithms and analog-quantum simulation on noisy hardware is needed. In this Perspective, we make this comparison for the simulation of model molecular Hamiltonians that describe intrinsically quantum models for molecules that possess linear vibronic coupling, comparing the accuracy and computational cost. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones toward the use of trapped-ion simulators beyond the reach of classical-digital methods. Finally, we identify dynamical regimes where classical-digital simulations seem to have the weakest performance compared to analog-quantum simulations. These regimes may provide the lowest hanging fruit to exploit potential quantum advantages.

  15. Higher-group symmetry of topological order and stabilizer codes

    Ryohei Kobayashi
    UMD
    Abstract
    Topologically ordered phases can host interesting classes of non-trivial topological defects of varying codimensions. Among the topological defects, the invertible defects form an algebraic structure called higher-group. In this talk we explain how the higher-group structure of invertible global symmetry emerges in discrete gauge theory of generic dimensions, and show various examples of the higher-group symmetry in topological order mainly focusing on (3+1)-dimensional stabilizer models. The emergent global symmetry of a stabilizer model is understood as a logical gate acting on the logical qubits. We explain that the higher-group structure of global symmetry in general leads to non-Pauli logical gate realized by the action of emergent global symmetry, e.g., Control-Z logical gate of (3+1)-dimensional Z2 toric code.

  16. A Family of Quantum Codes with Exotic Transversal Gates

    Eric Kubischta
    UMD
    Abstract
    Recently it has been shown that the binary icosahedral group 2I together with a certain non-Clifford gate forms the most efficient single-qubit universal gate set. In order for this gate set to be viable, one must construct a code with transversal gate group 2I. However, no such code has ever been demonstrated explicitly. We fill this void by constructing a novel family of quantum codes, each with 2I transversal, using a recent method of Omanakuttan and Gross.

  17. Experimental observation of thermalization with noncommuting charges

    Aleksander Lasek
    UMD/Quics
    Abstract
    Quantum simulators have recently enabled experimental observations of quantum many-body systems’ internal thermalisation. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number—in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6–15 spins in an approximate microcanonical subspace, a generalisation of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. The noncommuting charges are the three spin components. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. We report the first experimental observation of a novel non-Abelian thermal state, predicted by quantum thermodynamics. We observe reduced many-body thermalization in the presence of noncommuting charges. Quantum non-commutation effects are detectable and significant for relatively large realistic systems, despite decoherence. This work initiates the experimental testing of a subfield that has so far remained theoretical.

  18. Quantum Hamiltonian Descent

    Joseph Li
    UMD
    Abstract
    Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to quantum speedups in optimization relies on the quantum acceleration of intermediate steps of classical algorithms, while keeping the overall algorithmic trajectory and solution quality unchanged. We propose Quantum Hamiltonian Descent (QHD), which is derived from the path integral of dynamical systems referring to the continuous-time limit of classical gradient descent algorithms, as a truly quantum counterpart of classical gradient methods where the contribution from classically-prohibited trajectories can significantly boost QHD's performance for non-convex optimization. Moreover, QHD is described as a Hamiltonian evolution efficiently simulatable on both digital and analog quantum computers. By embedding the dynamics of QHD into the evolution of the so-called Quantum Ising Machine (including D-Wave and others), we empirically observe that the D-Wave-implemented QHD outperforms a selection of state-of-the-art gradient-based classical solvers and the standard quantum adiabatic algorithm, based on the time-to-solution metric, on non-convex constrained quadratic programming instances up to 75 dimensions. Finally, we propose a "three-phase picture" to explain the behavior of QHD, especially its difference from the quantum adiabatic algorithm.

  19. Verification of measurement induced phases without post selection

    Cheng-Ju Lin
    UMD/QuiCS
    Abstract
    The phenomenon measurement-induced phase transition attracted lots of attention recently. Nonetheless, verifying such phases on a quantum simulator requires multiple copies of the measured quantum states with the same measurement outcomes, making the verification impossible to scale to a large number of qubits --- the infamous post-selection barrier. We propose a hybrid quantum-classical verification protocol to overcome this post-selection barrier. It involves executing the hybrid circuit on a quantum simulator, generating measurement outcomes from the probability distribution dictated by quantum mechanics. Subsequently, we determine an "order parameter" via a classical calculation using only the measurement outcomes to distinguish the phases. We employ this protocol to verify the measurement-induced phase with and without symmetries. Our numerical simulation suggests that our protocol can verify the measurement-induced phases beyond the sizes done in the previous experiments.

  20. Flatband Localization and Interaction-Induced Delocalization of Photons

    Jeronimo Martinez
    Princeton University
    Abstract
    Lattices with dispersionless, or flat, energy bands have attracted significant interest in part due to the strong dependence of particle dynamics on interactions. Using superconducting transmon qubits, we design a plaquette of a lattice whose band structure consists entirely of flatbands under the addition of a synthetic magnetic field of pi. We first observe compact localization in the dynamics of a single particle, the hallmark of all-bands-flat physics. Next, we initialize two photons bound by interactions on the same site and observe an interaction-enabled delocalized walk across the plaquette. Finally, we initialize two photons on opposite sides of the plaquette and find a localized walk not in real-space but in Fock-space. These results mark the first experimental observation of a quantum walk that becomes delocalized due to interactions and establish superconducting circuits as a platform for studies of flat-band-lattice dynamics with strong interactions.

  21. Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus

    Qiang Miao
    Duke University
    Abstract
    We explain why and numerically confirm that there are no barren plateaus in the energy optimization of isometric tensor network states (TNS) for extensive Hamiltonians with finite-range interactions. Specifically, we consider matrix product states, tree tensor network states, and the multiscale entanglement renormalization ansatz. The variance of the energy gradient, evaluated by taking the Haar average over the TNS tensors, has a leading system-size independent term and decreases according to a power law in the bond dimension. For a hierarchical TNS with branching ratio $b$, the variance of the gradient with respect to a tensor in layer $\tau$ scales as $(b\eta)^\tau$, where $\eta$ is the second largest eigenvalue of the Haar-average doubled layer-transition channel and decreases algebraically with increasing bond dimension. The observed scaling properties of the gradient variance bear implications for efficient initialization procedures.

  22. Monopole Josephson Effects in a Dirac Spin Liquid

    Gautam Nambiar
    UMD
    Abstract
    Dirac Spin liquids (DSLs) are gapless featureless states, yet interesting by virtue of the effective field theory describing them - (2+1)-dimensional quantum electrodynamics. Further, a DSL is known to be a ``parent state'' of various seemingly unrelated ordered states, such as antiferromagnets and valence bond solids in the sense that one can obtain ordered states by condensing magnetic monopoles of the emergent gauge field. Can operators in the effective field theory, such as the emergent electric field, be externally induced and measured? In this work, we exploit the parent state picture to argue that the answer is yes. We propose a range of ``monopole Josephson effects'' that arise when two ordered states are separated by a region of the parent DSL. In particular, we show that one can induce an AC monopole Josephson effect, which manifests itself as an AC emergent electric field in the spin liquid, accompanied by a measurable spin current. Further, we show that this AC emergent electric field can be measured as a sharp tunable peak in Raman scattering. This work provides a theoretical proof of principle that emergent gauge fields in spin liquids can be externally induced, manipulated, and probed using more conventional states, which offers a generic platform for studying the exotic spin phases.

  23. Decoding Algorithms for Low-Depth Random-Circuit Codes

    Jon Nelson
    UMD
    Abstract
    Random quantum codes possess many desirable properties for quantum error correction but are computationally intractable to decode in the most general case. Meanwhile, recent work has demonstrated that codes generated from random Clifford circuits have high performance even at short circuit depths. Here, we exploit the restriction to low-depth circuits to develop efficient tensor network contraction algorithms for maximum likelihood decoding and minimum weight decoding, both of which scale polynomially in the number of qubits and exponentially in the circuit depth. Our methods utilize a correspondence between stabilizer error correction and statistical mechanics that relates logical error probabilities to the partition function of a classical Ising spin model. In this framework, the minimum weight error corresponds to the ground state spin configuration. Thus, the core subroutine of our decoding algorithms is to calculate either the partition function or ground state by performing tensor contractions. With these decoders, we are able to numerically estimate the depolarizing error threshold of codes generated from 1D low-depth random Clifford circuits and show that this threshold closely matches the hashing bound even when the decoding is sub-optimal. This makes progress toward the use of random circuit encodings in practical fault-tolerant protocols

  24. Beyond Heisenberg Limit Quantum Metrology through Quantum Signal Processing

    Murphy Yuezhen Niu
    UMD
    Abstract
    Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a quantum-metrology method based on the quantum-signal-processing framework to overcome these realistic noise-induced limitations in practical quantum metrology. Our algorithm separates the gate parameter ~(single-qubit Z phase) that is susceptible to time-dependent error from the target gate parameter ~(swap-angle between |10> and |01> states) that is largely free of time-dependent error. Our method achieves an accuracy of radians in standard deviation for learning in superconducting-qubit experiments, outperforming existing alternative schemes by two orders of magnitude. We also demonstrate the increased robustness in learning time-dependent gate parameters through fast Fourier transformation and sequential phase difference. We show both theoretically and numerically that there is an interesting transition of the optimal metrology variance scaling as a function of circuit depth from the pre-asymptotic regime to Heisenberg limit . Remarkably, in the pre-asymptotic regime our method's estimation variance on time-sensitive parameter scales faster than the asymptotic Heisenberg limit as a function of depth, . Our work is the first quantum-signal-processing algorithm that demonstrates practical application in laboratory quantum computers.

  25. Quantum Simulation of 1D Lattices with Superconducting Circuits

    Kellen O’Brien
    UMD
    Abstract
    The field of circuit QED has emerged as a rich platform for both quantum computation and quantum simulation. Lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials in the tight-binding limit [1] capable of realizing non-Euclidean geometries [2] and unconventional unit cells [3]. Combined with strong qubit-photon interactions, these systems can be used to study dynamical phase transitions, many-body phenomena, and spin models in driven-dissipative systems. Here we present preliminary measurements from circuit QED lattice systems, including a quasi-1D lattice with gapped flat bands and linear band crossings coupled to transmon qubits. Probing these systems allows us to study photon mediated qubit-qubit interactions as a model for interacting spins in a material defined by the same band structure. [1] D. Underwood et al., Phys. Rev. A 86, 023837 (2012) [2] A. J. Kollár et al., Nature 571, 45 (2019) [3] A. J. Kollár et al., Comm. Math. Phys. 376,1909 (2019) This work received support from the National Science Foundation (QLCI grant OMA-2120757, NSF grant PHY2047732) and the Air Force Office of Scientific Research (AFOSR grant FA9550-21-1-0129). Kellen O’Brien; Maya Amouzegar; Martin Ritter; Theo Gifford; Zhiyin Tu; Alicia Kollár

  26. Folding-Free ZNE: A Comprehensive Quantum Zero-Noise Extrapolation Approach for Mitigating Depolarizing and Decoherence Noise

    Hrushikesh Pramod Patil
    North Carolina State University
    Abstract
    Quantum computers in the NISQ era are prone to noise. A range of quantum error mitigation techniques has been proposed to address this issue. Zero-noise extrapolation (ZNE) stands out as a promising one. ZNE involves increasing the noise levels in a circuit and then using extrapolation to infer the zero noise case from the noisy results obtained. This paper presents a novel ZNE approach that does not require circuit folding or noise scaling to mitigate depolarizing and/or decoherence noise. To mitigate depolarizing noise, we propose leveraging the extreme/infinite noisy case, which allows us to avoid circuit folding. Specifically, the circuit output with extreme noise becomes the maximally mixed state. We show that using circuit-reliability metrics, simple linear extrapolation can effectively mitigate depolarizing noise. With decoherence noise, different states decay into the all-zero state at a rate that depends on the number of excited states and time. Therefore, we propose a state- and latency-aware exponential extrapolation that does not involve folding or scaling. When dealing with a quantum system affected by both decoherence and depolarizing noise, we propose to use our two mitigation techniques in sequence: first applying decoherence error mitigation, followed by depolarizing error mitigation. A common limitation of ZNE schemes is that if the circuit of interest suffers from high noise, scaling-up noise levels could not provide useful data for extrapolation. We propose using circuit-cut techniques to break a large quantum circuit into smaller sub-circuits to overcome this limitation. This way, the noise levels of the sub-circuits are lower than the original circuit, and ZNE can become more effective in mitigating their noises.

  27. Distance-preserving flag fault-tolerant protocols for planar color codes of distance 9

    Balint Pato
    Duke
    Abstract
    A fault-tolerant error correction (FTEC) scheme with low overhead that can be laid out in a planar configuration is attractive for two-dimensional quantum computing architectures. In this work, we study flag FTEC schemes with only two ancillary qubits per stabilizer generator for the [[49,1,9]] concatenated Steane code and the [[61,1,9]] hexagonal color code. The FTEC scheme for the [[49,1,9]] code requires a careful ordering of CNOT gates to achieve a distance-preserving decoder, while the ordering of CNOT gates for the [[61,1,9]] code can be arbitrary. We find pseudothresholds in the 10^(-3) regime for both codes under the circuit-level depolarizing noise model with no idling noise. We achieve these numbers by applying various techniques to a lookup-table-based decoder with Shor syndrome extraction method, including "meet in the middle" decoding and adaptive syndrome measurement protocols tailored for color codes. All our decoders preserve the full distance and as a result are competitive in the low error regime for the hexagonal color codes.

  28. Toward Quantum Computing Phase Diagrams of Gauge Theories with Physical Thermal Pure Quantum States

    Connor Powers
    UMD
    Abstract
    The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely unexplored theoretically due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a path around this sign problem, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of thermal-pure- quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate this approach by mapping the chiral phase diagram of a simple low-dimensional gauge theory at finite temperature and chemical potential. Computations of non-equal time correlation functions and robustness to various types of introduced errors are also explored.

  29. Quantum spin ice in three-dimensional Rydberg atom arrays

    Jeet Shah
    UMD
    Abstract
    Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z2 topological order [G. Semeghini et al., Science 374, 1242 (2021)], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of “magnetic” monopoles and the Higgs transition driven by a proliferation of “electric” charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator.

  30. Quantum spin ice in three-dimensional Rydberg atom arrays

    Jeet Shah
    UMD
    Abstract
    Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z2 topological order [G. Semeghini et al., Science 374, 1242 (2021)], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of “magnetic” monopoles and the Higgs transition driven by a proliferation of “electric” charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator.

  31. Floquet synthetic dimensions for quantized topological pumping and Weyl points

    Sashank Kaushik Sridhar
    UMD
    Abstract
    Dissipation is generally detrimental to observing topological effects, particularly when the systems consist of quantum spins or qubits. Here we introduce a photonic molecule subjected to multiple RF/optical drives and dissipation as a promising candidate system to observe quantized transport along Floquet synthetic dimensions. We also provide a path to realizing Weyl points and measuring the Berry curvature emanating from these reciprocal-space (k-space) magnetic monopoles. This illustrates capabilities for direct k-space engineering of a wide variety of Hamiltonians using modulation bandwidths that are well below the free-spectral range (FSR) of integrated photonic cavities.

  32. Non-Abelian transport distinguishes three usually equivalent notions of entropy production

    Twesh Upadhyaya
    UMD/QuICS
    Abstract
    We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities (“charges”) between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute. Noncommutation invites generalizations, which we posit and justify, of the three formulae. Charges’ noncommutation, we find, breaks the formulae’s equivalence. Furthermore, different formulae quantify different physical effects of charges’ noncommutation on entropy production. For instance, entropy production can signal contextuality---true nonclassicality---by becoming nonreal. This work opens up stochastic thermodynamics to noncommuting---and so particularly quantum---charges.

  33. Quantum chaotic speed limit on information scrambling

    Amit Vikram
    UMD
    Abstract
    The speed of information scrambling is a problem of central interest in many-body quantum dynamics. We show that the spectral form factor, a “quantum chaos” diagnostic that can be generalized to quantum operations and measured in present-day quantum simulators, sets a basis-independent quantum speed limit on scrambling via entanglement generation, within subsystems of a many-body system evolving under completely positive quantum operations. For Hamiltonian dynamics, this speed limit rigorously bounds the scrambling time in terms of the mathematical properties of the density of states, and further aids in the ergodic classification of quantum dynamical systems by their level statistics. We illustrate these bounds in the SYK model, where despite its “maximally chaotic” nature we show that the sustained scrambling of large fermion subsystems via entanglement generation requires an exponentially long time in the subsystem size.

  34. A theory of quantum differential equation solvers: limitations and fast-forwarding

    Daochen Wang
    UMD
    Abstract
    We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the ODE is inhomogeneous. On the one hand, for generic homogeneous linear ODEs, by proving worst-case lower bounds, we show that quantum algorithms suffer from computational overheads due to two types of "non-quantumness": real part gap and non-normality of the coefficient matrix. We then show that homogeneous ODEs in the absence of both types of "non-quantumness" are equivalent to quantum dynamics, and reach the conclusion that quantum algorithms for quantum dynamics work best. We generalize our results to the inhomogeneous case and find that existing generic quantum ODE solvers cannot be substantially improved. To obtain these lower bounds, we propose a general framework for proving lower bounds on quantum algorithms that are amplifiers, meaning that they amplify the difference between a pair of input quantum states. On the other hand, we show how to fast-forward quantum algorithms for solving special classes of ODEs which leads to improved efficiency. More specifically, we obtain quadratic improvements in the evolution time T for inhomogeneous ODEs with a negative semi-definite coefficient matrix, and exponential improvements in both T and the spectral norm of the coefficient matrix for inhomogeneous ODEs with efficiently implementable eigensystems, including various spatially discretized linear evolutionary partial differential equations. We give fast-forwarding algorithms that are conceptually different from existing ones in the sense that they neither require time discretization nor solving high-dimensional linear systems.

  35. Uncovering measurement-induced entanglement via feedforward

    Yuxin Wang
    University of Chicago
    Abstract
    Identifying different phases of entanglement generation that arise in monitored dynamics has recently emerged as a topic of intense study. However, a main challenge with observing those nontrivial phases lies in the fact that the entanglement generation is conditional, i.e., it only exists at the individual trajectory level. As such, detection of entanglement is contingent on post-selection over measurement records, posing formidable challenges for scalable experimentation. Here, we propose a novel approach to solving this problem, making use of autonomous measurement-and-feedforward processes. In such systems, the measurements create entanglement in trajectories, and the feedforward process retains distinguishing information about the trajectories in the system. The combination of these two processes thus results in an entangled unconditional state, which can quantitatively capture the features of conditional entanglement generation. As an interesting application, for the case with harmonic oscillators under linear dephasing, we show that this general mechanism can enable deterministic, unlimited entanglement growth in time. We further discuss how unconditional pure-state entanglement can be extracted via a protocol that effectively implements delayed conditional feedback. Our results have implications for detecting measurement-induced entanglement phase transitions in unconditional dynamics, thus simplifying the experimental feasibility of observing such phenomena.

  36. Simulating Nuclear Physics: Chiral Effective Field Theory on a Quantum Computer

    James Watson
    Abstract
    Understanding and simulating nuclear physics has remained a challenging task due to the combination of strong forces, many-body fermionic systems, and highly quantum behaviour. Here we examine simulating a specific formulation of nuclear physics known as “Chiral Effective Field Theory” which models interactions between protons and neutrons at low energies. We prove both new asymptotic bounds, and explicit resource costs for different formulations of Chiral EFT. We demonstrate how taking advantage of Hamiltonian symmetries and fermionic encodings can drastically reduce gate counts. For some tasks, we achieve a factor of 10^6 speed up over previous works.

  37. Equivalence between fermion-to-qubit mappings in two spatial dimensions

    Yijia Xu
    UMD/QuICS/JQI
    Abstract
    We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization in Chen et al. [Ann. Phys. (N. Y) 393, 234 (2018)], whose gauge constraints project onto the subspace of the toric code with emergent fermions. Starting from the exact bosonization and applying Clifford finite-depth generalized local unitary transformation, we can achieve all possible fermion-to-qubit mappings (up to the re-pairing of Majorana fermions). In particular, we discover a new supercompact encoding using 1.25 qubits per fermion on the square lattice. We prove the existence of finite-depth quantum circuits to obtain fermion-to-qubit mappings with qubit-fermion ratios r = 1 + 1 / 2k for positive integers k, utilizing the trivialness of quantum cellular automata in two spatial dimensions. Also, we provide direct constructions of fermion-to-qubit mappings with ratios arbitrarily close to 1. When the ratio reaches 1, the fermion-to-qubit mapping reduces to the one-dimensional Jordan-Wigner transformation along a certain path in the two-dimensional lattice. Finally, we explicitly demonstrate that the Bravyi-Kitaev superfast simulation, the Verstraete-Cirac auxiliary method, Kitaev’s exactly solved model, the Majorana loop stabilizer codes, and the compact fermion-to-qubit mapping can all be obtained from the exact bosonization.

  38. Qubit-oscillator concatenated codes: decoding formalism & code comparison

    Yijia Xu
    UMD/QuICS/JQI
    Abstract
    Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode’s conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.

  39. Propagation of Quantum Information in Tree Networks: Noise Thresholds for Infinite Propagation

    Shiv Akshar Yadavalli
    Duke University
    Abstract
    We study quantum networks with a tree structure, where information propagates from a root to leaves: at each node in the network, the received qubit interacts with fresh ancilla qubits, and then each qubit is sent through a noisy channel to a different node in the next level. As the tree's depth grows, there is competition between the decay of quantum information due to the noisy channels and the additional protection against noise that is achieved by further delocalizing information. In the classical setting, where each node just copies the input bit into multiple output bits, this model has been studied as the broadcasting or reconstruction problem on trees, which has broad applications. In this work, we study the quantum version of this problem, where the encoder at each node is a Clifford unitary that encodes the input qubit in a stabilizer code. We prove that above certain noise thresholds, which depend on the properties of the code such as its distance, as well as the properties of the encoder, information decays exponentially with the depth of the tree. On the other hand, by studying certain efficient decoders, we prove that for sufficiently small noise, classical information and entanglement propagate over a noisy tree with infinite depth. Indeed, we find that this property holds even for certain binary trees where at each node, the received qubit is encoded only in two qubits, which corresponds to a code with distance d=1.

  40. Spatially-Coupled QLDPC Codes

    Siyi Yang
    Duke University
    Abstract
    Spatially-coupled (SC) codes is a class of convolutional LDPC codes that has been well investigated in classical coding theory thanks to their high performance and compatibility with low-latency decoders. We describe toric codes as quantum counterparts of classical two-dimensional spatially-coupled (2D-SC) codes, and introduce spatially-coupled quantum LDPC (SC-QLDPC) codes as a generalization. We use the convolutional structure to represent the parity check matrix of a 2D-SC code as a polynomial in two indeterminates, and derive an algebraic condition that is both necessary and sufficient for a 2D-SC code to be a stabilizer code. This algebraic framework facilitates the construction of new code families. While not the focus of this paper, we note that small memory facilitates physical connectivity of qubits, and it enables local encoding and low-latency windowed decoding. In this paper, we use the algebraic framework to optimize short cycles in the Tanner graph of 2D-SC HGP codes that arise from short cycles in either component code. While prior work focuses on QLDPC codes with rate less than 1/10, we construct 2D-SC HGP codes with small memory, higher rates (about 1/3), and superior thresholds.

  41. Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies

    Yuxuan Zhang
    UMD/CMTC/JQI
    Abstract
    We show how to define a quantized many-body charge polarization $\vec{\mathscr{P}}$ for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magnetic field. For invertible topological states, $\vec{\mathscr{P}}$ is a $\Z_2 \times \Z_2$, $\Z_3$, $\Z_2$, or $\Z_1$ topological invariant in the presence of $M = 2$, $3$, $4$, or $6$-fold rotational symmetry, lattice (magnetic) translational symmetry, and charge conservation. $\vec{\mathscr{P}}$ manifests in the bulk of the system as (i) a fractional quantized contribution of $\vec{\mathscr{P}} \cdot \vec{b} \text{ mod 1}$ to the charge bound to lattice disclinations and dislocations with Burgers vector $\vec{b}$, (ii) a linear momentum for magnetic flux, and (iii) an oscillatory system size dependent contribution to the effective 1d polarization on a cylinder. We study $\vec{\mathscr{P}}$ in lattice models of spinless free fermions in a magnetic field. We derive predictions from topological field theory, which we match to numerical calculations for the effects (i)-(iii), demonstrating that these can be used to extract $\vec{\mathscr{P}}$ from microscopic models in an intrinsically many-body way. We show how, given a high symmetry point $\text{o}$, there is a topological invariant, the discrete shift $\mathscr{S}_{\text{o}}$, such that $\vec{\mathscr{P}}$ specifies the dependence of $\mathscr{S}_{\text{o}}$ on $\text{o}$. We derive colored Hofstadter butterflies, corresponding to the quantized value of $\vec{\mathscr{P}}$, which further refine the colored butterflies from the Chern number and discrete shift.