Quantum Interactive Dynamics

I will talk about how symmetry-preserving measurements with feedforward alter the phase classification of matrix product states in the presence of global on-site symmetries. Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward David Gunn, Georgios Styliaris, Tristan Kraft, Barbara Kraus, arXiv:2312.13838

Our understanding of quantum statistical mechanics is grounded in the eigenstate thermalization hypothesis (ETH). The ETH states that the matrix elements of an observable in the energy basis are random numbers whose magnitudes depend smoothly on the eigenstate energies, and for this reason it carries significant predictive power. Unfortunately, direct tests of the ETH are fundamentally limited to small systems: even with a fault-tolerant quantum computer, the time required to resolve a many-body eigenstate is exponential in the number of degrees of freedom. First I will introduce a deterministic quantum algorithm, based on quantum search, which allows for the efficient construction of states having inverse polynomial energy width, as well as superpositions of such states. I will then discuss how, using these states, it is possible to formulate a test for violations of ETH that is valid in individual systems. Finally, I will show that detecting a violation of ETH using this test is a Quantum Merlin Arthur (QMA) problem.

We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter-Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker-Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.

Rydberg atom arrays have emerged as a leading platform for quantum information science. Reaching system sizes of hundreds of long-lived qubits, these arrays are used for highly coherent analog quantum simulation, as well as digital quantum computation. Advanced quantum protocols such as quantum error correction, however, require midcircuit qubit operations, including the replenishment, reset, and readout of a subset of qubits. A compelling strategy to achieve these capabilities is a dual-species architecture in which a second atomic species can be controlled without crosstalk, and entangled with the first via Rydberg interactions. In this talk, I will introduce our dual-species Rydberg array consisting of rubidium (Rb) and cesium (Cs) atoms and present new regimes of interactions and dynamics not accessible in single-species architectures. I will share our recent results on interspecies interactions which we use to realize Rydberg blockade and implement quantum state transfer from one species to another. Furthermore, we generate a Bell state between Rb and Cs hyperfine qubits via an interspecies controlled-phase gate. Finally, we combine interspecies entanglement with native midcircuit readout to achieve quantum non-demolition measurement of a Rb qubit using an auxiliary Cs qubit. These techniques are crucial ingredients for scalable measurement-based protocols and real-time feedback control in large-scale quantum systems.

Quantum devices have matured to the point where multipartite entanglement can be created on 30+ qubits. One important capability of these devices is the creation of long-range entangled states, both as initial states for quantum simulation and for error correction within the same devices. Unfortunately, by definition, topologically ordered states require extensive unitary circuit depths for their preparation, which places constraints on the coherence times of near-term devices. I will talk about how constant-depth protocols based on measurement and feed-forward have recently been used to prepare toric code and non-Abelian topological order on Quantinuum's H-series trapped-ion computers.

TBA

The latest generations of quantum devices are rapidly developing the technology needed to perform real-time ("mid-circuit") measurements and feedback, giving us access to highly controlled far from equilibrium "active" quantum systems. This provides a large new arena for quantum many-body physics, and in my talk I will discuss the problem of defining robust quantum phases of matter in such non-equilibrium open systems. I will formulate conditions for the stability of these phases, putting it on a similar footing to the well-established theory of zero temperature phases of gapped quantum matter. Our formulation leads to desirable features, such as the robustness of long-range correlations within the phase, and I will describe physical mechanisms that give rise to such stability. These fundamental questions in many-body physics are also closely related to the problem of quantum error correction, particularly the problem of finding self-correcting codes that do not require non-local classical communication between the quantum device and a classical processor. TR, Sarang Gopalakrishnan, Curt von Keyserlingk: Defining stable phases of open quantum systems, ArXiv 2308.15495

The codespace of a quantum error-correcting code (QECC) can often be identified with the ground-space within a gapped phase of quantum matter. We argue that the stability of such a phase is directly related to a set of coherent error processes against which this quantum error-correcting code is robust: such a quantum code can recover from adiabatic quantum channels, corresponding to random adiabatic drift of code states through the phase, and with asymptotically perfect fidelity in the thermodynamic limit, as long as this adiabatic evolution keeps states sufficiently close to the initial ground-space. We further argue that when specific decoders -- such as minimum-weight perfect matching -- are applied to recover this information, an error-correcting threshold is generically encountered within the gapped phase. In cases where the adiabatic evolution is known, we explicitly show examples in which quantum information can be recovered by using stabilizer measurements and Pauli feedback, even up to a phase boundary. This provides examples in which non-local, coherent noise effectively decoheres in the presence of syndrome measurements in a stabilizer QECC.

In my talk, I will present protocols and experimental results for characterizing noisy intermediate-scale quantum dynamics. Firstly, I will introduce a learning algorithm designed to discover conservation laws given as sums of geometrically local observables in unknown dynamics. This algorithm leverages the classical shadow formalism for estimating expectation values of observables to identify all such conservation laws with rigorous performance guarantees. I will present numerical experiments that illustrate the algorithm's application in the context of lattice gauge theories and many-body localization. Secondly, I will introduce benchmarking protocols for quantum devices that rely on estimating fidelity to target states. I will particularly focus on highly-entangled quantum states generated by ergodic quantum dynamics, where emergent randomness enables efficient fidelity estimation schemes. Experimental results from a 60-atom Rydberg quantum simulator at the threshold of exact classical simulatability will be presented. Utilizing the extracted fidelity, I will also demonstrate a novel estimator for experimental mixed-state entanglement, showing that the Rydberg quantum simulator is competitive with state-of-the-art digital quantum devices performing random circuit evolution.

I will review recent progress on introducing engineered dissipation into unitary quantum circuits on a superconducting quantum processor, and the subsequent observation of cooling and quantum transport through the non-unitary dynamics.

Simulation of continuous time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision, but it inevitably leads to increased computational efforts. This is particularly costly for today's noisy intermediate scale quantum computers, where notable gate imperfections limit the circuit depth that can be executed at a given accuracy. Classical adaptive solvers are well-developed to save numerical computation times. However, it remains an outstanding challenge to make optimal usage of the available quantum resources by means of adaptive time steps. Here, we introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. The key conceptual element of our algorithm is a feedback loop which self-corrects the simulation errors by adapting time steps, thereby significantly outperforming conventional Trotter schemes on a fundamental level and reducing the circuit depth. It even allows for a controlled asymptotic long-time error, where usual Trotterized dynamics is facing difficulties. Another key advantage of our quantum algorithm is that any desired conservation law can be included in the self-correcting feedback loop, which has potentially a wide range of applicability. We demonstrate the capabilities by enforcing gauge invariance which is crucial for a faithful and long-sought quantum simulation of lattice gauge theories. Our algorithm can be potentially useful on a more general level whenever time discretization is involved concerning, for instance, also numerical approaches based on time-evolving block decimation methods. References: [1] PRX Quantum 4, 030319 (2023); [2] arXiv:2307.10327 (2023)

The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. Evolving the state using a space transfer matrix creates a bath, known as the influence matrix for the local observable. As a first step to assess the complexity of this approach, we systematically study the its entanglement -- dubbed temporal entanglement -- in chaotic quantum systems. While the von Neumann entanglement entropy generally follows a volume law (in time), we identify two marginal cases where the Rényi entropies with index greater than one can have sublinear growth: (i) pure space evolution in generic chaotic systems (ii) any space-like evolution in dual-unitary circuits. The sublinear Rényi entropy growth is due to large overlap of the influence matrices and a product state, which could lead to an efficient computational implementation of the space evolution.

The AKLT state provides a paradigmatic example of both a matrix product state and a symmetry-protected topological phase, and additionally holds promise as a resource state for measurement-based quantum computation. Having a nonzero correlation length, the AKLT state cannot be exactly prepared by a constant-depth unitary circuit composed of local gates. In this talk, I will demonstrates that this restriction can be evaded by augmenting a constant-depth circuit with midcircuit measurements and feedforward operations, such that the total preparation time is independent of system size. I will present experimental results collected on an IBM Quantum processor that indicate that our measurement-assisted scheme outperforms purely unitary protocol. Finally, I will summarize our efforts to extend our constant-depth preparation scheme to both short-range and long-range entangled matrix product states. In all, our scheme illustrates the promise of measurement-based depth-reduction strategies for NISQ-era devices.

I will discuss the dynamics of the Floquet east model (a Trotterized version of the kinetically constrained east model) at its deterministic point. Even though the dynamics is generated by permutation gates, the model exhibits many non-trivial features both in the classical and quantum setting, while its simplicity allows for exact solutions. The talk is based on [1,2]. [1] K. Klobas, C. De Fazio, J. P. Garrahan, arXiv:2305.07423 [2] B. Bertini, C. De Fazio, J. P. Garrahan, K. Klobas, arXiv:2310.06128

We define and study the Floquet Quantum East circuit model, a kinetically constrained quantum dynamics in discrete space-time, exhibiting a localization transition in infinite volume. The localization is established using perturbative arguments as well as convergent TEBD (time-evolving block decimation) method in real time.