Session M56: Quantum Stochastic Processes

Quantum Characterization and Control Using Continuous Weak Measurements

Continuous weak measurement provides a unique resource for probing the time evolution of quantum systems. This functionality has been used to faithfully reconstruct individual quantum trajectories in isolated qubits and in entangled pairs coupled to a Markovian bath.  We now extend these techniques to execute more complex quantum information processing tasks including tracking non-Markovian dynamics, continuous quantum error correction, and Hamiltonian reconstruction in superconducting circuits. In particular, we can reconstruct an a priori unknown time-dependent process with an algorithm to recover the density matrix from an incomplete set of continuous measurements. We show that it reliably extracts amplitudes of a variety of single-qubit and entangling two-qubit Hamiltonia. We further demonstrate how this technique reveals deviations from a theoretical control Hamiltonian that would have otherwise been missed by conventional techniques, thereby suggesting methods for identifying non-idealities in gates, certifying analog quantum simulators, and performing quantum metrology.   

Thermodynamics of quantum trajectories and its implementation on a quantum computer

Quantum computers have recently become available as noisy intermediate-scale quantum devices. These machines yield a useful environment for research on quantum systems and dynamics. Building on this opportunity, we investigate open-system dynamics that are simulated on a quantum computer by coupling a system of interest to an ancilla. After each interaction the ancilla is measured, and the sequence of measurements defines a quantum trajectory. Using a thermodynamic analogy, which identifies trajectories as microstates [1], we show how to bias the dynamics of the open system in order to enhance the probability of quantum trajectories with desired properties, e.g., particular measurement patterns or temporal correlations. We discuss how such a biased, generally non-Markovian, dynamics can be implemented on a unitary, gate-based quantum computer and show proof-of-principle results on the ibmq_jakarta machine [2]. While our analysis is solely conducted on small systems, it shows a practical way for implementing biased quantum dynamics that allows to investigate fluctuations and access rare events [3].

[1] J. P. Garrahan and I. Lesanovsky, Thermodynamics of Quantum Jump Trajectories, Physical Review Letters 104, 160601 (2010)

[2] M. Cech, I. Lesanovsky and F. Carollo Thermodynamics of quantum trajectories on a quantum computer Physical Review Letters 131, 120401 (2023)

[3] F. Carollo, J. P. Garrahan, I. Lesanovsky and C. Perez-Espigares Making rare events typical in Markovian open quantum systems Physical Review A 98, 010103(R) (2018)   

Simulating complex, stochastic processes with quantum physics

Stochastic processes with memory are as ubiquitous throughout the quantitative sciences as they are notorious for being difficult to simulate and predict. Weather patterns, stock prices, and biological evolution are just some of the most prominent examples.

In the last decades a sophisticated framework, called 'computational mechanics', has been developed that studies the complexity of such processes in terms of the minimal memory required for their simulation. More recently, it was discovered that this memory requirement for simulation may be further reduced by using a quantum instead of a classical memory substrate. Based on these results, we have developed a generic method for constructing unitary quantum simulators for a large class of stochastic processes, which can yield an unbounded scaling advantage.

In this talk I will give a brief an introduction to computational mechanics and statistical complexity as well as their extension to quantum memory. I will then describe the construction of a unitary quantum simulator which is applicable to a large class of stochastic processes. Finally, I will highlight some of the implications of the results, and in particular, unbounded scaling advantage.   

Time-series quantum reservoir computing with quantum measurements

The impact of interaction with the environment and measurement is significant in most quantum technologies, but it becomes even more critical in platforms requiring continuous monitoring. A challenging example is (classical) time-series processing such as speech recognition and chaotic series prediction and the search for enhanced data processing capabilities is driving research into quantum approaches. A promising avenue for sequential data analysis is quantum machine learning, with computational models such as quantum neural networks and reservoir computing (RC). Classical RC displays appealing features such as easy training and energy efficiency, and has recently been proposed in quantum settings. Quantum RC is better suited to quantum state processing and promises enhanced capabilities exploiting the enlarged Hilbert space. However, real-time processing and the achievement of a quantum advantage with efficient use of resources are prominent challenges towards viable experimental realizations. Our goal is to establish how quantum measurements can be efficiently incorporated into a realistic protocol. We discuss the conditions for efficient time-series processing while maintaining the necessary processing memory and preserving the quantum advantage offered by large Hilbert spaces. Efficient quantum RC is demonstrated, considering a transverse-field Ising network as a reservoir, for memory and prediction tasks with two successful measurement protocols. One repeats part of the experiment after each projective measurement. An alternative one uses weak measurements operating online where information can be extracted accurately and without compromising the required memory, despite back-action effects. We also propose a photonic platform suitable for real-time quatum RC. This is based on optical pulses circulating in a closed loop and operating in the continuous variable regime. While ideal operation achieves maximum capacities, statistical noise is shown to undermine any quantum improvement. We propose a strategy to overcome this limitation and maintain QRC performance as the size of the system is scaled up. The role of quantum squeezing is also discussed.   

Thermodynamic unification of optimal transport

Optimal transport is a mature field of mathematics and statistics, focused on the theory of optimal planning and cost associated with the transportation of probability distributions. Recently, a profound connection between optimal transport and stochastic thermodynamics has emerged, particularly in the context of continuous-state overdamped Langevin dynamics. This connection has revealed that the problem of minimizing entropy production can be mapped to the optimal transport problem. Moreover, this connection has led to critical applications, including the establishment of tight speed limits and the finite-time Landauer principle.

In this talk, I will introduce a thermodynamic framework for discrete optimal transport, which will illustrate the analogous relationship between stochastic thermodynamics and optimal transport within discrete-state systems. Specifically, I will present variational formulas that establish connections between stochastic thermodynamics of discrete Markov processes and discrete Wasserstein distances. These formulas not only unify the relationship between thermodynamics and optimal transport theory in both discrete and continuous cases but also extend it to the quantum realm. Notably, they yield remarkable applications of stochastic and quantum thermodynamics, such as stringent thermodynamic speed limits and the finite-time Landauer principle at arbitrary temperatures.