Session Y35: Thermodynamics in Quantum Information I

Ideal Projective Measurements Have Infinite Resource Costs

We show that it is impossible to perform ideal projective measurements on quantum systems using finite resources. We identify three fundamental features of ideal projective measurements and show that when limited by finite resources only one of these features can be salvaged. Our framework is general enough to accommodate any system and measuring device (pointer) models, but for illustration we use an explicit model of an N-particle pointer. For a pointer that perfectly reproduces the statistics of the system, we provide tight analytic expressions for the energy cost of performing the measurement. This cost may be broken down into two parts: first, the cost of preparing the pointer in a suitable state, and second, the cost of a global interaction between the system and pointer in order to correlate them. It turns out that even under the assumption that the interaction can be controlled perfectly, achieving perfect correlation is infinitely expensive. We provide protocols for achieving optimal correlation given finite resources for the most general system and pointer Hamiltonians, phrasing our results as fundamental bounds in terms of the dimensions of these systems.  Finally, we show on how our results affect Jarzynski and Crook's relations in the context of the two point measurement scheme.   

Thermodynamic Constraints on Quantum Information Gain and Error-Correction.

Quantum error correction (QEC) is a procedure by which the quantum state of a system is protected against a known type of noise, by preemptively adding redundancy to that state. Such a procedure is commonly applied in quantum computing when thermal noise is present. Interestingly, thermal noise has also been known to play a central role in quantum thermodynamics (QTD). This fact hints at the applicability of certain QTD statements in the QEC of thermal noise, which has been discussed previously in the context of Maxwell's demon. In this article, we view QEC as a quantum heat engine with a feedback controller (demon). The main task of this engine is to correct the effects of the hot bath (thermal noise) by attempting to close its own cycle with respect to the system state, corresponding to a perfect QEC. We derive an upper bound to the measurement heat that is dissipated during the error identification stage, thereby granting a physical meaning to negative values of quantum information gain. We also derive the second law of thermodynamics in the context of this QEC engine, operating with general quantum measurements. Finally, we show that, under a set of physically motivated assumptions, this leads to a fundamental trade-off relation between the fidelity of the QEC and the super-Carnot efficiencies that heat engines with feedback controllers have been known to possess.   

Driven-dissipative dynamics in superconducting circuit lattices coupled to quantum baths

Understanding the influence of noise and environment on quantum systems is of fundamental importance for applications in quantum information sciences. Engineered environment/baths can be used as a resource for controlling and manipulating entanglement, and has attracted much attention. Recently a dissipatively stabilized Mott insulator in superconducting circuits was realized by coupling a narrowband incoherent bath with a Bose-Hubbard lattice. Here, we propose experiments to explore the dynamics of quantum correlations in strongly correlated lattices in the presence of broadband baths. We discuss schemes for realizing the dynamically tunable baths. By creating two baths to serve as source and drain we can implement an effective chemical potential for photons to prepare driven-dissipative many-body states. The baths also enable energy selective transport measurements across the lattices, providing insights into the quantum thermodynamics of interacting channels. We will discuss results from numerical simulations and our experimental progress.   

The thermodynamic cost of quantum measurements in the circuit quantum electrodynamics architecture

Quantum measurements are basic operations in the study of quantum information. As with classical computers, all logical operations demand resources. Here we investigate the resources required to perform quantum measurements of a qubit. We utilize different quantum and classical states of light in a circuit quantum electrodynamics setup to perform measurements, characterizing both the measurement backaction and measurement efficiency. We find that in the strong dispersive limit the thermal light is capable of performing quantum measurements with comparable efficiency to coherent light. We also analyze the energetic and entropic costs of these quantum measurements at different measurement strengths. This work demonstrates a new efficient approach to quantum measurements in circuit quantum electrodynamics. Furthermore, we connect concepts in information thermodynamics to quantum measurement by comparing the information gain per photon for each input field.   

Entanglement Annealing and Fluctuations

As quantum computing has entered the era of NISQ computers, numerical simulations of quantum computational models have grown in popularity as a tool for analyzing and characterizing properties of quantum systems. Among these properties is the transition to quantum chaos observed in random quantum circuits, which can be studied by complexity in the entanglement pattern of quantum states. Understanding the onset of irreversibility and chaotic behavior in quantum evolutions is important both in fundamental theory and in the optimization of the resources needed to develop quantum technology. Entanglement complexity is revealed by the degree of success of an entanglement cooling algorithm, the universality of its fluctuations, and the entanglement spectrum statistics. Previously, it has been shown that random circuits entangle a system to such a level of complexity that it entirely hinders our ability to disentangle it. On the other hand, random Clifford circuits feature non-complex entanglement that can be efficiently undone. In this work, we study the entanglement complexity generated by doping Clifford circuits with non-Clifford resources and show how this drives the transition to universal fluctuations of entanglement and higher entanglement complexity.   

Complexity Growth in Integrable and Chaotic Models

Defining quantum complexity has been a long standing problem in condensed matter physics, quantum information and more recently quantum gravity. Using gate complexity from the theory of computation, one can upper-bound the unitary evolution by computing the length of the geodesic generated by the Hamiltonian on the U(N) manifold. In this formalism, one can study a type of local obstruction to complexity growth that is the appearance of conjugate points along the geodesic. We show that perturbatively, in the free SYK_q=2 model, the conjugate point appears at the length of order of O(N^1/2), and that for an integrable interacting theory - a deformed free SYK_q=2, the complexity is upper bounded by O(poly(N)), and that in the chaotic SYK_q>2, the conjugate points move away to O(exp(N)). This matches up with the intuition that integrable theory should generate simple unitaries and chaotic Hamiltonians should generate complex unitary dynamics. To combine the complexity theory and the quantum thermalization, we explore the complexity of the eigenstate of free, integrable interacting and chaotic Hamiltonian and use the eigenstate thermalization hypothesis to predict the appearance of conjugate points in chaotic systems.   

Characterizing work fluctuations in non-Hermitian dynamics of a superconducting qubit

In quantum systems, work fluctuations can be determined through pairs of projective energy measurements on an ensemble. The resulting work distribution can be related to the equilibrium free energy change by the Jarzynski equality. However, for open quantum systems, the equality may require modifications. Here we study the validity of the equality in non-Hermitian dynamics of a superconducting qubit, where an effective non-Hermitian Hamiltonian is realized on a sub-manifold of states of a dissipative transmon circuit. We show that the Jarzynski equality remains valid for dynamics confined to parameter regions with effective parity-time symmetry, where the system eigenenergies remain real. Outside these regions, the complex energy spectrum results in a violation of the equality. Characterization of this violation forms the basis for an extension of the Jarzynski equality for non-Hermitian dynamics, where complex energy evolution can be related to changes in information.   

Operator Growth and Symmetry-Resolved Coefficient Entropy in Quantum Maps

Operator growth, or operator spreading, describes the process where a "simple" operator acquires increasing complexity under the Heisenberg time evolution of a chaotic dynamics, therefore has been a key concept in the study of quantum chaos in both single-particle and many-body systems. An explicit way to quantify the complexity of an operator is the Shannon entropy of its operator coefficients over a chosen set of operator basis, dubbed "coefficient entropy". However, it remains unclear if the basis-dependency of the coefficient entropy may result in a false diagnosis of operator growth, or the lack thereof. Here, we will examine the validity of coefficient entropy in the presence of hidden symmetries. Using the quantum cat map as an example, we show that under a generic choice of operator basis, the coefficient entropy fails to capture the suppression of operator growth caused by the symmetries. We further propose "symmetry-resolved coefficient entropy" as the proper diagnosis of operator complexity, which takes into account generic unknown symmetries, and demonstrate its effectiveness in the case of quantum cat maps.   

Quantum bounds from fluctuation-dissipation relations

One may express the out of time order correlators (OTOC) as two-point functions in a replicated space. The quantum bound to chaos derives then from the usual quantum fluctuation-dissipation relations (FDT). Motivated by this result, I will discuss how the quantum FDT acts as a blurring (on a Planckian timescale) of general two-point functions expressed in the time-domain, thus imposing bounds on their rate of change.   

Quantum thermodynamically consistent local master equations

Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics. In contrast, here we rigorously prove that local master equations are consistent with thermodynamics and its laws without resorting to a microscopic model, as done in previous works [1]. In particular, we consider a quantum system in contact with multiple baths and identify the relevant contributions to the total energy, heat currents, and entropy production rate. We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents. We confirm the results for the quantum heat currents by using a heuristic argument that connects the quantum probability currents with the energy currents, using an analogous approach as in classical stochastic thermodynamics. Finally, we prove an integral quantum fluctuation theorem for the entropy production in the system that is valid for any Lindblad master equation [2].    

Two-qubit quantum heat engine with non-ideal measurements

The role of quantum correlations and the resource accounting of control have been two areas of study in quantum thermodynamics. While measurement engines model the resource accounting of control, one way to assess the role of such correlations is to investigate the thermodynamic performance of measurement engines with and without quantum correlations. A complete analysis of the thermodynamic performance has to account for the cost of measurements and correlations incurred in the operation of such an engine. We discuss the role of entanglement in measurement engines by contrasting examples of measurement engines which have the same work output but with varying entanglement. We account for the cost of resetting, correlating the engine to a pointer state and also the cost of cooling the pointer state.   

Observing thermalization and chaos in a 1+1d Quantum field theory using Hamilton truncation

We study thermal equilibrium and out-of-equilibrium dynamics of \phi^4 theory in 1+1d using Hamiltonian truncation. The equation of state obtained from the density of states agrees with field theory expectation. Eigenvalue spacings follow Wigner-Dyson statistics, and real time observables such as the spectral form factor comply with random matrix theory. We test for the emergence of hydrodynamic sound by studying real time dynamics between the local equilibration time and Thouless time.   

Heat engine entropy flow controlled by entanglement

We calculate the entropy flow of a two-qubit heat engine and its dependence on entanglement between the qubits. Each qubit is weakly coupled to a heat reservoir, each at a different temperature and the qubits can exchange energy via a Jaynes-cummings like interaction. The individual qubits are driven externally to manipulate their states and control their entanglement. We find that the entanglement creates a nontrivial entropy flow which is purely quantum mechanical and can not be associated with the heat flow through the system. By manipulating the entanglement we can manipulate this new flow to either increase or reduce the total entropy flow.