Erasure Protocol Research Articles

Adiabatic computing for optimal thermodynamic efficiency of information processing

Landauer's principle makes a strong connection between information theory and thermodynamics by stating that erasing a one-bit memory at temperature [Formula: see text] requires an average energy larger than [Formula: see text], with [Formula: see text] Boltzmann's constant. This tiny limit has been saturated in model experiments using quasistatic processes. For faster operations, an overhead proportional to the processing speed and to the memory damping appears. In this article, we show that underdamped systems are a winning strategy to reduce this extra energetic cost. We prove both experimentally and theoretically that, in the limit of vanishing dissipation mechanisms in the memory, the physical system is thermally insulated from its environment during fast erasures, i.e., fast protocols are adiabatic as no heat is exchanged with the bath. Using a fast optimal erasure protocol, we also show that these adiabatic processes produce a maximum adiabatic temperature [Formula: see text], and that Landauer's bound for fast erasures in underdamped systems becomes the adiabatic bound: [Formula: see text].

Cooperative quantum information erasure

We demonstrate an information erasure protocol that resets N qubits at once. The method displays exceptional performances in terms of energy cost (it operates nearly at Landauer energy cost kTln⁡2), time duration (∼μs) and erasure success rate (∼99,9%). The method departs from the standard algorithmic cooling paradigm by exploiting cooperative effects associated to the mechanism of spontaneous symmetry breaking which are amplified by quantum tunnelling phenomena. Such cooperative quantum erasure protocol is experimentally demonstrated on a commercial quantum annealer and could be readily applied in next generation hybrid gate-based/quantum-annealing quantum computers, for fast, effective, and energy efficient initialisation of quantum processing units.

Thermodynamic optimization of quantum algorithms: On-the-go erasure of qubit registers

We consider two bottlenecks in quantum computing: limited memory size and noise caused by heat dissipation. Trying to optimize both, we investigate ``on-the-go erasure'' of quantum registers that are no longer needed for a given algorithm: freeing up auxiliary qubits as they stop being useful would facilitate the parallelization of computations. We study the minimal thermodynamic cost of erasure in these scenarios, applying results on the Landauer erasure of entangled quantum registers. For the class of algorithms solving the Abelian hidden subgroup problem, we find optimal on-the-go erasure protocols. We conclude that there is a trade-off: if we have enough partial information about a problem to build efficient on-the-go erasure, we can use it to instead simplify the algorithm, so that fewer qubits are needed to run the computation in the first place. We provide explicit protocols for these two approaches.

Phase shift in periodically driven non-equilibrium systems: its identification and a bound

Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that unites all these quite different systems is some form of lag between the driving of the system and its response. For periodic steady states, we quantify this lag by introducing a generalized phase difference and prove a tight upper bound for it. In its most general version, this bound depends only on the relative speed of the driving.

Thermodynamics of memory erasure via a spin reservoir.

Thermodynamics with multiple conserved quantities offers a promising direction for designing novel devices. For example, Vaccaro and Barnett's [J. A. Vaccaro and S. M. Barnett, Proc. R. Soc. A 467, 1770 (2011)1364-502110.1098/rspa.2010.0577; S. M. Barnett and J. A. Vaccaro, Entropy 15, 4956 (2013)ENTRFG1099-430010.3390/e15114956] proposed information erasure scheme, where the cost of erasure is solely in terms of a conserved quantity other than energy, allows for new kinds of heat engines. In recent work, we studied the discrete fluctuations and average bounds of the erasure cost in spin angular momentum. Here we clarify the costs in terms of the spin equivalent of work, called spinlabor, and the spin equivalent of heat, called spintherm. We show that the previously found bound on the erasure cost of γ^{-1}ln2 can be violated by the spinlabor cost, and only applies to the spintherm cost. We obtain three bounds for spinlabor for different erasure protocols and determine the one that provides the tightest bound. For completeness, we derive a generalized Jarzynski equality and probability of violation which shows that for particular protocols the probability of violation can be surprisingly large. We also derive an integral fluctuation theorem and use it to analyze the cost of information erasure using a spin reservoir.

Information and Thermodynamics: Fast and Precise Approach to Landauer's Bound in an Underdamped Micromechanical Oscillator.

The Landauer principle states that at least k_{B}Tln2 of energy is required to erase a 1-bit memory, with k_{B}T the thermal energy of the system. We study the effects of inertia on this bound using as one-bit memory an underdamped micromechanical oscillator confined in a double-well potential created by a feedback loop. The potential barrier is precisely tunable in the few k_{B}T range. We measure, within the stochastic thermodynamic framework, the work and the heat of the erasure protocol. We demonstrate experimentally and theoretically that, in this underdamped system, the Landauer bound is reached with a 1% uncertainty, with protocols as short as 100ms.

Secure memory erasure in the presence of man-in-the-middle attackers

Memory erasure protocols serve to clean up a device’s memory before the installation of new software. Although this task can be accomplished by direct hardware manipulation, remote software-based memory erasure protocols have emerged as a more efficient and cost-effective alternative. Existing remote memory erasure protocols, however, still rely on non-standard adversarial models to operate correctly, thereby requiring additional hardware to restrict the adversary’s capabilities. In this work, we provide a formal definition of secure memory erasure within a symbolic security model that utilizes the standard Dolev–Yao adversary. Our main result consists of a restriction on the Dolev–Yao adversary that we prove necessary and sufficient to solve the problem of finding a protocol that satisfies secure memory erasure. We also provide a description of the resulting protocol using standard cryptographic notation, which we use to analyze the security and communication complexity trade-off commonly present in this type of protocols.

Can We Break the Landauer Bound in Spin-Based Electronics?

We found that the minimum energy of reading or erasing a spin datum should be expressed by $\Delta E=2~\mu _{B}B$ , in contrast to ${\Delta E=k}_{B}T\,\,ln(2)$ proposed by Landauer in 1961. The physics of using a spin’s orientation to represent a bit of information is fundamentally different from that of using a particle’s position in classical charge-based data storage: the former is quantum-dynamic (independent of temperature below the Curie point), whereas the latter is thermodynamic (dependent on temperature). Quantitatively, this new energy bound associated with a new information erasure protocol was estimated as $1.64\times {10}^{-36}J$ , 15 orders of magnitude lower than the Landauer bound ( $3 \times {10}^{-21}J$ ), at no cost of angular momentum and increased total entropy. In this new information erasure protocol, there is no need to move the electron from one side of the potential well to the other side otherwise the energy used to retain the defined spin state still needs to be greater than the existing thermal fluctuation (the Landauer bound). We verified our new energy bound based on a number of experiments including the Rydberg atom and the spin-spin interaction.

Quantum Fluctuations Hinder Finite-Time Information Erasure near the Landauer Limit.

Information is physical but information is also processed in finite time. Where computing protocols are concerned, finite-time processing in the quantum regime can dynamically generate coherence. Here we show that this can have significant thermodynamic implications. We demonstrate that quantum coherence generated in the energy eigenbasis of a system undergoing a finite-time information erasure protocol yields rare events with extreme dissipation. These fluctuations are of purely quantum origin. By studying the full statistics of the dissipated heat in the slow-driving limit, we prove that coherence provides a non-negative contribution to all statistical cumulants. Using the simple and paradigmatic example of single bit erasure, we show that these extreme dissipation events yield distinct, experimentally distinguishable signatures.

Thermodynamics of Majority-Logic Decoding in Information Erasure.

We investigate the performance of majority-logic decoding in both reversible and finite-time information erasure processes performed on macroscopic bits that contain N microscopic binary units. While we show that for reversible erasure protocols single-unit transformations are more efficient than majority-logic decoding, the latter is found to offer several benefits for finite-time erasure processes: Both the minimal erasure duration for a given erasure and the minimal erasure error for a given erasure duration are reduced, if compared to a single unit. Remarkably, the majority-logic decoding is also more efficient in both the small-erasure error and fast-erasure region. These benefits are also preserved under the optimal erasure protocol that minimizes the dissipated heat. Our work therefore shows that majority-logic decoding can lift the precision-speed-efficiency trade-off in information erasure processes.

Analysis of Heat Dissipation and Reliability in Information Erasure: A Gaussian Mixture Approach.

This article analyzes the effect of imperfections in physically realizable memory. Motivated by the realization of a bit as a Brownian particle within a double well potential, we investigate the energetics of an erasure protocol under a Gaussian mixture model. We obtain sharp quantitative entropy bounds that not only give rigorous justification for heuristics utilized in prior works, but also provide a guide toward the minimal scale at which an erasure protocol can be performed. We also compare the results obtained with the mean escape times from double wells to ensure reliability of the memory. The article quantifies the effect of overlap of two Gaussians on the the loss of interpretability of the state of a one bit memory, the required heat dissipated in partially successful erasures and reliability of information stored in a memory bit.

Nonequilibrium uncertainty principle from information geometry

With a statistical measure of distance, we derive a classical uncertainty relation for processes traversing nonequilibrium states both transiently and irreversibly. The geometric uncertainty associated with dynamical histories that we define is an upper bound for the entropy production and flow rates, but it does not necessarily correlate with the shortest distance to equilibrium. For a model one-bit memory device, we find that expediting the erasure protocol increases the maximum dissipated heat and geometric uncertainty. A driven version of Onsager's three-state model shows that a set of dissipative, high-uncertainty initial conditions, some of which are near equilibrium, scar the state space.

Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes

In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the nonequilibrium regime and cannot be ignored, making such processes difficult to understand and treat. Here we derive an emergent fluctuation relation that virtually guarantees the average heat produced to be dissipated into the reservoir either when the system or reservoir is large (or both) or when the temperature is high. The implication of our result is that for nonequilibrium processes, heat fluctuations away from its average value are suppressed independently of the underlying dynamics exponentially quickly in the dimension of the larger subsystem and linearly in the inverse temperature. We achieve these results by generalizing a concentration of measure relation for subsystem states to the case where the global state is mixed.

Two-axis-twisting spin squeezing by multipass quantum erasure

Many-body entangled states are key elements in quantum information science and quantum metrology. One important problem in establishing a high degree of many-body entanglement using optical techniques is the leakage of the system information via the light that creates such entanglement. We propose an all-optical interference-based approach to erase this information. Unwanted atom-light entanglement can be removed by destructive interference of three or more successive atom-light interactions, with only the desired effective atom-atom interaction left. This quantum erasure protocol allows implementation of Heisenberg-limited spin squeezing using coherent light and a cold or warm atomic ensemble. Calculations show that significant improvement in the squeezing exceeding 10 dB is obtained compared to previous methods, and substantial spin squeezing is attainable even under moderate experimental conditions. Our method enables the efficient creation of many-body entangled states with simple setups, and thus is promising for advancing technologies in quantum metrology and quantum information processing.

Memory erasure using time-multiplexed potentials.

We study the thermodynamics of a Brownian particle under the influence of a time-multiplexed harmonic potential of finite width. The memory storage mechanism and the erasure protocol based on time-multiplexed potentials are utilized to experimentally realize erasure with work performed close to Landauer's bound. We quantify the work performed on the system with respect to the duty ratio of time multiplexing, which also provides a handle for approaching reversible erasures. A Langevin dynamics based simulation model is developed for the proposed memory bit and the erasure protocol, which guides the experimental realization. The study also provides insight into transport on the microscale.

Discrete Fluctuations in Memory Erasure without Energy Cost.

According to Landauer's principle, erasing one bit of information incurs a minimum energy cost. Recently, Vaccaro and Barnett (VB) explored information erasure within the context of generalized Gibbs ensembles and demonstrated that for energy-degenerate spin reservoirs the cost of erasure can be solely in terms of a minimum amount of spin angular momentum and no energy. As opposed to the Landauer case, the cost of erasure in this case is associated with an intrinsically discrete degree of freedom. Here we study the discrete fluctuations in this cost and the probability of violation of the VB bound. We also obtain a Jarzynski-like equality for the VB erasure protocol. We find that the fluctuations below the VB bound are exponentially suppressed at a far greater rate and more tightly than for an equivalent Jarzynski expression for VB erasure. We expose a trade-off between the size of the fluctuations and the cost of erasure. We find that the discrete nature of the fluctuations is pronounced in the regime where reservoir spins are maximally polarized. We also state the first laws of thermodynamics corresponding to the conservation of spin angular momentum for this particular erasure protocol. Our work will be important for novel heat engines based on information erasure schemes that do not incur an energy cost.

Erasure without Work in an Asymmetric Double-Well Potential.

According to Landauer's principle, erasing a memory requires an average work of at least kTln2 per bit. Recent experiments have confirmed this prediction for a one-bit memory represented by a symmetric double-well potential. Here, we present an experimental study of erasure for a memory encoded in an asymmetric double-well potential. Using a feedback trap, we find that the average work to erase can be less than kTln2. Surprisingly, erasure protocols that differ subtly give measurably different values for the asymptotic work, a result we explain by showing that one protocol is symmetric with the respect to time reversal, while the other is not. The differences between the protocols help clarify the distinctions between thermodynamic and logical reversibility.

A scheme for performing strong and weak sequential measurements of non-commuting observables

Quantum systems usually travel a multitude of different paths when evolving through time from an initial to a final state. In general, the possible paths will depend on the future and past boundary conditions, as well as the system’s dynamics. We present a gedanken experiment where a single system apparently follows mutually exclusive paths simultaneously, each with probability one, depending on which measurement was performed. This experiment involves the measurement of observables that do not correspond to Hermitian operators. Our main result is a scheme for measuring these operators. The scheme is based on the erasure protocol [Brodutch and Cohen (Phys. Rev. Lett. 116:070404, 2016)] and allows a wide range of sequential measurements at both the weak and strong limits. At the weak limit the back action of the measurement cannot be used to account for the surprising behaviour and the resulting weak values provide a consistent yet strange account of the system’s past.

Maxwell Demon Dynamics: Deterministic Chaos, the Szilard Map, and the Intelligence of Thermodynamic Systems

We introduce a deterministic chaotic system-the Szilard map-that encapsulates the measurement, control, and erasure protocol by which Maxwellian demons extract work from a heat reservoir. Implementing the demon's control function in a dynamical embodiment, our construction symmetrizes the demon and the thermodynamic system, allowing one to explore their functionality and recover the fundamental trade-off between the thermodynamic costs of dissipation due to measurement and those due to erasure. The map's degree of chaos-captured by the Kolmogorov-Sinai entropy-is the rate of energy extraction from the heat bath. Moreover, an engine's statistical complexity quantifies the minimum necessary system memory for it to function. In this way, dynamical instability in the control protocol plays an essential and constructive role in intelligent thermodynamic systems.

Capturing the Landauer bound through the application of a detailed Jarzynski equality for entropic memory erasure.

The states of an overdamped Brownian particle confined in a two-dimensional bilobal enclosure are considered to correspond to two binary values: 0 (left lobe) and 1 (right lobe). An ensemble of such particles represents bits of entropic information. An external bias is applied on the particles, equally distributed in two lobes, to drive them to a particular lobe erasing one kind of bit of information. It has been shown that the average work done for the entropic memory erasure process approaches the Landauer bound for a very slow erasure cycle. Furthermore, the detailed Jarzynski equality holds to a very good extent for the erasure protocol, so that the Landauer bound may be calculated irrespective of the time period of the erasure cycle in terms of the effective free-energy change for the process. The detailed Jarzynski equality applied to two subprocesses, namely the transition from entropic memory state 0 to state 1 and the transition from entropic memory state 1 to state 1, connects the work done on the system to the probability to occupy the two states under a time-reversed process. In the entire treatment, the work appears as a boundary effect of the physical confinement of the system not having a conventional potential energy barrier. Finally, an analytical derivation of the detailed and classical Jarzynski equality for Brownian movement in confined space with varying width has been proposed. Our analytical scheme supports the numerical simulations presented in this paper.