ABSTRACT. We show how to obtain perfect samples from a quantum Gibbs state on a quantum computer. To do so, we adapt one of the "Coupling from the Past"- algorithms proposed by Propp and Wilson. The algorithm has a probabilistic run-time and produces perfect samples without any previous knowledge of the mixing time of a quantum Markov chain. To implement it, we assume we are able to perform the phase estimation algorithm for the underlying Hamiltonian and implement a quantum Markov chain that satisfies certain conditions, implied e.g. by detailed balance, and is primitive. We analyse the expected run-time of the algorithm, which is linear in the mixing time and quadratic in the dimension. We also analyse the circuit depth necessary to implement it, which is proportional to the sum of the depth necessary to implement one step of the quantum Markov chain and one phase estimation. This algorithm is stable under noise in the implementation of different steps.

ABSTRACT. Passivity is a fundamental concept in thermodynamics that demands a quantum system’s energy cannot be lowered by any reversible, unitary process acting on the system. In the limit of many such systems, passivity leads in turn to the concept of complete passivity, thermal states, and the emergence of a thermodynamic temperature. Here we only consider a single system and show that every passive state except the thermal state is unstable under a weaker form of reversibility. Indeed, we show that given a single copy of any athermal quantum state, an optimal amount of energy can be extracted from it when we utilise a machine that operates in a reversible cycle. This means that for individual systems the only form of passivity that is stable under general reversible processes is complete passivity, and thus provides a physically motivated identification of thermal states when we are not operating in the thermodynamic limit.

ABSTRACT. Quantum information boom in recent decades has led to new algorithms defeating classical computation in some tasks or bringing brand new possibilities. One of proposed protocol introduces measurement-based selection and modification to implement nonlinear evolution. This evolution has been proven to exhibit chaotic features in a particular set of states - pure states.

We use the dimension of fractal structure in parameter space to characterise the chaotic dynamics. We show that this chaos is not lost when the pure states are disturbed. Furthermore, while the purity serves as a control parameter the fractal dimension enjoys a phase transition - the fractal structure is resistant to disturbations (its dimension remains constant) unless passing the transition points. We also present arguments that the attractor areas explode/collapse exponentially.

ABSTRACT. Fast and reliable reset of a qubit is a key prerequisite for any quantum technology. For real world open quantum systems undergoing non-Markovian dynamics, reset implies not only purification, but in particular erasure of initial correlations between qubit and environment. Here, we derive optimal reset protocols using a combination of geometric and numerical control theory. For factorizing initial states, we find a lower limit for the entropy reduction of the qubit as well as a speed limit. The time-optimal solution is determined by the maximum coupling strength. Initial correlations, remarkably, allow for faster reset and smaller errors. Entanglement is not necessary.

ABSTRACT. Time remains one of the least well understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here we explore these questions by introducing a model of time measurements that is complete and self-contained. Specifically, our autonomous quantum clock consists of a system out of equilibrium --- a prerequisite for any system to function as a clock --- powered by minimal resources, namely two thermal baths at different temperatures. Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock's performance in terms of its accuracy and resolution. Our results furthermore imply that a fundamental entropy production is associated with the operation of *any* autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power. More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond.

ABSTRACT. We study the possibility to achieve perfect state transfer in a one-dimensional gas of strongly-interacting cold atoms. First, we show that these systems give one the opportunity to engineer Heisenberg Hamiltonians with tunable spin-spin interactions. Therefore one can design chains that enjoy perfect state transfer. We illustrate this statement by analyzing dynamics in a simple yet non-trivial four-body system.

A. Volosniev et al, Phys. Rev. A 91, 023620 (2015) O. Marchukov et al, Nature Communications 7, 13070 (2016)

ABSTRACT. Realization of the silicon quantum computer on nuclear spins 31P:28Si requires the placement of phosphorus atoms (qubits) with very high accuracy. The most accurate method for donor-based silicon devices is the scanning tunneling microscopy (STM) lithography which allows to place P atoms with precision ~10Å. This spatial limitation is related to a need to have three clean Si dimers for the phosphine dissociation on the Si(100)-2x1-H surface. We propose a method for P incorporation into the upper Si(100) layer with atomic precision on the place of the selected Si atom. The mask on the Si(100) surface is formed by the chlorine monolayer and then it is patterned with the STM-tip to create Si vacancy. To investigate the phosphine adsorption on the Si(001)-2x1-Cl surface with vacancies in the adsorbate layer and combined vacancies with removal of silicon atoms, we performed DFT calculations. As a starting point of our method realization, we prepared Si(100)-2x1-Cl surface with a low defect density. A STM tip is used to desorb Cl with Si atoms. Observed STM images were compared to simulated images that helps to identify the type of the created defects. This work was supported by Grant No.16-12-00050 from the Russian Science Foundation.

ABSTRACT. We address the estimation of the magnetic field B acting on an ensemble of atoms with total spin J subjected to collective transverse noise. By preparing an initial spin coherent state, for any measurement performed after the evolution, the mean-square error of the estimate is known to scale as 1/J, i.e. no quantum enhancement is obtained. Here, we consider the possibility of continuously monitoring the atomic environment, and conclusively show that strategies based on time-continuous non-demolition measurements followed by a final strong measurement may achieve Heisenberg-limited scaling 1/J 2 and also a quantum-enhanced scaling in terms of the interrogation time. We also find that time-continuous schemes are robust against detection losses, as we prove that the quantum enhancement can be recovered also for finite measurement efficiency. Finally, we analytically prove the optimality of our strategy.

ABSTRACT. Dynamical decoupling is the method of choice for sensing weak oscillating signals. However, due to the required pulsing rate, state of the art decoupling sequences are limited to detect signals in the kHz to MHz frequency range. Sensing of higher frequencies is possible with relaxometry measurements, where the bandwidth is limited by the pure dephasing time of the probe system.

We present a general scheme that relaxes this limitation and allows for the enhanced detection of high frequency signals with a coherence time limited sensitivity. By the application of continuous driving fields robustness to both external and controller noise is achieved in such a way that the signal induces rotations of the robust qubit. This results in a significantly enhanced coherence time and enables high resolution sensing.

While our scheme is general and suitable to a variety of atomic and solid-state systems, we experimentally demonstrated it with the Nitrogen Vacancy center in diamond, utilizing its ground sub-states as a qubit. With coherence times of up to 1.43 milliseconds we performed high-frequency sensing with a sub-kHz resolution, reaching a smallest detectable magnetic field strength of 4 nT at 1.6 GHz.

ABSTRACT. It was suggested that two entangled fermions can behave like a single boson and that the bosonic quality is proportional to the degree of entanglement between the two particles. The relation between bosonic quality and entanglement is quite natural if one takes into account the fact that entanglement appears in bound states of interacting systems. However, entanglement can still be present in spatially separated subsystems that do not interact anymore. These systems are often a subject of studies on quantum nonlocality and foundations of quantum physics. Here, we ask whether an entangled spatially separated fermionic pair can exhibit bosonic properties. We show that in certain conditions the answer to this question can be positive. In particular, we propose a nonlocal bunching scenario in which two such pairs form an analogue of a two-partite bosonic Fock state.

ABSTRACT. We prove the optimality of a measurement scheme two phase conjugated input states introduced by N. J. Cerf and S. Iblisdir in 2001. We propose an extended and implementable measurement scheme which measures simultaneously n parameters encoded in the quadratures of n input coherent states.