Quantum Physics (quant-ph)

Abstract: In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts can thus be characterized by the inner products of nonorthogonal states in that Hilbert space. Here, we use measurement outcomes that are shared by different contexts to derive specific quantitative relations between the inner products of the Hilbert space vectors that represent the different contexts. It is shown that the probabilities that describe the paradoxes of quantum contextuality can be derived from a very small number of inner products, demonstrating that quantum contextuality is a necessary consequence of the quantitative relations between Hilbert space vectors representing different measurement contexts. The application of our analysis to a product space of two systems reveals that the non-locality of quantum entanglement can be traced back to a local inner product representing the relation between measurement contexts in only one system. Our results thus indicate that the essential non-classical features of quantum mechanics can all be derived systematically from the quantitative relations between different measurement contexts described by the Hilbert space formalism.

Abstract: Diffusion noise represents a major constraint to successful liquid state nano-NMR spectroscopy. Using the Fisher information as a faithful measure, we calculate theoretically and show experimentally that phase sensitive protocols are superior in most experimental scenarios, as they maximize information extraction from correlations in the sample. We derive the optimal experimental parameters for quantum heterodyne detection and present the most accurate statistically polarized nano-NMR Qdyne experiments to date, leading the way to resolve chemical shifts and $J$-couplings at the nano-scale.

Abstract: We extend the idea of classical cyclic redundancy check codes to quantum cyclic redundancy check codes. This allows us to construct codes quantum stabiliser codes which can correct burst errors where the burst length attains the quantum Reiger bound. We then consider a certain family of quantum cyclic redundancy check codes for which we present a fast linear time decoding algorithm.

Abstract: Thermal noise is a major obstacle to observing quantum behavior in macroscopic systems. To mitigate its effect, quantum optomechanical experiments are typically performed in a cryogenic environment. However, this condition represents a considerable complication in the transition from fundamental research to quantum technology applications. It is therefore interesting to explore the possibility of achieving the quantum regime in room temperature experiments. In this work we test the limits of sideband cooling vibration modes of a SiN membrane in a cavity optomechanical experiment. We obtain an effective temperature of a few mK, corresponding to a phononic occupation number of around 100. We show that further cooling is prevented by the excess classical noise of our laser source, and we outline the road toward the achievement of ground state cooling

Abstract: Single-crystal diamond substrates presenting a high concentration of negatively charged nitrogen-vacancy centers (NV-) are on high demand for the development of optically pumped solid-state sensors such as magnetometers, thermometers or electrometers. While nitrogen impurities can be easily incorporated during crystal growth, the creation of vacancies requires further treatment. Electron irradiation and annealing is often chosen in this context, offering advantages with respect to irradiation by heavier particles that negatively affect the crystal lattice structure and consequently the NV- optical and spin properties. A thorough investigation of electron irradiation possibilities is needed to optimize the process and improve the sensitivity of NV-based sensors. In this work we examine the effect of electron irradiation in a previously unexplored regime: extremely high energy electrons, at 155 MeV. We develop a simulation model to estimate the concentration of created vacancies and experimentally demonstrate an increase of NV- concentration by more than 3 orders of magnitude following irradiation of a nitrogen-rich HPHT diamond over a very large sample volume, which translates into an important gain in sensitivity. Moreover, we discuss the impact of electron irradiation in this peculiar regime on other figures of merits relevant for NV sensing, i.e. charge state conversion efficiency and spin relaxation time. Finally, the effect of extremely high energy irradiation is compared with the more conventional low energy irradiation process, employing 200 keV electrons from a transmission electron microscope, for different substrates and irradiation fluences, evidencing sixty-fold higher yield of vacancy creation per electron at 155 MeV.

Abstract: The phenomenon of quantum entanglement underlies several important protocols that enable emerging quantum technologies. Being an extremely delicate resource entangled states easily get perturbed by their external environment, and thus makes the question of entanglement certification immensely crucial for successful implementation of the protocols involving entanglement. In this work, we propose a set of entanglement criteria for multi-qubit systems that can be easily verified by measuring certain thermodynamic quantities. In particular, the criteria depend on the difference in optimal works extractable from an isolated quantum system under global and local interactions, respectively. As a proof of principle, we demonstrate the proposed thermodynamic criteria on nuclear spin registers of up to 10 qubits using Nuclear Magnetic Resonance architecture. We prepare noisy Greenberger-Horne-Zeilinger class of states in star-topology systems and certify their entanglement through our proposed criteria. We also provide elegant means of entanglement certification in many-body systems when only partial or even no knowledge about the state is available.

Abstract: The decomposition for controlled-$ZX$ gate in [Phys. Rev. A, 87, 062318 (2013)] has a shallow circuit depth $8n-20$ with no ancilla. Here we modify this decomposition to decompose $n$-qubit Toffoli gate with only $2n-3$ additional single-qubit gates. The circuit depth is unchanged and no ancilla is needed. We explicitly show that the circuit after decomposition can be easily constructed in present physical systems.

Abstract: In this work we study the robustness of two modifications of quantum random walk search algorithm on hypercube. In the first previously suggested modification, on each even iteration only quantum walk is applied. And in the second, the closest neighbors of the solution are measured classically. In our approach the traversing coin is constructed by both generalized Householder reflection and an additional phase multiplier and we investigate the stability of the algorithm to deviations in those phases. We have shown that the unmodified algorithm becomes more robust when a certain relation between those phases is preserved. The first modification we study here does not lead to any change in the robustness of quantum random walk search algorithm. However, when a measurement of the first and second neighbors is included, there are some differences. The most important one, in view of our study of the robustness, is an increase in the stability of the algorithm, especially for large coin dimensions.

Abstract: We provide a general framework to compute the probability distribution $F_r(t)$ of the first detection time of a 'state of interest' in a generic quantum system subjected to random projective measurements. In our 'quantum resetting' protocol, resetting of a state is not implemented by an additional classical stochastic move, but rather by the random projective measurement. We then apply this general framework to Poissoinan measurement protocol with a constant rate $r$ and demonstrate that exact results for $F_r(t)$ can be obtained for a generic two level system. Interestingly, the result depends crucially on the detection schemes involved and we have studied two complementary schemes, where the state of interest either coincides or differs from the initial state. We show that $F_r(t)$ at short times vanishes universally as $F_r(t)\sim t^2$ as $t\to 0$ in the first scheme, while it approaches a constant as $t\to 0$ in the second scheme. The mean first detection time, as a function of the measurement rate $r$, also shows rather different behaviors in the two schemes. In the former, the mean detection time is a nonmonotonic function of $r$ with a single minimum at an optimal value $r^*$, while in the later, it is a monotonically decreasing function of $r$, signalling the absence of a finite optimal value. These general predictions for arbitrary two level systems are then verified via explicit computation in the Jaynes-Cummings model of light-matter interaction. We also generalise our results to non-Poissonian measurement protocols with a renewal structure where the intervals between successive independent measurements are distributed via a general distribution $p(\tau)$ and show that the short time behavior of $F_r(t)\sim p(0)\, t^2$ is universal as long as $p(0)\ne 0$. This universal $t^2$ law emerges from purely quantum dynamics that dominates at early times.

Abstract: Charge state instabilities have been a bottleneck for the implementation of solid-state spin systems and pose a major challenge to the development of spin-based quantum technologies. Here we investigate the stabilization of negatively charged nitrogen-vacancy (NV$^-$) centers in phosphorus-doped diamond at liquid helium temperatures. Photoionization of phosphorous donors in conjunction with charge diffusion at the nanoscale enhances NV$^0$ to NV$^-$ conversion and stabilizes the NV$^-$ charge state without the need for an additional repump laser. The phosphorus-assisted stabilization is explored and confirmed both with experiments and our theoretical model. Stable photoluminescence-excitation spectra are obtained for NV$^-$ centers created during the growth. The fluorescence is continuously recorded under resonant excitation to real-time monitor the charge state and the ionization and recombination rates are extracted from time traces. We find a linear laser power dependence of the recombination rate as opposed to the conventional quadratic dependence, which is attributed to the photo-ionization of phosphorus atoms.

Abstract: Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate algorithm for solving combinatorial optimization problems on quantum computers. However, in many cases QAOA requires computationally intensive parameter optimization. The challenge of parameter optimization is particularly acute in the case of weighted problems, for which the eigenvalues of the phase operator are non-integer and the QAOA energy landscape is not periodic. In this work, we develop parameter setting heuristics for QAOA applied to a general class of weighted problems. First, we derive optimal parameters for QAOA with depth $p=1$ applied to the weighted MaxCut problem under different assumptions on the weights. In particular, we rigorously prove the conventional wisdom that in the average case the first local optimum near zero gives globally-optimal QAOA parameters. Second, for $p\geq 1$ we prove that the QAOA energy landscape for weighted MaxCut approaches that for the unweighted case under a simple rescaling of parameters. Therefore, we can use parameters previously obtained for unweighted MaxCut for weighted problems. Finally, we prove that for $p=1$ the QAOA objective sharply concentrates around its expectation, which means that our parameter setting rules hold with high probability for a random weighted instance. We numerically validate this approach on general weighted graphs and show that on average the QAOA energy with the proposed fixed parameters is only $1.1$ percentage points away from that with optimized parameters. Third, we propose a general heuristic rescaling scheme inspired by the analytical results for weighted MaxCut and demonstrate its effectiveness using QAOA with the XY Hamming-weight-preserving mixer applied to the portfolio optimization problem. Our heuristic improves the convergence of local optimizers, reducing the number of iterations by 7.2x on average.

Abstract: The superposition principle is one of the founding principles of quantum theory. Spatial quantum superpositions have so far been tested only with small systems, from photons and elementary particles to atoms and molecules. Such superpositions for massive objects have been a long-standing sought-after goal. This is important not only in order to confirm quantum theory in new regimes, but also in order to probe the quantum-gravity interface. In addition, such an experiment will enable to test exotic theories, and may even enable new technology. Creating such superpositions is notoriously hard because of environmental decoherence, whereby the large object couples strongly to the environment which turns the delicate quantum state into a statistical mixture (classical state). However, advances in the technology of isolation could in future suppress such decoherence. Here we present a decoherence channel which is not external but internal to the object, and consequently improved isolation would not help. This channel originates from the phonons (sound waves) within the object. We show that such phonons are excited as part of any splitting process, and thus we establish a fundamental and universal limit on the possibility of future spatial quantum superpositions with massive objects.

Abstract: The main aim of the present paper is to define an active matter in a quantum framework and investigate difference and commonalities of quantum and classical active matters. Although the research field of active matter has been expanding wider and wider, most research is conducted in classical systems; on the contrary, there is no universal theoretical framework for quantum active matter. We here propose a truly quantum active-matter model with a non-Hermitian quantum walk and show numerical results in one- and two-dimensional systems. We aim to reproduce similar results that Schweitzer \textit{et al.} obtained with their classical active Brownian particle; that is, the Brownian particle, with a finite energy take-up, becomes active and climbs up a potential wall. We realize such a system with non-Hermitian quantum walks. We introduce new internal states, the ground state and the excited state, and a new non-Hermitian operator $N(g)$ for an asymmetric transition between both states. The non-Hermiticity parameter $g$ promotes transition to the excited state and hence the particle takes up energy from the environment. We realize a system without momentum conservation by manipulating a parameter $\theta$ for the coin operator for a discrete-time quantum walk; we utilize the property that the continuum limit of a one-dimensional discrete-time quantum walk gives the Dirac equation with its mass proportional to the parameter $\theta$. With our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a non-trivial way as we increase the non-Hermiticity parameter $g$, which is similar to the classical active Brownian particle. Meanwhile, we also observe unique features of quantum walks, namely, ballistic propagation of peaks (1D) and the walker staying on the constant energy plane (2D).

Abstract: In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number t of non-Clifford gates. To tackle this problem, we introduce a novel algebraic framework for t-doped stabilizer states by utilizing tools from stabilizer entropy. Leveraging this new structure, we develop an algorithm that uses sampling from the distribution obtained by squaring expectation values of Pauli operators that can be obtained by Bell sampling on the state and its conjugate in the computational basis. The algorithm requires resources of complexity $O(\exp(t)\poly(n))$ and exhibits an exponentially small probability of failure.