QUROPE Quantum Information Processing and Communication in Europe

In this work, we derive Robertson-Heisenberg like uncertainty relation for two incompatible observables in a pre- and post-selected (PPS) system. The newly defined standard deviation and the uncertainty relation in the PPS system have physical meanings which we present here. We demonstrate two unusual properties in the PPS system using our uncertainty relation. First, for commuting observables, the lower bound of the uncertainty relation in the PPS system does not become zero even if the initially prepared state i.e., pre-selection is the eigenstate of both the observables when specific post-selections are considered. This implies that for such case, two commuting observables can disturb each other's measurement results which is in fully contrast with the Robertson-Heisenberg uncertainty relation. Secondly, unlike the standard quantum system, the PPS system makes it feasible to prepare sharply a quantum state (pre-selection) for non-commuting observables {(to be detailed in the main text)}. Some applications of uncertainty and uncertainty relation in the PPS system are provided: $(i)$ detection of mixedness of an unknown state, $(ii)$ stronger uncertainty relation in the standard quantum system, ($iii$) ``purely quantum uncertainty relation" that is, the uncertainty relation which is not affected (i.e., neither increasing nor decreasing) under the classical mixing of quantum states, $(iv)$ state dependent tighter uncertainty relation in the standard quantum system, and $(v)$ tighter upper bound for the out-of-time-order correlation function.

We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus. Specifically, we develop a canonical form in the ZX calculus and prove canonicity as well as efficient reducibility of any Clifford encoder into the canonical form. The diagrams produced by our compiler visualize information propagation and entanglement structure of the encoder, revealing properties that may be obscured in the circuit or stabilizer-tableau representation. Consequently, our canonical representation may be an informative technique for the design of new stabilizer quantum codes via graph theory analysis.

Variational quantum algorithms, which consist of optimal parameterized quantum circuits, are promising for demonstrating quantum advantages in the noisy intermediate-scale quantum (NISQ) era. Apart from classical computational resources, different kinds of quantum resources have their contributions to the process of computing, such as information scrambling and entanglement. Characterizing the relation between the complexity of specific problems and quantum resources consumed by solving these problems is helpful for us to understand the structure of VQAs in the context of quantum information processing. In this work, we focus on the quantum approximate optimization algorithm (QAOA), which aims to solve combinatorial optimization problems. We study information scrambling and entanglement in QAOA circuits, respectively, and discover that for a harder problem, more quantum resource is required for the QAOA circuit to obtain the solution in most cases. We note that in the future, our results can be used to benchmark the complexity of quantum many-body problems by information scrambling or entanglement accumulation in the computing process.

In this paper we aim to push the analogy between thermodynamics and quantum resource theories one step further. Previous inspirations were based predominantly on thermodynamic considerations concerning scenarios with a single heat bath, neglecting an important part of thermodynamics that studies heat engines operating between two baths at different temperatures. Here, we investigate the performance of resource engines, which replace the access to two heat baths at different temperatures with two arbitrary constraints on state transformations. The idea is to imitate the action of a two--stroke heat engine, where the system is sent to two agents (Alice and Bob) in turns, and they can transform it using their constrained sets of free operations. We raise and address several questions, including whether or not a resource engine can generate a full set of quantum operations or all possible state transformations, and how many strokes are needed for that. We also explain how the resource engine picture provides a natural way to fuse two or more resource theories, and we discuss in detail the fusion of two resource theories of thermodynamics with two different temperatures, and two resource theories of coherence with respect to two different bases.

Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic description for a spin-$\frac{1}{2}$ particle: Dirac's equation. Employing its energy-momentum tensor and going to the non-relativistic limit we find a locally conserved non-relativistic energy density that is defined via the Terletsky-Margenau-Hill quasiprobability (which is hence selected among other options). It coincides with the weak value of energy, and also with the hydrodynamic energy in the Madelung representation of quantum dynamics, which includes the quantum potential. Moreover, we find a new form of spin-related energy that is finite in the non-relativistic limit, emerges from the rest energy, and is (separately) locally conserved, though it does not contribute to the global energy budget. This form of energy has a holographic character, i.e., its value for a given volume is expressed via the surface of this volume. Our results apply to situations where local energy representation is essential; e.g. we show that the energy transfer velocity for a large class of free wave-packets (including Gaussian and Airy wave-packets) is larger than its group (i.e. coordinate-transfer) velocity.

In image processing, image segmentation is the process of partitioning a digital image into multiple image segment. Among state-of-the-art methods, Markov Random Fields (MRF) can be used to model dependencies between pixels, and achieve a segmentation by minimizing an associated cost function. Currently, finding the optimal set of segments for a given image modeled as a MRF appears to be NP-hard. In this paper, we aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of Synthetic Aperture Radar images. For that purpose, we propose an hybrid quantum annealing classical optimization Expectation Maximization algorithm to obtain optimal sets of segments. After proposing suitable formulations, we discuss the performances and the scalability of our approach on the D-Wave quantum computer. We also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimization problems.

Measurements are able to fundamentally affect quantum dynamics. We here show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable synchronization at the level of single trajectories. We formulate general criteria for this quantum phenomenon to occur, and demonstrate that the number of synchronized realizations can be controlled from none to all. We additionally find that ergodicity is typically broken, since time and ensemble averages may exhibit radically different synchronization behavior. We further introduce a quantum type of multiplexing that involves individual trajectories with distinct synchronization frequencies. Measurement-induced synchronization appears as a genuine nonclassical form of synchrony that exploits quantum superpositions.

The non-isometric holographic model of the black hole interior stands out as a potential resolution of the long-standing black hole information puzzle since it remedies the friction between the effective calculation and the microscopic description. In this study, combining the final-state projection model, the non-isometric model of black hole interior and Hayden-Preskill thought experiment, we investigate the information recovery from decoding Hawking radiation and demonstrate the emergence of the Page time in this setup. We incorporate the effective modes into the scrambling inside the horizon, which are usually disregarded in Hayden-Preskill protocols, and show that the Page time can be identified as the transition of information transmission channels from the EPR projection to the local projections. This offers a new perspective on the Page time. We compute the decoupling condition under which retrieving information is feasible and show that this model computes the black hole entropy consistent with the quantum extremal surface calculation. Assuming the full knowledge of the dynamics of the black hole interior, we show how Yoshida-Kitaev decoding strategy can be employed in the modified Hayden-Preskill protocol. Furthermore, we perform experimental tests of both probabilistic and Grover's search decoding strategies on the 7-qubit IBM quantum processors to validate our analytical findings and confirm the feasibility of retrieving information in the non-isometric model. This study would stimulate more interests to explore black hole information problem on the quantum processors.

Spin defects in van der Waals materials offer a promising platform for advancing quantum technologies. Here, we propose and demonstrate a powerful technique based on isotope engineering of host materials to significantly enhance the coherence properties of embedded spin defects. Focusing on the recently-discovered negatively charged boron vacancy center ($\mathrm{V}_{\mathrm{B}}^-$) in hexagonal boron nitride (hBN), we grow isotopically purified $\mathrm{h}{}^{10}\mathrm{B}{}^{15}\mathrm{N}$ crystals. Compared to $\mathrm{V}_{\mathrm{B}}^-$ in hBN with the natural distribution of isotopes, we observe substantially narrower and less crowded $\mathrm{V}_{\mathrm{B}}^-$ spin transitions as well as extended coherence time $T_2$ and relaxation time $T_1$. For quantum sensing, $\mathrm{V}_{\mathrm{B}}^-$ centers in our $\mathrm{h}{}^{10}\mathrm{B}{}^{15}\mathrm{N}$ samples exhibit a factor of $4$ ($2$) enhancement in DC (AC) magnetic field sensitivity. For additional quantum resources, the individual addressability of the $\mathrm{V}_{\mathrm{B}}^-$ hyperfine levels enables the dynamical polarization and coherent control of the three nearest-neighbor ${}^{15}\mathrm{N}$ nuclear spins. Our results demonstrate the power of isotope engineering for enhancing the properties of quantum spin defects in hBN, and can be readily extended to improving spin qubits in a broad family of van der Waals materials.

Hamiltonian approach in quantum theory provides a new thinking for option pricing with stochastic interest rates. For barrier options, the option price changing process is similar to the infinite high barrier scattering problem in quantum mechanics; for double barrier options, the option price changing process is analogous to a particle moving in a infinite square potential well. Using Hamiltonian approach, the expressions of pricing kernels and option prices under Vasicek stochastic interest rate model could be derived. Numerical results of options price as functions of underlying prices are also shown.

We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2 \times Z_2$ symmetry, and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical point with a continuous phase transition. We compute the critical exponents $z$, $\beta$, $\gamma$ and $\nu$, and the central charge $c$ numerically using exact diagonalization (ED) for systems with periodic boundary conditions. We find that both $z$ and $c$ are equal to $1$, implying that the critical point is governed by a conformal field theory. The values obtained for $\beta/\nu$, $\gamma/\nu$, and $\nu$ from ED suggest that the model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between the four-state Potts model and two decoupled transverse field Ising models. An analysis on larger systems but with open boundaries using density-matrix renormalization group calculations, however, shows that the self-dual point may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates. A subset of these eigenstates have wave functions which are independent of $h$ and have unusual entanglement structure, suggesting that they are quantum many-body scars. The number of such states scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if $h \gg 1$ or $h \ll 1$. If $h$ is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

We study experimentally and numerically the noisy evolution of multipartite entangled states, focusing on superconducting-qubit devices accessible via the cloud. We find that a valid modeling of the dynamics requires one to properly account for coherent frequency shifts, caused by stochastic charge-parity fluctuations. We introduce an approach modeling the charge-parity splitting using an extended Markovian environment. This approach is numerically scalable to tens of qubits, allowing us to simulate efficiently the dissipative dynamics of some large multiqubit states. Probing the continuous-time dynamics of increasingly larger and more complex initial states with up to 12 coupled qubits in a ring-graph state, we obtain a good agreement of the experiments and simulations. We show that the underlying many-body dynamics generate decays and revivals of stabilizers, which are used extensively in the context of quantum error correction. Furthermore, we demonstrate the mitigation of two-qubit coherent interactions (crosstalk) using tailored dynamical decoupling sequences. Our noise model and the numerical approach can be valuable to advance the understanding of error correction and mitigation and invite further investigations of their dynamics.

Ordering identities in the Weyl-Heisenberg algebra generated by single-mode boson operators are investigated. A boson string composed of creation and annihilation operators can be expanded as a linear combination of other such strings, the simplest example being a normal ordering. The case when each string contains only one annihilation operator is already combinatorially nontrivial. Two kinds of expansion are derived: (i) that of a power of a string $\Omega$ in lower powers of another string $\Omega'$, and (ii) that of a power of $\Omega$ in twisted versions of the same power of $\Omega'$. The expansion coefficients are shown to be, respectively, generalized Stirling numbers of Hsu and Shiue, and certain generalized Eulerian numbers. Many examples are given. These combinatorial numbers are binomial transforms of each other, and their theory is developed, emphasizing schemes for computing them: summation formulas, Graham-Knuth-Patashnik (GKP) triangular recurrences, terminating hypergeometric series, and closed-form expressions. The results on the first type of expansion subsume a number of previous results on the normal ordering of boson strings.

We consider a 4D spherically-symmetric static finite spacetime region as a collection of quanta in the semi-classical Einstein equation and study the entropy including the self-gravity. For sufficiently excited states, we estimate the entropy in a WKB-like method considering local consistency with thermodynamics and find its upper bound. The saturation condition uniquely determines the entropy-maximized spacetime as a radially uniform dense configuration with near-Planckian curvatures and a surface just outside the Schwarzschild radius. The interior metric is a non-perturbative solution in $\hbar$, leading to the species bound. The maximum entropy then saturates the Bousso bound and coincides with the Bekenstein-Hawking formula. Thus, the Bousso bound in this class of spacetime is verified by constructing the saturating configuration that has no horizon and stores information inside.

We present optimized distillation schemes for preparing Greenberger-Horne-Zeilinger (GHZ) states. Our approach relies on training variational quantum circuits with white noise affected GHZ states as inputs. Optimizing for a single iteration of the scheme, we find that it is possible to achieve an increased fidelity to the GHZ state, although further iterations decrease the fidelity. The same scheme, acting on coherently distorted pure-state inputs, is effective only in certain special cases. We show that radically different results can be achieved, however, when one optimizes for the output after two iterations of the protocol. In this case, the obtained schemes are more effective in distilling GHZ states from inputs affected by white noise. Moreover, they can also correct several types of coherent pure-state errors.

Quantum non-Markovianity in tripartite quantum states $\rho_{ABC}$ represents a correlation between systems $A$ and $C$ when conditioned on the system $B$ and is known to have both classical and quantum contributions. However, a systematic characterization of the latter is missing. To address this, we propose a faithful measure for non-Markovianity of genuine quantum origin called squashed quantum non-Markovianity (sQNM). It is based on the quantum conditional mutual information and is defined by the left-over non-Markovianity after squashing out all non-quantum contributions. It is lower bounded by the squashed entanglement between non-conditioning systems in the reduced state and is delimited by the extendibility of either of the non-conditioning systems. We show that the sQNM is monogamous, asymptotically continuous, convex, additive on tensor-product states, and generally super-additive. We characterize genuine quantum non-Markovianity as a resource via a convex resource theory after identifying free states with vanishing sQNM and free operations that do not increase sQNM in states. We use our resource-theoretic framework to bound the rate of state transformations under free operations and to study state transformation under non-free operations; in particular, we find the quantum communication cost from Bob ($B$) to Alice ($A$) or Charlie ($C$) is lower bounded by the change in sQNM in the states. The sQNM finds operational meaning; in particular, the optimal rate of private communication in a variant of conditional one-time pad protocol is twice the sQNM. Also, the minimum deconstruction cost for a variant of quantum deconstruction protocol is given by twice the sQNM of the state.

The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers. Quantumly, however, despite the fact that at least \emph{four} definitions of quantum $\mathsf{PH}$ exist, it has been challenging to prove analogues for these of even basic facts from $\mathsf{PH}$. This work studies three quantum-verifier based generalizations of $\mathsf{PH}$, two of which are from [Gharibian, Santha, Sikora, Sundaram, Yirka, 2022] and use classical strings ($\mathsf{QCPH}$) and quantum mixed states ($\mathsf{QPH}$) as proofs, and one of which is new to this work, utilizing quantum pure states ($\mathsf{pureQPH}$) as proofs. We first resolve several open problems from [GSSSY22], including a collapse theorem and a Karp-Lipton theorem for $\mathsf{QCPH}$. Then, for our new class $\mathsf{pureQPH}$, we show one-sided error reduction for $\mathsf{pureQPH}$, as well as the first bounds relating these quantum variants of $\mathsf{PH}$, namely $\mathsf{QCPH}\subseteq \mathsf{pureQPH} \subseteq \mathsf{EXP}^{\mathsf{PP}}$.

Quantum Computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry methods. An essential requirement for ground state quantum algorithms to be practical is the initialisation of the qubits to a high-quality approximation of the sought-after ground state. Quantum State Preparation (QSP) allows the preparation of approximate eigenstates obtained from classical calculations, but it is frequently treated as an oracle in quantum information. In this study, we conduct QSP on the ground state of prototypical strongly correlated systems, up to 28 qubits, using the Hyperion GPU-accelerated state-vector emulator. Various variational and non-variational methods are compared in terms of their circuit depth and classical complexity. Our results indicate that the recently developed Overlap-ADAPT-VQE algorithm offers the most advantageous performance for near-term applications.

In this paper, we investigate $k$-nonseparable $(2\leq k\leq n)$ entanglement measures based on geometric mean of all entanglement values of $k$-partitions in $n$-partite quantum systems. We define a class of entanglement measures called $k$-GM concurrence which explicitly detect all $k$-nonseparable states in multipartite systems. It is rigorously shown that the $k$-GM concurrence complies with all the conditions of an entanglement measure. Compared to $k$-ME concurrence [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.062323} {Phys. Rev. A \textbf{86}, 062323 (2012)}], the measures proposed by us emerge several different aspects, embodying that (i) $k$-GM concurrence can reflect the differences in entanglement but $k$-ME concurrence fails at times, (ii) $k$-GM concurrence does not arise sharp peaks when the pure state being measured varies continuously, while $k$-ME concurrence appears discontinuity points, (iii) the entanglement order is sometimes distinct. In addition, we establish the relation between $k$-ME concurrence and $k$-GM concurrence, and further derive a strong lower bound on the $k$-GM concurrence by exploiting the permutationally invariant part of a quantum state. Furthermore, we parameterize $k$-GM concurrence to obtain two categories of more generalized entanglement measures, $q$-$k$-GM concurrence $(q>1, 2\leq k\leq n)$ and $\alpha$-$k$-GM concurrence $(0\leq\alpha<1, 2\leq k\leq n)$, which fulfill the properties possessed by $k$-GM concurrence as well. Moreover, $\alpha$-$2$-GM concurrence $(0<\alpha<1)$, as a type of genuine multipartite entanglement measures, is proven in detail satisfying the requirement that the GHZ state is more entangled than the $W$ state in multiqubit systems.

Metastability in open system dynamics describes the phenomena of initial relaxation to longlived metastable states before decaying to the asymptotic stable states. It has been predicted in continuous-time stochastic dynamics of both classical and quantum systems. Here we present a general theory of metastability in discrete-time open quantum dynamics, described by sequential quantum channels. We focus on a general class of quantum channels on a target system, induced by an ancilla system with a pure-dephasing coupling to the target system and under Ramsey sequences. Interesting metastable behaviors are predicted and numerically demonstrated by decomposing the average dynamics into stochastic trajectories. Examples and applications are also discussed.