Classical turbo codes efficiently approach the Shannon limit, and so bringing these over to the quantum scenario would allow for rapid transmission of quantum information. Early on in the work of defining the quantum analogue, it was shown that an efficient recursive subroutine (quantum convolutional codes) would always be catastrophic. This result may have stunted the further research into this coding scheme. In this document, we prove that this previously proven no-go theorem is no longer always true if we extend the coding scheme into qudit space with dimension some prime larger than 2. This removes a blockade in the development of quantum turbo codes and hopefully will stimulate further research in this area.

In this paper, we prove how to extend a subset of quantum stabilizer codes into a qudit hybrid code storing $\log_2 p$ classical bits over a qudit space with dimension $p$, with $p$ prime. Our proof also gives an explicit procedure for finding the entire collection of stabilizer algebras for all of the subcodes of the hybrid code. This allows extra classical information to be transmitted without having to arduously search for additional codes and their associated codewords, and also provides a first lower bound to the amount of classical information able to be transmitted in a qudit hybrid code, but unfortunately only allows for $\log_2 p$ classical bits to be decoded by a receiver.

Neutral atom array serves as an ideal platform to study the quantum logic gates, where intense efforts have been devoted to improve the two-qubit gate fidelity. We report our recent findings in constructing a different type of two-qubit controlled-PHASE quantum gate protocol with neutral atoms enabled by Rydberg blockade, which aims at both robustness and high-fidelity. It relies upon modulated driving pulse with specially tailored smooth waveform to gain appropriate phase accumulations for quantum gates. The major features include finishing gate operation within a single pulse, not necessarily requiring individual site addressing, not sensitive to the exact value of blockade shift while suppressing population leakage error and rotation error. We anticipate its fidelity to be reasonably high under realistic considerations for errors such as atomic motion, laser power fluctuation, power imbalance, spontaneous emission and so on. Moreover, we hope that such type of protocol may inspire future improvements in quantum gate designs for other categories of qubit platforms and new applications in other areas of quantum optimal control.

We study the smoothness of the black hole horizon in the Hayden-Preskill thought experiment by using two particular toy models based on variants of Haar random unitary. The first toy model corresponds to the case where the coarse-grained entropy of a black hole is larger than its entanglement entropy. We find that, while the outgoing mode and the remaining black hole are entangled, the Hayden-Preskill recovery cannot be performed. The second toy model corresponds to the case where the system consists of low energy soft modes and high energy heavy modes. We find that the Hayden-Preskill recovery protocol can be carried out via soft modes whereas heavy modes give rise to classical correlations between the outgoing mode and the remaining black hole. We also point out that the procedure of constructing the interior partners of the outgoing soft mode operators can be interpreted as the Hayden-Preskill recovery, and as such, the known recovery protocol enables us to explicitly write down the interior operators. Hence, while the infalling mode needs to be described jointly by the remaining black hole and the early radiation in our toy model, adding a few extra qubits from the early radiation is sufficient to reconstruct the interior operators.

Recently we pointed out that the black hole interior operators can be reconstructed by using the Hayden-Preskill recovery protocols. Building on this observation, we propose a resolution of the firewall problem by presenting a state-independent reconstruction of interior operators. Our construction avoids the non-locality problem which plagued the "$A=R_{B}$" or "$\text{ER}=\text{EPR}$" proposals. We show that the gravitational backreaction by the infalling observer, who simply falls into a black hole, disentangles the outgoing mode from the early radiation. The infalling observer crosses the horizon smoothly and sees quantum entanglement between the outgoing mode and the interior mode which is distinct from the originally entangled qubit in the early radiation. Namely, quantum operation on the early radiation cannot influence the experience of the infalling observer since description of the interior mode does not involve the early radiation at all. We also argue that verification of quantum entanglement by the outside observer does not create a firewall. Instead it will perform the Hayden-Preskill recovery which saves an infalling observer from crossing the horizon.

One of the main subjects of this paper is to study quantum property testing with local measurement. In particular, we establish a novel $\ell_2$ norm connection between quantum property testing problems and the corresponding distribution testing problems. This connection opens up the potential to derive efficient testing algorithms using techniques developed for classical property testing. As the first demonstration of these possibilities, we designed two streaming algorithms: one for quantum state tomography, the other for quantum closeness testing. Each employs a fixed one-qubit measurement of each qubit no matter the size of the system, and their simplicity means they can be easily implemented with current technology.

To the best of our knowledge, no streaming algorithm has yet been used for quantum property testing. So, to illustrate their usefulness, we achieve the following: independence testing for quantum states; identity and independence testing for quantum state collections; and conditional independence for classical-quantum-quantum states. Additionally, with a dimension splitting technique, we derive matching lower bound up to log factor for independence testing with joint measurement.

We study the controllable single-photon scattering via a one-dimensional waveguide which is coupled to a two-level emitter and a single-mode cavity simultaneously. The emitter and the cavity are also coupled to each other and form a three-level system with cyclic transitions within the zero- and single-excitation subspaces. As a result, the phase of emitter-cavity coupling strength serves as a sensitive control parameter. When the emitter and cavity locate at the same point of the waveguide, we demonstrate the Rabi splitting and quasidark-state--induced perfect transmission for the incident photons. More interestingly, when they locate at different points of the waveguide, a controllable nonreciprocal transmission can be realized and the non-reciprocity is robust to the weak coupling between the system and environment. Furthermore, we demonstrate that our theoretical model is experimentally feasible with currently available technologies.

We present a general quantum algorithm for solving finite-horizon dynamic programming problems. Up to polylogarithmic factors, our algorithm provides a quadratic quantum advantage in terms of the number of states of a given dynamic programming problem. This speedup comes at the expense of the appearance of other polynomial factors representative of the number of actions of the dynamic programming problem, the maximum value of the instantaneous reward, and the time horizon of the problem. Our algorithm can be applied to combinatorial optimization problems solved classically using dynamic programming techniques. As one application, we show that the travelling salesperson problem can be solved in $O^*(\lceil c \rceil^4 \sqrt{2^n})$ on a quantum computer, where $n$ is the number of vertices of the underlying graph and $\lceil c \rceil$ is its maximum edge-weight. As another example, we show that the minimum set-cover problem can be solved in $O(\sqrt{2^n} \operatorname{poly}(m, n))$, where $m$ is the number of sets used to cover a universe of size $n$. Finally, we prove lower bounds for the query complexity of quantum algorithms and classical randomized algorithms for solving dynamic programming problems, and show that no greater-than-quadratic speedup in either the number of states or number of actions can be achieved for solving dynamic programming problems using quantum algorithms.

In this work we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated to infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.

We present a self-calibrating, SI-traceable broadband Rydberg-atom-based radio-frequency (RF) electric field probe (the Rydberg Field Probe or RFP) and measurement instrument (Rydberg Field Measurement System or RFMS). The RFMS comprises an atomic RF field probe (RFP), connected by a ruggedized fiber-optic patch cord to a portable mainframe control unit with a software interface for RF measurement and analysis including real-time field readout and RF waveform visualization. The instrument employs electromagnetically induced transparency (EIT) readout of spectral signatures from RF-sensitive Rydberg states of an atomic vapor for continuous, pulsed, and modulated RF field measurement. The RFP exploits resonant and off-resonant Rydberg-field interactions to realize broadband RF measurements at frequencies ranging from ~10 MHz to sub-THz over a wide dynamic range. The RFMS incorporates an RF-field-free atomic reference and a laser-frequency tracker to ensure reliability and accuracy of the RF measurement. We characterize the RFP and measure polar field and polarization patterns of the RFP at 12.6 GHz RF in the far-field of a standard gain horn antenna. Measurements at 2.5 GHz are also performed. Measured patterns are in good agreement with simulations. A detailed calibration procedure and uncertainty analysis are presented that account for deviations from an isotropic response over a $4\pi$ solid angle, arising from dielectric structures external to the atomic measurement volume. Contributions to the measurement uncertainty from the fundamental atomic measurement method and associated analysis as well as material, geometry, and hardware design choices are accounted for. A calibration (C) factor is used to establish absolute-standard SI-traceable calibration of the RFP. Pulsed and modulated RF field measurement, and time-domain RF-pulse waveform imaging are also demonstrated.

Sensitive microwave detectors are critical instruments in radioastronomy, dark matter axion searches, and superconducting quantum information science. The conventional strategy towards higher-sensitivity bolometry is to nanofabricate an ever-smaller device to augment the thermal response. However, this direction is increasingly more difficult to obtain efficient photon coupling and maintain the material properties in a device with a large surface-to-volume ratio. Here we advance this concept to an ultimately thin bolometric sensor based on monolayer graphene. To utilize its minute electronic specific heat and thermal conductivity, we develop a superconductor-graphene-superconductor (SGS) Josephson junction bolometer embedded in a microwave resonator of resonant frequency 7.9 GHz with over 99\% coupling efficiency. From the dependence of the Josephson switching current on the operating temperature, charge density, input power, and frequency, we demonstrate a noise equivalent power (NEP) of 7 $\times 10^{-19}$ W/Hz$^{1/2}$, corresponding to an energy resolution of one single photon at 32 GHz and reaching the fundamental limit imposed by intrinsic thermal fluctuation at 0.19 K.

We analyze interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that "quantum nonlocality" is the basic factor differing quantum and classical realizations of entanglement. Instead, we point to the breakthrough Grangier et al. experiment on coincidence detection which was done in 1986 and played the crucial role in rejection of (semi-)classical field models in favor of quantum mechanics. Classical entanglement sources produce light beams with the coefficient of second order coherence $g^{(2)}(0) \geq 1.$ This feature of classical entanglement is obscured by using intensities of signals in different channels, instead of counting clicks of photo-detectors. Interplay between intensity and clicks counting is not just a technicality. We elevate this issue to the high foundational level.

Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is hidden in Hamiltonian dynamics, that is, the classical time evolution of variables including redundant degrees of freedom can be formulated as Nambu mechanics. In the present paper, we show that the Nambu mechanical structure is also hidden in some quantum or semiclassical dynamics, that is, in some cases, the quantum or semiclassical time evolution of expectation values of quantum mechanical operators including composite operators can be formulated as Nambu mechanics. We present a procedure to find hidden Nambu structures in quantum/semiclassical systems of one degree of freedom, and give two examples: the exact quantum dynamics of a harmonic oscillator and semiclassical wave packet dynamics. Our formalism can be extended to many-degrees-of-freedom systems, however, there is a serious difficulty in this case due to interactions between degrees of freedom. To illustrate our formalism, we present two sets of numerical results on semiclassical dynamics, in a one-dimensional metastable potential model and a simplified Henon--Heiles model of two interacting oscillators.

We introduce a method for the conditional generation of nonclassical states of light in a cavity. We consider two-level atoms traveling along the transverse direction to the cavity axis and show that by conditioning on one of the output measurements nonclassical field states are generated. The two-level atoms are prepared in the ground state and we conditioned on the events in which they are also detected in the ground state. Nonclassical properties of the cavity mode are identified and characterized. This includes: quadrature squeezing, sub-Poissonian photon-number distributions, and negative Wigner functions. We determine the optimal parameter regions where the corresponding nonclassical features are most distinct.

An amplifier combining noise performances as close as possible to the quantum limit with large bandwidth and high saturation power is highly desirable for many solid state quantum technologies such as high fidelity qubit readout or high sensitivity electron spin resonance for example. Here we introduce a new Traveling Wave Parametric Amplifier based on Superconducting QUantum Interference Devices. It displays a 3 GHz bandwidth, a -102 dBm 1-dB compression point and added noise near the quantum limit. Compared to previous state-of-the-art, it is an order of magnitude more compact, its characteristic impedance is in-situ tunable and its fabrication process requires only two lithography steps. The key is the engineering of a gap in the dispersion relation of the transmission line. This is obtained using a periodic modulation of the SQUID size, similarly to what is done with photonic crystals. Moreover, we provide a new theoretical treatment to describe the non-trivial interplay between non-linearity and such periodicity. Our approach provides a path to co-integration with other quantum devices such as qubits given the low footprint and easy fabrication of our amplifier.

This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constraint two-qubit operations on limited couplings, an input circuit must be transformed into an equivalent output circuit obeying the constraints. The transformation often requires additional gates that can affect the accuracy of running the circuit. Based upon a previous work of quantum circuit mapping that leverages gate commutation rules, this paper shows algorithms that utilize both transformation and commutation rules. Experiments on a standard benchmark dataset confirm the algorithms with more rules can find even better circuit mappings compared with the previously-known best algorithms.

Brillouin light scattering in ferromagnetic materials usually involves one magnon and two photons and their total angular momentum is conserved. Here, we experimentally demonstrate the presence of a helicity-changing two-magnon Brillouin light scattering in a ferromagetic crystal, which can be viewed as a four-wave mixing process involving two magnons and two photons. Moreover, we observe an unconventional helicity-changing one-magnon Brillouin light scattering, which apparently infringes the conservation law of the angular momentum. We show that the crystal angular momentum intervenes to compensate the missing angular momentum in the latter scattering process.

Discrete time crystals are periodically driven systems characterized by a response with periodicity $nT$, with $T$ the period of the drive and $n>1$. Typically, $n$ is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-$1/2$ systems with $n$ restricted to $2$. Here we show that a clean spin-$1/2$ system in the presence of long-range interactions and transverse field can sustain a huge variety of different 'higher-order' discrete time crystals with integer and, surprisingly, even fractional $n > 2$. We characterize these non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.

Encoding a qubit in logical quantum states with wavefunctions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. Using a circuit-quantum-electrodynamics architecture, we experimentally realize a superconducting $0-\pi$ qubit, which hosts protected states suitable for quantum-information processing. Multi-tone spectroscopy measurements reveal the energy level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. We find that the parity symmetry of the qubit results in charge-insensitive levels connecting the protected states, allowing for logical operations. The measured relaxation (1.6 ms) and dephasing times (25 $\mu$s) demonstrate that our implementation of the $0-\pi$ circuit not only broadens the family of superconducting qubits, but also represents a promising candidate for the building block of a fault-tolerant quantum processor.

The family of $n$-bit Toffoli gates, with the 2-bit Toffoli gate as the figurehead, are of great interest in quantum information as they can be used as universal gates and in quantum error correction, among other things. Here we present a simple single-step implementation of arbitrary $n$-bit Toffoli gates. The gate time of the implementation is independent of the number of control qubits, and the fidelities of our systems are well above 0.98 for up to five control qubits, with the major contribution to error coming from the qubit decoherence time. We discuss an implementation of the gates using superconducting circuits, however, the ideas presented in this paper is not limited to such implementation. We also show how these ideas can be used to make a series of CNOT-gates more efficient by performing all CNOT-gates in a single time step. Lastly we combine all of the above to create efficient quantum error correction codes. Specifically we simulate the three-qubit bit flip code and the Steane seven-qubit encoding, both with high fidelity.