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We propose an ultrafast femtosecond time scale trichromatic $\pi$-pulse illumination scheme for coherent excitation and manipulation of low-lying Rydberg states in rubidium. Selective population of ${nP}_{3/2}$ levels with principal quantum numbers $n\lesssim 12$ using 75-fs laser pulses is achieved. The density-matrix equations of a four-level ladder system beyond the rotating-wave approximation have to be solved to clarify the balance between the principal quantum numbers, the duration of the laser pulses, and the associated ac-Stark effects for the fastest optimal excitation. The mechanism is robust for femtosecond control using different level configurations for applications in ultrafast quantum information processing and spectroscopy.

We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multiobjective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables and prove an inequality for the optimal region that both strengthens and generalizes Bell's theorem. To solve the optimization problem (rather than simply bound it), we develop a genetic algorithm treating as individuals causal networks. By applying our algorithm to a photonic Bell experiment, we demonstrate the trade-off between the quantitative relaxation of one or more local causality assumptions and the ability of data to match quantum correlations.

We consider the dependence of the recently proposed action/complexity duality conjecture on time and on the underlying topology of the bulk spacetime. For the former, we compute the dependence of the CFT complexity on a boundary temporal parameter and find it to be commensurate with corresponding computations carried out in terms of the rate of change of the bulk action on a Wheeler deWitt (WDW) patch. For the latter, we compare the action/complexity relation for ($d+1$)-dimensional Schwarzschild AdS black holes to those of their geon counterparts, obtained via topological identification in the bulk spacetime. The complexity/action duality relation holds in both cases, but with the proportionality changed by a factor of 4, indicating sensitivity to spacetime topology.

Generating ground states of any local Hamiltonians seems to be impossible in quantum polynomial time. In this paper, we give evidence for the impossibility by applying an argument used in the quantum-computational-supremacy approach. More precisely, we show that if ground states of any 3-local Hamiltonians can be approximately generated in quantum polynomial time with postselection, then $\mathsf{PP}=\mathsf{PSPACE}$. Our result is superior to the existing findings in the sense that we reduce the impossibility to an unlikely relation between classical complexity classes. We also discuss what makes efficiently generating the ground states hard for postselected quantum computation.

We propose fast phase gates of single nuclear spins interacting with single electron spins. The gate operation utilizes geometric phase shifts of the electron spin induced by fast and slow rotating fields; the path difference depending on nuclear-spin states enables nuclear phase shifts. The gate time is inversely proportional to the frequency of the slow rotating field. As an example, we use nitrogen-vacancy centers in diamond, and show, in principle, the phase-gate time orders of magnitude to be shorter than previously reported. We also confirmed the robustness of the gate against decoherence and systematic errors.

We perform hole burning with a low-drift stabilized laser within the zero phonon line of the $4f-5d$ transition in ${\mathrm{Ce}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ at 2 K. The narrowest spectral holes appear for small applied magnetic fields and are $6\pm 4$ MHz wide (FWHM). This puts an upper bound on the homogeneous linewidth of the transition to $3\pm 2$ MHz, which is close to lifetime limited. The spin level relaxation time is measured to $72\pm 21$ ms with a magnetic field of 10 mT. A slow permanent hole burning mechanism is observed. If the excitation frequency is not changed the fluorescence intensity is reduced by more than $50\%$ after a couple of minutes of continuous excitation. The spectral hole created by the permanent hole burning has a width in the tens of MHz range, which indicates that a trapping mechanism occurs via the $5d$ state.

We propose a scheme for frequency-domain quantum computation (FDQC) in which the errors due to crosstalk are suppressed using extra physical systems coupled to a cavity. FDQC is a promising method to realize large-scale quantum computation, but crosstalk is a major problem. When physical systems employed as qubits satisfy specific resonance conditions, gate errors due to crosstalk increase. In our scheme, the errors are suppressed by controlling the resonance conditions using extra physical systems.

Although it is well-known that all quantum states can be produced by single-qubit measurements on the cluster states, it is not a simple task to explicitly find which measurement patterns on the cluster states can generate different quantum states. In this paper, we introduce a general scheme to find measurement patterns corresponding to Calderbank–Shor–Steane (CSS) topological states containing Kitaev's toric code states and color code states on different lattices and in different dimensions. Furthermore, we find a measurement pattern for generating non-Abelian anyons where measurement-induced defects on a toric code state play the role of Ising anyons. We also support our scheme by a graphical notation where, by following a few simple graphical transformations, one will be able to convert a CSS topological state to a cluster state. Our scheme can also be used for experimental realization of anyons on cluster states.

We propose an efficient scheme for implementing the universal controlled-phase gate with logical qubits encoded in the superpositions of $2d$ circularly distributed coherent states ($d$ is a positive integer), which have the advantage of protecting quantum information against the $(d-1)$-photon loss errors. We first demonstrate explicitly how to engineer dispersive interaction between the microwave cavity modes and multilevel transmon ancilla in circuit quantum electro-dynamical (QED) system. With the cat-state qubits, we realize the two-qubit controlled phase gate, and its operation time scales as $1/d$. This means that it will be less susceptible to environmental disturbances if we employ larger $d$ to encode information. Finally, we employ the experimentally reachable parameters in circuit QED system to numerically study the influence of the photon loss, the qubit relaxation, and the Kerr nonlinearity. The average fidelity for a controlled-phase gate has reached 0.9955 for $d=8$ when the system imperfections are considered. The results demonstrate the great potential of our scheme for quantum computation in circuit QED system.

Undoing a unitary operation, i.e., reversing its action, is the task of canceling the effects of a unitary evolution on a quantum system, and it may be easily achieved when the unitary is known. Given a unitary operation without any specific description, however, it is a hard and challenging task to realize the inverse operation. Recently, a universal quantum circuit has been proposed [Phys. Rev. Lett. 123, 210502 (2019)] to undo an arbitrary unknown $d$-dimensional unitary $U$ by implementing its inverse with a certain probability. In this paper, we report the experimental reversal of three single-qubit unitaries $(d=2)$ by linear optical elements. The experimental results prove the feasibility of the reversing scheme, showing that the average fidelity of inverse unitaries is $F=0.9767\pm 0.0048$, in close agreement with the theoretical prediction.

We investigate the efficiency of quantum adiabatic optimization when overcoming potential barriers to get from a local to a global minimum. Specifically we look at $n$ qubit systems with symmetric cost functions $f:{\{0,1\}}^n\to \mathbb{R}$, where the ground state must tunnel through a potential barrier of width $n^{\alpha }$ and height $n^{\beta }$. By the quantum adiabatic theorem the time delay sufficient to ensure tunneling grows quadratically with the inverse spectral gap during this tunneling process. We analyze barrier sizes with $1/2\le \alpha +\beta$ and $\alpha <1/2$ and show that the minimum gap scales polynomially as $n^{1/2-\alpha -\beta }$ when $2\alpha +\beta \le 1$ and exponentially as $n^{-\beta /2}exp(-C{n}^{(2\alpha +\beta -1)/2})$ when $1<2\alpha +\beta$. Our proof uses elementary techniques and confirms and extends an unpublished folklore result by Goldstone from 2002, which used large spin and instanton methods. Parts of our result also refine recent results by Kong and Crosson [arXiv:1511.06991] and Jiang et al. [arXiv:1603.01293] about the exponential gap scaling.

In view of the fundamental importance and many promising potential applications, non-Abelian statistics of topologically protected states have attracted much attention recently. However, due to the operational difficulties in solid-state materials, experimental realization of non-Abelian statistics is lacking. The superconducting quantum circuit system is scalable and controllable, and thus is a promising platform for quantum simulation. Here we propose a scheme to demonstrate non-Abelian statistics of topologically protected zero-energy edge modes on a chain of superconducting circuits. Specifically, we can realize topological phase transition by varying the hopping strength and magnetic field in the chain, and the realized non-Abelian operation can be used in topological quantum computation. Considering the advantages of the superconducting quantum circuits, our protocol may shed light on quantum computation via topologically protected states.

Topological qubits based on $SU(N)$-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with twofold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical $Z$ rotation by an angle $2\pi /N$, for any integer $N>2$, is provided by a global twist operation, which is of a topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.

We report experimental observation of two distinct quantum interference patterns in the absorption spectra when a transmon superconducting qubit is subjected to a bichromatic microwave field with the same Rabi frequencies. Within the two-mode Floquet formalism with no dissipation processes, we propose a graph-theoretical representation to model the interaction Hamiltonian for each of these observations. This theoretical framework provides a clear visual representation of various underlying physical processes in a systematic way beyond rotating-wave approximation. The presented approach is valuable to gain insights into the behavior of multichromatic field driven quantum two-level systems, such as two-level atoms and superconducting qubits. Each of the observed interference patterns is represented by appropriate graph products on the proposed color-weighted graphs. The underlying mechanisms and the characteristic features of the observed fine structures are identified by the transitions between the graph vertices, which represent the doubly dressed states of the system. The good agreement between the numerical simulation and experimental data confirms the validity of the theoretical method. Such multiphoton interference may be used in manipulating the quantum states and/or generate nonclassical microwave photons.

Several information measures have recently been defined that capture the notion of recoverability. In particular, the fidelity of recovery quantifies how well one can recover a system $A$ of a tripartite quantum state, defined on systems $ABC$, by acting on system $C$ alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. The quantum interactive proof system giving this operational meaning requires four messages exchanged between the prover and verifier, but by forcing the prover to perform actions in superposition, we construct a different proof system that requires only two messages. The result is that the associated decision problem is in QIP(2) and another argument establishes it as hard for QSZK (both classes contain problems believed to be difficult to solve for a quantum computer). We finally prove that the regularized relative entropy of recovery is equal to the optimal type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the type I error is constrained to be no larger than a constant.

Quantum mechanics is known to provide significant improvements in information processing tasks when compared to classical models. These advantages range from computational speedups to security improvements. A key question is where these advantages come from. The toy model developed by Spekkens [R. W. Spekkens, Phys. Rev. A 75, 032110 (2007)] mimics many of the features of quantum mechanics, such as entanglement and no cloning, regarded as being important in this regard, despite being a local hidden variable theory. In this work, we study several protocols within Spekkens' toy model where we see it can also mimic the advantages and limitations shown in the quantum case. We first provide explicit proofs for the impossibility of toy bit commitment and the existence of a toy error correction protocol and consequent $k$-threshold secret sharing. Then, defining a toy computational model based on the quantum one-way computer, we prove the existence of blind and verified protocols. Importantly, these two last quantum protocols are known to achieve a better-than-classical security. Our results suggest that such quantum improvements need not arise from any Bell-type nonlocality or contextuality, but rather as a consequence of steering correlations.

Noninteracting bosons were proposed to be used for a demonstration of quantum-computing supremacy in a boson-sampling setup. A similar demonstration with fermions would require that the fermions are initially prepared in an entangled state. I suggest that pairwise entanglement of fermions would be sufficient for this purpose. Namely, it is shown that computing multiparticle scattering amplitudes for fermions entangled pairwise in groups of four single-particle states is #P-hard. In linear algebra, such amplitudes are expressed as exterior products of two-forms of rank 2. In particular, a permanent of a $N\times N$ matrix may be expressed as an exterior product of $N^2$ two forms of rank 2 in dimension $2N^2$, which establishes the #P-hardness of the latter.

Quantum walks with memory (QWM) are a type of modified quantum walks that record the walker's latest path. As we know, only two kinds of QWM have been presented up to now. It is desired to design more QWM for research, so that we can explore the potential of QWM. In this work, by presenting the one-to-one correspondence between QWM on a regular graph and quantum walks without memory (QWoM) on a line digraph of the regular graph, we construct a generic model of QWM on regular graphs. This construction gives a general scheme for building all possible standard QWM on regular graphs and makes it possible to study properties of different kinds of QWM. Here, by taking the simplest example, which is QWM with one memory on the line, we analyze some properties of QWM, such as variance, occupancy rate, and localization.

In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms addressing nonsquare matrices. Towards this kind of problems defined by $Ax=b$ where $A\in {\mathbb{R}}^{m\times n}$, we propose a quantum algorithm inspired by the classical multirow iteration method and provide an explicit quantum circuit based on the quantum comparator and quantum random access memory. The time complexity of our quantum multirow iteration algorithm is $O\left(K{log}_{2}m\right)$, with $K$ representing the number of iteration steps, which demonstrates an exponential speedup compared to the classical version.. Based on the convergence of the classical multirow iteration algorithm, we prove that our quantum algorithm converges faster than the quantum one-row iteration algorithm presented by Shao and Xiang [C. Shao and H. Xiang, Phys. Rev. A 101, 022322 (2020)]. Moreover, our algorithm places less demand on the coefficient matrix, making it suitable for solving inconsistent systems and quadratic optimization problems.