Probing Quantum Telecloning on Superconducting Quantum Processors

A dynamical quantum phase transition can occur during time evolution of sudden quenched quantum systems across a phase transition. It corresponds to the nonanalytic behavior at a critical time of the rate function of the quantum state return amplitude, analogous to nonanalyticity of the free energy density at the critical temperature in macroscopic systems. A variety of many-body systems can be represented in momentum space as a spin-1/2 state evolving on the Bloch sphere, where each momentum mode is decoupled and thus can be simulated independently by a single qubit. Here, we report the observation of a dynamical quantum phase transition in a superconducting qubit simulation of the quantum quench dynamics of many-body systems. We take the Ising model with a transverse field as an example for demonstration. In our experiment, the spin state, which is initially polarized longitudinally, evolves based on a Hamiltonian with adjustable parameters depending on the momentum and strength of the transverse magnetic field. The time evolving quantum state is read out by state tomography. Evidence of dynamical quantum phase transitions, such as paths of time evolution states on the Bloch sphere, non-analytic behavior of the dynamical free energy and the emergence of Skyrmion lattice in momentum-time space, is observed. The experimental data agrees well with theoretical and numerical calculations. The experiment demonstrates for the first time explicitly the topological invariant, both topologically trivial and non-trivial, for dynamical quantum phase transitions. Our results show that the quantum phase transitions of this class of many-body systems can be simulated successfully with a single qubit by varying certain control parameters over the corresponding momentum range.

We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single qubit and two-qubit quantum gates can achieve high fidelities around or above 99.9% in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.98% for single ensemble qubit gate and 99.94% for two-qubit gate even when the Rabi frequency of the gate laser acquires 10% fluctuations. We also find that the optimized scheme can also reduce errors caused by higher-order perturbation terms in deriving the Hamiltonian of the ensemble atoms. To address the experimental issue of decoherence error between the ground state and Rydberg levels in Rydberg ensemble, we introduce a dispersive coupling regime between Rydberg and ground levels, based on which the Rydberg state is adiabatically discarded. The numerical simulation demonstrate that the quantum gate is enhanced. By combining strong Rydberg atom interactions, nonadiabatic geometric quantum computation, dynamical invariant and optimal control theory together, our scheme shows a new route to construct fast and robust quantum gates with mesoscopic atomic ensembles. Our study contributes to the ongoing effort in developing quantum information processing with Rydberg atoms trapped in optical lattices or tweezer arrays.

The Controlled-NOT (CNOT) quantum gate associated with single qubit gates is universal for building all quantum circuits. Although CNOTs based on trapped ions and superconducting qubits have become experimentally feasible, the deterministically functioning quantum CNOT gate with photonic qubits will lead to practical realization of quantum computers in a deterministic manner, and will therefore provide an exponential increase in processing power with lowest decoherence time. Based on a previously proposed CNOT model utilizing a quantum cloner (with a fidelity of 78 %), we present in this work our design of the Compact CNOT gate providing a fidelity of 90.31 %, and give physical realization constraints for building CNOT based decomposition of the Toffoli gate and more generalized photonic CnNOT gates. The photonic qubits are encoded by circularly polarized single photons and the design of the gate is based on copying the polarization degree of freedom by quantum cloners. Our model is based on spin of electron in a quantum dot embedded in a double sided optical microcavity which behaves like a beam splitter. Circularly polarizing beam splitters, beam splitters, delay lines, photonic circulators, single qubit operations and other photonic devices are used for the design and decomposition. We show that the fidelity of the decomposed CnNOT gates is highly dependent on the errors of the non-perfect photonic devices used and more specifically to the theoretical optimal limit of 5/6 of the quantum cloners required for each CNOT in the decomposition.

Multi-photon entangled states from two-crystal geometry parametric down-conversion and their application in quantum teleportation

We propose an optimal $1\ensuremath{\rightarrow}2$ quantum cloning method based on the maximin principle by making full use of a priori information of amplitude and phase about the general cloned qubit input set, which is a simply connected region enclosed by a ``longitude-latitude grid'' on the Bloch sphere. Theoretically, the fidelity of the optimal quantum cloning machine derived from this method is the largest in terms of the maximin principle compared with that of any other machine. The problem solving is an optimization process that involves six unknown complex variables, six vectors in an uncertain-dimensional complex vector space, and four equality constraints. Moreover, by restricting the structure of the quantum cloning machine, the optimization problem is simplified as a three-real-parameter suboptimization problem with only one equality constraint. We obtain the explicit formula for a suboptimal quantum cloning machine. Additionally, the fidelity of our suboptimal quantum cloning machine is higher than or at least equal to that of universal quantum cloning machines and phase-covariant quantum cloning machines. It is also underlined that the suboptimal cloning machine outperforms the ``belt quantum cloning machine'' for some cases.

In recent years, quantum technology has been rapidly developed. As security analyses for symmetric ciphers continue to emerge, many require an evaluation of the resources needed for the quantum circuit implementation of the encryption algorithm. In this regard, we propose the quantum circuit decision problem, which requires us to determine whether there exists a quantum circuit for a given permutation f using M ancilla qubits and no more than K quantum gates within the circuit depth D. Firstly, we investigate heuristic algorithms and classical SAT-based models in previous works, revealing their limitations in solving the problem. Hence, we innovatively propose an improved SAT-based model incorporating three metrics of quantum circuits. The model enables us to find the optimal quantum circuit of an arbitrary 3 or 4-bit S-box under a given optimization goal based on SAT solvers, which has proved the optimality of circuits constructed by the tool, LIGHTER-R. Then, by combining different criteria in the model, we find more compact quantum circuit implementations of S-boxes such as RECTANGLE and GIFT. For GIFT S-box, our model provides the optimal quantum circuit that only requires 8 gates with a depth of 31. Furthermore, our model can be generalized to linear layers and improve the previous SAT-based model proposed by Huang et al. in ASIACRYPT 2022 by adding the criteria on the number of qubits and the circuit depth.

A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single-qubit quantum channels ${{T}_{t}}$ specified by a generator $\mathcal{L}$. This algorithm requires only single-qubit and controlled-not gates and approximates the channel ${T}_{t}={e}^{t\mathcal{L}}$ up to the chosen accuracy $\ensuremath{\epsilon}$, with a slightly superlinear cost ${O((\ensuremath{\parallel}\mathcal{L}\ensuremath{\parallel}}_{(1\ensuremath{\rightarrow}1)}t{)}^{1+1/2k}/{\ensuremath{\epsilon}}^{1/2k})$ for any integer $k$. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilized which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a nonunitary single-qubit quantum channel.

The travelling salesman problem (TSP) is a popular NP-hard combinatorial optimization problem that requires finding the optimal way for a salesman to travel through different cities once and return to the initial city. The existing methods of solving TSPs on quantum systems are either gate-based or binary variable-based encoding. Both approaches are resource-expensive in terms of the number of qubits, while performing worse compared to existing classical algorithms, even for small-sized problems.
A novel encoding scheme is needed to map the TSP problem onto a quantum system, which is addressed in this work.
We introduce a distinct geometric approach to encode the TSP on a single qubit and present a quantum-inspired algorithm to solve the problem by invoking the principle of \textit{quantum superposition}.
The cities are represented as quantum states on the Bloch sphere, while the preparation of superposition states allows us to traverse multiple paths at once. The underlying framework of our algorithm is a quantum-inspired version of the classical Brachistochrone approach.
Optimal control methods are employed to create a selective superposition of the quantum states to find the shortest route of a given TSP.
The numerical simulations solve a sample of four to nine cities for which exact solutions are obtained. The algorithm can be implemented on any quantum platform capable of efficiently rotating a qubit and allowing state tomography measurements. For the TSP problem sizes considered in this work, our algorithm is more resource-efficient and accurate than existing quantum algorithms, with the potential for scalability.

Optimal control of a driven single dissipative qubit is formulated as an inverse problem. We show that direct inversion is possible which allows an analytic construction of optimal control fields. Exact inversion is shown to be possible for dissipative qubits which can be described by a Lindblad equation. It is shown that optimal solutions are not unique. For a qubit with weak coupling to phonons we choose, among the set of exact solutions for the dissipationless qubit, one which minimizes the dissipative contribution in the kinetic equations. Examples are given for state trapping and $Z$-gate operation. Using analytic expressions for optimal control fields, favorable domains for dynamic stabilization in the Bloch sphere are identified. In the case of approximate inversion, the identified approximate solution may be used as a starting point for further optimization following standard methods.

One of the simplest and least resource-intensive methods to suppress decoherence for qubit operations, namely, dynamical decoupling (DD), is investigated for a broad range of realistic noise sources with time-retarded feedback. By way of example, the Carr-Purcell-Meiboom-Gill sequence is analyzed in a numerically rigorous manner accounting also for correlations between qubits and environments. Since experimentally noise sources are characterized through spectral densities, we adopt the spin-boson model as a suitable framework to describe the qubit dynamics under DD for a given spectral density J(ω)∝ωs. Motivated by the situation for superconducting qubits, the spectral exponent s is varied from s=1 (Ohmic bath) to a substantially small value 0<s≪1 (deep sub-Ohmic bath), in order to investigate the impact of time-nonlocal back action on DD performances for enhanced coherence times. As reference to the DD schemes, dynamics of a single qubit subject to Ramsey sequences without any pules and Hahn echo sequences are also investigated. Published by the American Physical Society 2025

We present what we believe to be a novel proposal for the implementation of temporal-modes quantum gates based on the third-order nonlinear process of difference frequency generation in an integrated photonic circuit, which allows switching from one Pauli gate to another by tuning the phase difference between the two pump pulses (in case of the σ x and σ y Pauli gates) and between the two states comprising the basis of single temporal-modes qubits (in the case of the σ z Pauli gate). We demonstrate that our proposal enables the preparation of any single temporal-mode qubit and rotations on the Bloch sphere by changing externally controllable parameters. We also analyze the effects of fabrication errors on the predicted quantum gate fidelity, finding that, even if some waveguide parameter deviates from the design, slight tuning of pump wavelengths can lead to recovering high-fidelity values.

The complexity of timing optimization of high-performance circuits has been increasing rapidly in proportion to the shrinking CMOS device size and rising magnitude of process variations. Addressing these significant challenges, this paper presents a timing optimization algorithm for CMOS dynamic logic and a Path Oriented IN Time (POINT) optimization flow for mixed-static-dynamic CMOS logic, where a design is partitioned into static and dynamic circuits. Implemented on a 64-b adder and International Symposium on Circuits and Systems (ISCAS) benchmark circuits, the POINT optimization algorithm has shown an average improvement in delay by 38% and delay uncertainty from process variations by 35% in comparison with a state-of-the-art commercial optimization tool.

Dynamical decoupling and Hamiltonian engineering are well-established techniques that have been used to control qubit systems. However, designing the corresponding methods for qudit systems has been challenging due to the lack of a Bloch sphere representation, more complex interactions, and additional control constraints. By identifying several general structures associated with such problems, we develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. Our formalism significantly simplifies qudit pulse-sequence design while naturally incorporating robustness conditions necessary for experimental practicality. We experimentally demonstrate these techniques in a strongly interacting, disordered ensemble of spin-1 nitrogen-vacancy centers, achieving more than an order-of-magnitude improvement in coherence time over existing pulse sequences. We further describe how our techniques enable the engineering of exotic many-body phenomena such as quantum many-body scars, and open up new opportunities for quantum metrology with enhanced sensitivities. These results enable wide-reaching new applications for dynamical decoupling and Hamiltonian engineering in many-body physics and quantum metrology. Published by the American Physical Society 2024

In this work, we propose the generation of a hybrid entangled resource (HER) and its further application in a quantum teleportation scheme from an experimentally feasible point of view. The source for HER preparation is based on the four-wave mixing process in a photonic crystal fiber, from which one party of its output bipartite state is used to herald a single photon or a single photon added coherent state. From the heralded state and linear optics, the HER is created. In the proposed teleportation protocol, Bob uses the HER to teleport qubits with different spectral properties. Bob makes a Bell measurement in the single photon basis and characterizes the scheme with its average quantum teleportation fidelity. Fidelities close to one are expected for qubits in a wide spectral range. The work also includes a discussion about the fidelity dependence on the geometrical properties of the medium through which the HER is generated. An important remark is that no spectral filtering is employed in the heralding process, which emphasizes the feasibility of this scheme without compromising photon flux.

Physical entities are not truly teleported in so-called quantum teleportation, only their states are. Similarly, physical entities are not truly cloned in so-called quantum cloning, only their states are. The celebrated no-cloning theorem tells us that a universal cloning machine, able to perfectly clone arbitrary states, cannot be built. However, this only applies to discernible quantum entities. For the indiscernible ones, which are already perfect clones of one another, the additional cloning of their state is in fact a natural process, which happens in a spontaneous way, as soon as they are allowed to interact.