Quantum Physics (quant-ph)

Abstract: We investigate the limits on cooling and work extraction via Markovian thermal processes assisted by a finite dimensional memory. Here the memory is a d-dimensional quantum system with trivial Hamiltonian and initially in a maximally mixed state. For cooling a qubit system, we consider two paradigms, cooling under coherent control and cooling under incoherent control. For both paradigms, we derive the optimal ground state populations under the set of general thermal processes (TP) and the set of Markovian thermal processes (MTP), and further propose memory assisted protocols, which bridge the gap between the performances of TP and MTP. For the task of work extraction, we prove that when the target system is a qubit in the excited state, the minimum extraction error achieved by TP can be approximated by Markovian thermal processes assisted by a large enough memory. Our results can bridge the performances of TP and MTP in thermal processes including cooling and work extraction.

Abstract: Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is currently no widely agreed metric that is universally adopted. In this paper, we propose using classical and quantum Fisher information (FI) as alternative metrics to detect and measure quantum synchronization. We establish the connection between FI and quantum synchronization, demonstrating that both classical and quantum FI can be deployed as more general indicators of quantum phase synchronization, in some regimes where all other existing measures fail to provide reliable results. We show advantages in FI-based measures, especially in 2-to-1 synchronization. Furthermore, we analyze the impact of noise on the synchronization measures, revealing the robustness and susceptibility of each method in the presence of dissipation and decoherence. Our results open up new avenues for understanding and exploiting quantum synchronization.

Abstract: In usual restriction terms of the Quadratic Unconstrained Binary Optimization (QUBO) hamiltonians, a integer number of logical qubits R, called the Integer Restriction Coefficient (IRC), are forced to stay active. In this paper we gather the well-known methods of implementing these restrictions, as well as some novel methods that show to be more efficient in some frequently implemented cases. Moreover, it is mathematically allowed to ask for fractional values of $R$. For these Fractionary Restriction Coefficients (FRC) we show how they can reduce the number of qubits needed to implement the restriction hamiltonian even further. Lastly, we characterize the response of DWave's Advantage$\_$system4.1 Quantum Annealer (QA) when faced with the implementation of FRCs, and offer a summary guide of the presented methods and the situations each of them is to be used.

Abstract: Eigenstate coalescence in non-Hermitian systems is widely observed in diverse scientific domains encompassing optics and open quantum systems. Recent investigations have revealed that adiabatic encircling of exceptional points (EPs) leads to a nontrivial Berry phase in addition to an exchange of eigenstates. Based on these phenomena, we propose in this work an exhaustive classification framework for EPs in non-Hermitian physical systems. In contrast to previous classifications that only incorporate the eigenstate exchange effect, our proposed classification gives rise to finer $\mathbb{Z}_2$ classifications depending on the presence of a $\pi$ Berry phase after the encircling of the EPs. Moreover, by mapping arbitrary one-dimensional systems to the adiabatic encircling of EPs, we can classify one-dimensional non-Hermitian systems characterized by topological phase transitions involving EPs. Applying our exceptional classification to various one-dimensional models, such as the non-reciprocal Su--Schrieffer--Heeger (SSH) model, we exhibit the potential for enhancing the understanding of topological phases in non-Hermitian systems. Additionally, we address exceptional bulk-boundary correspondence and the emergence of distinct topological boundary modes in non-Hermitian systems.

Abstract: The Quantum Approximate Optimization Algorithm (QAOA) is a prospective hybrid quantum-classical algorithm, which is widely used to solve combinatorial optimization problems. One major bottleneck of QAOA lies in finding optimal parameters of the quantum circuit, which motivates one to search for heuristic parameter initialization strategies. Interpolation strategy (INTERP) is a parameter initialization strategy in QAOA for Maxcut. INTERP produces an initial guess of the parameters for level $i+1$ by executing linear interpolation to the optimized parameters at level $i$, where $i=1,2,...,p$ and $p$ is the circuit depth. INTERP greatly reduces the time to find quasi-optimal solutions compared with random initialization. Also for Maxcut, we first propose INTERP+ strategy using multi-interpolation. Compared with INTERP, INTERP+ cuts down at least half the number of rounds of optimization. The simulation results demonstrate that INTERP+ saves about 2/3 of running time compared with INTERP and can obtain the same quasi-optimal solutions as INTERP. In addition, we present Multi-INTERP+ by introducing multi-start and selection. Numerous simulation results demonstrate that Multi-INTERP+ can not only get the same quasi-optimal solutions as INTERP but also get higher average performance than INTERP and INTERP+.

Abstract: As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new Heisenberg-limited QPE algorithm for early quantum computers based on compressed sensing. More specifically, given many copies of a proper initial state and queries to some unitary operators, our algorithm is able to recover the frequency with a total runtime $\mathcal{O}(\epsilon^{-1}\text{poly}\log(\epsilon^{-1}))$, where $\epsilon$ is the accuracy. Moreover, the maximal runtime satisfies $T_{\max}\epsilon \ll \pi$, which is comparable to the state of art algorithms, and our algorithm is also robust against certain amount of noise from sampling. We also consider the more general quantum eigenvalue estimation problem (QEEP) and show numerically that the off-grid compressed sensing can be a strong candidate for solving the QEEP.

Abstract: Interference in photons emitted from multiple atoms has been studied extensively. We show that a single atom can induce interference in its emitted light when tunnelling in a double-well potential coupled to an optical cavity. The phase in the cavity field interference can be modulated by the double-well spacing. By controlling the coherent tunnelling, blockade of single-photon excitations is found in the destructive interference regime, where super-Poissonian bunched light is generated. Furthermore, we show that the atomic flux of the coherent tunnelling motion generates chiral cavity fields. The direction of the chirality oscillates for many cycles before the decoherence of the atomic motion and the decay of the cavity photons. Our work opens new ways for manipulating photons with controllable quantum states of atoms for quantum information applications.

Abstract: Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and sampling problems. Here, we present a classical pre-processing routine for variational Hamiltonian simulation that circumvents the need of a quantum optimization by expanding rigorous error bounds in a perturbative regime for suitable time steps. The resulting cost function is efficiently computable on a classical computer. We show that there always exists potential for optimization with respect to a Trotter sequence of the same order and that the cost value has the same scaling as for Trotter in simulation time and system size. Unlike previous work on classical pre-processing, the method is applicable to any Hamiltonian system independent of locality and interaction lengths. Via numerical experiments for spin-lattice models, we find that our approach significantly improves digital quantum simulations capabilities with respect to Trotter sequences for the same resources. For short times, we find accuracy improvements of more than three orders of magnitude for our method as compared to Trotter sequences of the same gate number. Moreover, for a given gate number and accuracy target, we find that the pre-optimization we introduce enables simulation times that are consistently more than 10 times longer for a target accuracy of 0.1%.

Abstract: One-way quantum repeaters where loss and operational errors are counteracted by quantum error correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimal resource overhead by interspersing repeater nodes that each specializes in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.

Abstract: Self-testing is a powerful method for certifying quantum systems. Initially proposed in the device-independent (DI) setting, self-testing has since been relaxed to the semi-device-independent (semi-DI) setting. In this study, we focus on the self-testing of a specific type of non-projective qubit measurements belonging to a one-parameter family, using the semi-DI prepare-and-measure (PM) scenario. Remarkably, we identify the simplest PM scenario discovered so far, involving only four preparations and four measurements, for self-testing the fourth measurement. This particular measurement is a four-outcome non-projective positive operator-valued measure (POVM) and falls in the class of semisymmetric informationally complete (semi-SIC) POVMs introduced by Geng et al. [Phys. Rev. Lett. 126, 100401 (2021)]. To achieve this, we develop analytical techniques for semi-DI self-testing in the PM scenario. Our results shall pave the way towards self-testing any extremal qubit POVM within a potentially minimal PM scenario.

Abstract: Image processing is a fascinating field for exploring quantum algorithms. However, achieving quantum speedups turns out to be a significant challenge. In this work, we focus on image filtering to identify a class of images that can achieve a substantial speedup. We show that for images that can be efficiently encoded as quantum states, a filtering algorithm can be constructed with a polynomial complexity in terms of the qubit number. Our algorithm combines the quantum Fourier transform with the amplitude amplification technique. To demonstrate the advantages of our approach, we apply it to three typical filtering problems. Furthermore, we highlight the importance of efficient encoding by illustrating that for images that cannot be efficiently encoded, the quantum advantage will diminish. Our work contributes to the understanding of the potential benefits of quantum image filtering and provides insights into the types of images that can achieve a substantial speedup.

Abstract: We report on the experimental demonstration of a source that generates spectrally multimode squeezed states of light over the infrared C-Band. This is achieved using a single-pass Spontaneous Parametric Down Conversion (SPDC) process in a periodically-poled KTP waveguide that is pumped with the second harmonic of a femtosecond laser. Our measurements show significant squeezing in more than 21 frequency modes, with a maximum squeezing value over 2.5 dB. Moreover, we demonstrate multiparty entanglement across 8 individual frequency bands by measuring the covariance matrix of their quadratures. Finally, we use reconfigurable mode-selective homodyne detection to mold the output into cluster states of various shapes. This result paves the way for the implementation of continuous variable quantum information protocols at telecommunication wavelengths, with applications in multiparty, entanglement-based quantum communication and computation.

Abstract: Quantum control techniques are employed to perform adiabatic quantum computing in the presence of noise. First, we analyze the adiabatic entanglement protocol (AEP) for two qubits. In this case, we found that this protocol is very robust against noise. The reason behind this fact is related to the chosen Hamiltonians, where the ground state of the initial Hamiltonian is not affected by the noise. The optimal control solution, in this case, is to leave the system in its ground state and apply a fast pulse to entangle the qubits at the end of the time evolution. Secondly, we probe a system composed of three qubits, where the goal is to teleport the first qubit to the third qubit. In this case, the ground state of the system does not share the same robustness against noise as in the case of AEP. To improve the robustness against noise, we propose the inclusion of a local control field that can drive the system to an intermediate state, which is more robust against noise in comparison to other states. The target state is also achieved by a fast pulse at the final time. We found that this approach provides a significant gain in the fidelity and can improve the adiabatic quantum computing in the so-called Noisy Intermediate-Scale Quantum (NISQ) devices in a near future.