Quantum Physics (quant-ph)

Abstract: We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases, generalizing the random Pauli measurement protocol ($n = 1$). We show that entangled measurements ($n\geq 2$) enable nontrivial and potentially advantageous trade-offs in the sample complexity of learning Pauli expectation values. This is sharply illustrated by shadows based on two-qubit Bell measurements: the scaling of sample complexity with Pauli weight $k$ improves quadratically (from $\sim 3^k$ down to $\sim 3^{k/2}$) for many operators, while others become impossible to learn. Tuning the amount of entanglement in the measurement bases defines a family of protocols that interpolate between Pauli and Bell shadows, retaining some of the benefits of both. For large $n$, we show that randomized measurements in $n$-qubit GHZ bases further improve the best scaling to $\sim (3/2)^k$, albeit on an increasingly restricted set of operators. Despite their simplicity and lower hardware requirements, these protocols can match or outperform recently-introduced ``shallow shadows'' in some practically-relevant Pauli estimation tasks.

Abstract: Measurement-based quantum computation is a promising approach for realizing blind and cloud quantum computation. To obtain reliable results in this model, it is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. However, previous verification protocols for this task are too resource consuming or noise susceptible to be applied in practice. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension in the adversarial scenario, which leads to a robust and efficient protocol for verifying blind measurement-based quantum computation. Our protocol requires only local Pauli measurements and is thus easy to realize with current technologies. Nevertheless, it can achieve the optimal scaling behaviors with respect to the system size and the target precision as quantified by the infidelity and significance level, which has never been achieved before. Notably, our protocol can exponentially enhance the scaling behavior with the significance level.

Abstract: Quantum secret sharing plays an important role in quantum communications and secure multiparty computation. In this paper, we present a new measurement-device-independent quantum secret sharing protocol, which can double the space distance between the dealer and each sharer for quantum transmission compared with prior works. Furthermore, it is experimentally feasible with current technology for requiring just three-particle Greenberger-Horne-Zeilinger states and Bell state measurements.

Abstract: In quantum state tomography, particularly with pure states, unique determinedness (UD) holds significant importance. This study presents a new variational approach to examining UD, offering a robust solution to the challenges associated with the construction and validation of UD measurement schemes. We put forward an effective algorithm that minimizes a specially defined loss function, enabling the differentiation between UD and non-UD measurement schemes. This leads to the discovery of numerous optimal pure-state Pauli measurement schemes across a variety of dimensions. Additionally, we discern an alignment between uniquely determined among pure states (UDP) and uniquely determined among all states (UDA) in qubit systems when utilizing Pauli measurements, underscoring its unique characteristics. We further bridge the gap between our loss function and the stability of state recovery, bolstered by a theoretical framework. Our study not only propels the understanding of UD in quantum state tomography forward, but also delivers valuable practical insights for experimental applications, highlighting the need for a balanced approach between mathematical optimality and experimental pragmatism.

Abstract: Verifying the quality of a random number generator involves performing computationally intensive statistical tests on large data sets commonly in the range of gigabytes. Limitations on computing power can restrict an end-user's ability to perform such verification. There are also applications where the user needs to publicly demonstrate that the random bits they are using pass the statistical tests without the bits being revealed. We report the implementation of an entanglement-based protocol that allows a third party to publicly perform statistical tests without compromising the privacy of the random bits.

Abstract: Analyzing the properties of complex quantum systems is crucial for further development of quantum devices, yet this task is typically challenging and demanding with respect to required amount of measurements. A special attention to this problem appears within the context of characterizing outcomes of noisy intermediate-scale quantum devices, which produce quantum states with specific properties so that it is expected to be hard to simulate such states using classical resources. In this work, we address the problem of characterization of a boson sampling device, which uses interference of input photons to produce samples of non-trivial probability distributions that at certain condition are hard to obtain classically. For realistic experimental conditions the problem is to probe multi-photon interference with a limited number of the measurement outcomes without collisions and repetitions. By constructing networks on the measurements outcomes, we demonstrate a possibility to discriminate between regimes of indistinguishable and distinguishable bosons by quantifying the structures of the corresponding networks. Based on this we propose a machine-learning-based protocol to benchmark a boson sampler with unknown scattering matrix. Notably, the protocol works in the most challenging regimes of having a very limited number of bitstrings without collisions and repetitions. As we expect, our framework can be directly applied for characterizing boson sampling devices that are currently available in experiments.

Abstract: Noiseless linear amplifiers (NLAs) provide a powerful tool to achieve long-distance continuous-variable quantum key distribution (CV-QKD) in the presence of realistic setups with non unit reconciliation efficiency. We address a NLA-assisted CV-QKD protocol implemented via realistic physical NLAs, namely, quantum scissors (QS) and single-photon catalysis (SPC), and compare their performance with respect to the ideal NLA $g^{\hat{n}}$. We investigate also the robustness of two schemes against inefficient conditional detection, and discuss the two alternative scenarios in which the gain associated with the NLA is either fixed or optimized.

Abstract: The quantum perceptron, the variational circuit, and the Grover algorithm have been proposed as promising components for quantum machine learning. This paper presents a new quantum perceptron that combines the quantum variational circuit and the Grover algorithm. However, this does not guarantee that this quantum variational perceptron with Grover's algorithm (QVPG) will have any advantage over its quantum variational (QVP) and classical counterparts. Here, we examine the performance of QVP and QVP-G by computing their loss function and analyzing their accuracy on the classification task, then comparing these two quantum models to the classical perceptron (CP). The results show that our two quantum models are more efficient than CP, and our novel suggested model QVP-G outperforms the QVP, demonstrating that the Grover can be applied to the classification task and even makes the model more accurate, besides the unstructured search problems.

Abstract: Preparation of bosonic and general cavity quantum states usually relies on using open-loop control to reach a desired target state. In this work, a measurement-based feedback approach is used instead, exploiting the non-linearity of weak measurements alongside a coherent drive to prepare these states. The extension of previous work on Lyapunov-based control is shown to fail for this task. This prompts for a different approach, and reinforcement learning (RL) is resorted to here for this purpose. With such an approach, cavity eigenstate superpositions can be prepared with fidelities over 98$\%$ using only the measurements back-action as the non-linearity, while naturally incorporating detection of cavity photon jumps. Two different RL frameworks are analyzed: an off-policy approach recently introduced called truncated quantile critic~(TQC) and the on-policy method commonly used in quantum control, namely proximal policy optimization~(PPO). It is shown that TQC performs better at reaching higher target state fidelity preparation.

Abstract: Implementing quantum error correction (QEC) protocols is a challenging task in today's era of noisy intermediate-scale quantum devices. We present quantum circuits for a universal, noise-adapted recovery map, often referred to as the Petz map, which is known to achieve close-to-optimal fidelity for arbitrary codes and noise channels. While two of our circuit constructions draw upon algebraic techniques such as isometric extension and block encoding, the third approach breaks down the recovery map into a sequence of two-outcome POVMs. In each of the three cases we improve upon the resource requirements that currently exist in the literature. Apart from Petz recovery circuits, we also present circuits that can directly estimate the fidelity between the encoded state and the recovered state. As a concrete example of our circuit constructions, we implement Petz recovery circuits corresponding to the $4$-qubit QEC code tailored to protect against amplitude-damping noise. The efficacy of our noise-adapted recovery circuits is then demonstrated through ideal and noisy simulations on the IBM quantum processors.

Abstract: XOR oblivious transfer (XOT) is a classical cryptographic primitive which is apparently weaker than 1-out-of-2 oblivious transfer, yet still universal for secure two-party computation. In ideal XOT, Bob initially has two bits, and Alice may choose to obtain either the first bit of Bob's, or the second bit, or their exclusive-or, but does not obtain any more information, while Bob does not learn anything about her choice. In this work we present a quantum protocol which implements the functionality of XOT on classical inputs, with complete security for Alice's input, but only partial security for Bob's input. On the hybrid security front, the protocol can be easily combined with a classical XOR homomorphic encryption scheme to save quantum costs when evaluating linear functions.

Abstract: Cooling of systems to sub-kelvin temperatures is usually done using either a cold bath of particles or spontaneous photon scattering from a laser field; in either case, cooling is driven by interaction with a well-ordered, cold (i.e. low entropy) system. However, there have recently been several schemes proposed for ``cooling by heating,'' in which raising the temperature of some mode drives the cooling of the desired system faster. We discuss how to cool a trapped ion to its motional ground state using unfiltered sunlight at $5800\,\mathrm{K}$ to drive the cooling. We show how to treat the statistics of thermal light in a single-mode fiber for delivery to the ion, and show experimentally how the black-body spectrum is strongly modified by being embedded in quasi-one-dimension. Quantitative estimates for the achievable cooling rate with our measured fiber-coupled, low-dimensional sunlight show promise for demonstrating this implementation of cooling by heating.

Abstract: It has previously been established that adiabatic quantum computation, operating based on a continuous Zeno effect due to dynamical phases between eigenstates, is able to realise an optimal Grover-like quantum speedup. In other words is able to solve an unstructured search problem with the same $\sqrt{N}$ scaling as Grover's original algorithm. A natural question is whether other manifestations of the Zeno effect can also support an optimal speedup in a physically realistic model (through direct analog application rather than indirectly by supporting a universal gateset). In this paper we show that they can support such a speedup, whether due to measurement, decoherence, or even decay of the excited state into a computationally useless state. Our results also suggest a wide variety of methods to realise speedup which do not rely on Zeno behaviour. We group these algorithms into three families to facilitate a structured understanding of how speedups can be obtained: one based on phase kicks, containing adiabatic computation and continuous-time quantum walks; one based on dephasing and measurement; and finally one based on destruction of the amplitude within the excited state, for which we are not aware of any previous results. These results suggest that there may be exciting opportunities for new paradigms of analog quantum computing based on these effects.

Abstract: The interference of non-classical states of light enables quantum-enhanced applications reaching from metrology to computation. Most commonly, the polarisation or spatial location of single photons are used as addressable degrees-of-freedom for turning these applications into praxis. However, the scale-up for the processing of a large number of photons of such architectures is very resource demanding due to the rapidily increasing number of components, such as optical elements, photon sources and detectors. Here we demonstrate a resource-efficient architecture for multi-photon processing based on time-bin encoding in a single spatial mode. We employ an efficient quantum dot single-photon source, and a fast programmable time-bin interferometer, to observe the interference of up to 8 photons in 16 modes, all recorded only with one detector--thus considerably reducing the physical overhead previously needed for achieving equivalent tasks. Our results can form the basis for a future universal photonics quantum processor operating in a single spatial mode.