Quantum Physics (quant-ph)

Abstract: Quantum computing presents a promising approach for machine learning with its capability for extremely parallel computation in high-dimension through superposition and entanglement. Despite its potential, existing quantum learning algorithms, such as Variational Quantum Circuits(VQCs), face challenges in handling more complex datasets, particularly those that are not linearly separable. What's more, it encounters the deployability issue, making the learning models suffer a drastic accuracy drop after deploying them to the actual quantum devices. To overcome these limitations, this paper proposes a novel spatial-temporal design, namely ST-VQC, to integrate non-linearity in quantum learning and improve the robustness of the learning model to noise. Specifically, ST-VQC can extract spatial features via a novel block-based encoding quantum sub-circuit coupled with a layer-wise computation quantum sub-circuit to enable temporal-wise deep learning. Additionally, a SWAP-Free physical circuit design is devised to improve robustness. These designs bring a number of hyperparameters. After a systematic analysis of the design space for each design component, an automated optimization framework is proposed to generate the ST-VQC quantum circuit. The proposed ST-VQC has been evaluated on two IBM quantum processors, ibm_cairo with 27 qubits and ibmq_lima with 7 qubits to assess its effectiveness. The results of the evaluation on the standard dataset for binary classification show that ST-VQC can achieve over 30% accuracy improvement compared with existing VQCs on actual quantum computers. Moreover, on a non-linear synthetic dataset, the ST-VQC outperforms a linear classifier by 27.9%, while the linear classifier using classical computing outperforms the existing VQC by 15.58%.

Abstract: We propose a scheme for calibrating the D-Wave quantum annealer's internal parameters to obtain well-approximated samples to train a restricted Boltzmann machine (RBM). Empirically, samples from the quantum annealer obey the Boltzmann distribution, making them suitable for RBM training. However, it is hard to obtain appropriate samples without compensation. Existing research often estimates internal parameters, such as the inverse temperature, for compensation. Our scheme utilizes samples for RBM training to estimate the internal parameters, enabling it to train a model simultaneously. Furthermore, we consider additional parameters beyond inverse temperature and demonstrate that they contribute to improving sample quality. We evaluate the performance of our scheme by comparing the Kullback-Leibler divergence of the obtained samples with classical Gibbs sampling. Our results indicate that our proposed scheme demonstrates performance on par with Gibbs sampling. In addition, the training results with our estimation scheme are better than those of the Contrastive Divergence algorithm, known as a standard training algorithm for RBM.

Abstract: We report an algorithm, based on quantum optics formulation, where a coherent state is used as the elementary quantum resource for the image representation. We provide an architecture with constituent optical elements in linear order with respect to the image resolution. The obtained phase-distributed multimode coherent state is fed into an image retrieval scheme and we identify the appropriate laser intensity parameter for similarity measurement. The use of the principle of quantum superposition in the similarity measurement protocol enables us to encode multiple input images. We demonstrate the viability of the protocol through an objective quality assessment of images by adding consecutive layers of noises. The results are in good agreement with the expected outcome. The image distortion-sensitivity analysis of the metric establishes the further merit of the model. Our quantum algorithm has wider applicability also in supervised machine learning tasks.

Abstract: Quantum computers are capable of calculating the energy gap of two electronic states by using the quantum phase difference estimation (QPDE) algorithm. The Bayesian inference based implementations for the QPDE have been reported so far, but this approach is not projective, and the quality of the calculated energy gap depends on the input wave functions being used. Here, we report the inverse quantum Fourier transformation based QPDE with $N_a$ of ancillary qubits, which allows us to compute the difference of eigenenergies based on the single-shot projective measurement. As a proof-of-concept demonstrations, we report numerical experiments for the singlet--triplet energy gap of hydrogen molecule and the vertical excitation energies of halogen-substituted methylenes (CHF, CHCl, CF$_2$, CFCl and CCl$_2$) and formaldehyde (HCHO).

Abstract: We theoretically investigate a scheme to entangle two squeezed magnon modes in a double cavitymagnon system, where both cavities are driven by a two-mode squeezed vacuum microwave field. Each cavity contains an optical parametric amplifier as well as a macroscopic yttrium iron garnet (YIG) sphere placed near the maximum bias magnetic fields such that this leads to the excitation of the relevant magnon mode and its coupling with the corresponding cavity mode. We have obtained optimal parameter regimes for achieving the strong magnon-magnon entanglement and also studied the effectiveness of this scheme towards the mismatch of both the cavity-magnon couplings and decay parameters. We have also explored the entanglement transfer efficiency including Gaussian quantum steering in our proposed system

Abstract: Motivated by the very recent experimental breakthroughs, we theoretically explore optomechanical cooling and squeezing in a non-Hermitian ternary coupled system composed of an optical cavity and two mechanical resonators. A closed-contour interaction is formed embodied by a global phase that constitutes a synthetic $U(1)$ gauge field. We illustrate over a realistic parameter set the cooling of either mechanical resonator by the synthetic field. A stark disparity between the optical heating versus mechanical cooling factors is observed which is rooted in the high damping constant ratio of the optical and mechanical oscillators. Additionally, an amplitude modulation is imposed over the cavity-pumping laser to attain mechanical squeezing. A set of complementary numerical approaches are employed: the time-integrator method for the instantaneous behavior, and the Floquet technique for the steady-state or modulated characteristics. The latter is further supported by the James' effective Hamiltonian method which explicitly reveals the role of upper-sideband modulation in squeezing. We identify the symmetry, namely, the invariance of the system under simultaneous swapping of the two mechanical resonators together with closed-loop phase reversal, which enables targeted cooling or squeezing of either mechanical resonator. We also elaborate on the intricate role of proximity to the exceptional points on the enhancement of cooling and squeezing.

Abstract: The nonadiabatic holonomic quantum computation is robust against the built-in noise and decoherence. In this work, we theoretically propose a scheme to realize the CNOT nonadiabatic holonomic quantum gate in a surface electron system, which is a promising two-dimensional platform for quantum computation. The holonomic gate is realized by a three-level structure that combines the Rydberg levels and spin states with the assistance of an external inhomogeneous magnetic field. When the integral of the Rabi frequency of the time-dependent driving fields with respect to time equals $\pi$, the nonadiabatic holonomic evolution can be realized. Thus, the controlled-NOT gate encoded on the Rydberg states and spin states is put into practice via state-selective driving fields. The fidelity of the output state exceeds 0.99 with experimentally achievable parameters.

Abstract: Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a lower entropy limit $S \geq k \ln 2$. Conceptual tensions with the third law of thermodynamics and the additivity of entropy are resolved. Black hole entropy is also surveyed. Further claims for vanishing entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time, also implies $S \geq k \ln 2$. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of a quantum of entropy enable one to speak about a principle of the entropy limit that is valid across nature.

Abstract: The recycling of quantum correlations has attracted widespread attention both theoretically and experimentally. Previous works show that bilateral sharing of nonlocality is impossible under mild measurement strategy and 2-qubit entangled state can be used to witness entanglement arbitrary many times by sequential and independent pairs of observers. However, less is known about the bilateral sharing of EPR steering yet. Here, we aim at investigating the EPR steering sharing between sequential pairs of observers. We show that an unbounded number of sequential Alice-Bob pairs can share the EPR steering as long as the initially shared state is an entangled two-qubit pure state. The claim is also true for particular class of mixed entangled states.

Abstract: The Cross-resonance (CR) gate architecture that exploits fixed-frequency transmon qubits and fixed couplings is a leading candidate for quantum computing. Nonetheless, without the tunability of qubit parameters such as qubit frequencies and couplings, gate operations can be limited by the presence of quantum crosstalk arising from the always-on couplings. When increasing system sizes, this can become even more serious considering frequency collisions caused by fabrication uncertainties. Here, we introduce a CR gate-based transmon architecture with passive mitigation of both quantum crosstalk and frequency collisions. Assuming typical parameters, we show that ZZ crosstalk can be suppressed while maintaining XY couplings to support fast, high-fidelity CR gates. The architecture also allows one to go beyond the existing literature by extending the operating regions in which fast, high-fidelity CR gates are possible, thus alleviating the frequency-collision issue. To examine the practicality, we analyze the CR gate performance in multiqubit lattices and provide an intuitive model for identifying and mitigating the dominant source of error. For the state-of-the-art precision in setting frequencies, we further investigate its impact on the gates. We find that ZZ crosstalk and frequency collisions can be largely mitigated for neighboring qubits, while interactions beyond near neighbor qubits can introduce new frequency collisions. As the strength is typically at the sub-MHz level, adding weak off-resonant drives to selectively shift qubits can mitigate the collisions. This work could be useful for suppressing quantum crosstalk and improving gate fidelities in large-scale quantum processors based on fixed-frequency qubits and fixed couplings.

Abstract: Spins in silicon that are accessible via a telecom-compatible optical transition are a versatile platform for quantum information processing that can leverage the well-established silicon nanofabrication industry. Key to these applications are long coherence times on the optical and spin transitions to provide a robust system for interfacing photonic and spin qubits. Here, we report telecom-compatible Er3+ sites with long optical and electron spin coherence times, measured within a nuclear spin-free silicon crystal (<0.01% 29Si) using optical detection. We investigate two sites and find 0.1 GHz optical inhomogeneous linewidths and homogeneous linewidths below 70 kHz for both sites. We measure the electron spin coherence time of both sites using optically detected magnetic resonance and observe Hahn echo decay constants of 0.8 ms and 1.2 ms at around 11 mT. These optical and spin properties of Er3+:Si are an important milestone towards using optically accessible spins in silicon for a broad range of quantum information processing applications.

Abstract: We introduce the qudit ZH-calculus and show how to generalise the phase-free qubit rules to qudits. We prove that for prime dimensions $d$, the phase-free qudit ZH-calculus is universal for matrices over the ring $\mathbb{Z}[e^{2\pi i/d}]$. For qubits, there is a strong connection between phase-free ZH-diagrams and Toffoli+Hadamard circuits, a computationally universal fragment of quantum circuits. We generalise this connection to qudits, by finding that the two-qudit $|0\rangle$-controlled $X$ gate can be used to construct all classical reversible qudit logic circuits in any odd qudit dimension, which for qubits requires the three-qubit Toffoli gate. We prove that our construction is asymptotically optimal up to a logarithmic term. Twenty years after the celebrated result by Shi proving universality of Toffoli+Hadamard for qubits, we prove that circuits of $|0\rangle$-controlled $X$ and Hadamard gates are approximately universal for qudit quantum computing for any odd prime $d$, and moreover that phase-free ZH-diagrams correspond precisely to such circuits allowing postselections.

Abstract: Quantum computers have the potential to change the way we solve computational problems. Due to the noisy nature of qubits, the need arises to correct physical errors occurring during computation. The surface code is a promising candidate for such error correction that shows high threshold and which can store a logical quantum state on hardware with square-grid connectivity, a type of device that already exists. However, for logical quantum computation, the measurement of some irregular, non-local stabilisers is required, and it is not currently known how to do this without modifying the connectivity of the hardware. Here, we present a method to achieve this, closing this gap on the path to fault-tolerant quantum computation. We introduce a method of tangled syndrome extraction circuits, which enables measurement of observables between distant qubits. As an application of our tangling technique, we show how to measure the aforementioned irregular non-local stabilisers, without physically modifying the hardware itself. We present a concrete scheme that enables general lattice surgery with the planar code. Therefore, tangling enables fault-tolerant logical quantum computation using the surface code on square-grid connectivity architectures.

Abstract: The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ) providing approximate solutions for combinatorial optimisation problems. The QAOA utilizes a quantum-classical loop, consisting of a quantum ansatz and a classical optimizer, to minimize some cost function computed on the quantum device. This paper presents an investigation into the impact of realistic noise on the classical optimizer and the determination of optimal circuit depth for the Quantum Approximate Optimization Algorithm (QAOA) in the presence of noise. We find that, while there is no significant difference in the performance of classical optimizers in a state vector simulation, the Adam and AMSGrad optimizers perform best in the presence of shot noise. Under the conditions of real noise, the SPSA optimizer, along with ADAM and AMSGrad, emerge as the top performers. The study also reveals that the quality of solutions to some 5 qubit minimum vertex cover problems increases for up to around six layers in the QAOA circuit, after which it begins to decline. This analysis shows that increasing the number of layers in the QAOA in an attempt to increase accuracy may not work well in a noisy device.

Abstract: We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass. We observe that entanglement plays an important role in the emergence of replica symmetry breaking in a fully connected, frustrated spin network of up to fifteen spin-1/2 particles. A glassy energy landscape emerges as the system is pumped through a Hepp-Lieb-Dicke superradiant transition. We find that the quantum dynamics, whose individual trajectories involve entangled states, reach steady-state spin configurations of lower energy than that of semiclassical trajectories. Cavity emission allows monitoring of the continuous stochastic evolution of spin configurations, while backaction from this projects entangled states into states of broken Ising and replica symmetry. Each many-body quantum trajectory simulation of the same spin network constitutes a replica. The emergence of spin glass order manifests itself through the simultaneous absence of magnetization and the presence of nontrivial spin overlap density distributions among replicas. Moreover, these overlaps reveal incipient ultrametric order, in line with the Parisi RSB solution ansatz for the Sherrington-Kirkpatrick model. A nonthermal Parisi order parameter distribution, however, highlights the driven-dissipative nature of this quantum optical spin glass. This practicable system could serve as a testbed for exploring how quantum effects enrich the physics of spin glasses.