Quantum Physics (quant-ph)

Abstract: We introduce a method to optimize the error behavior of quantum amplitude estimation by optimizing the initial state of the quantum phase estimation circuit. Such optimized quantum amplitude estimation (OQAE) algorithm can achieve a standard deviation (STD) $\sim 2.565/L$, which overwhelms existing algorithm with an STD about $>4/L$, where $L$ is the number of oracle calls.

Abstract: Quantum computing holds tremendous potential for various applications, but its security remains a crucial concern. Quantum circuits need high-quality compilers to optimize the depth and gate count to boost the success probability on current noisy quantum computers. There is a rise of efficient but unreliable/untrusted compilers; however, they present a risk of tampering such as Trojan insertion. We propose TrojanNet, a novel approach to enhance the security of quantum circuits by detecting and classifying Trojan-inserted circuits. In particular, we focus on the Quantum Approximate Optimization Algorithm (QAOA) circuit that is popular in solving a wide range of optimization problems. We investigate the impact of Trojan insertion on QAOA circuits and develop a Convolutional Neural Network (CNN) model, referred to as TrojanNet, to identify their presence accurately. Using the Qiskit framework, we generate 12 diverse datasets by introducing variations in Trojan gate types, the number of gates, insertion locations, and compiler backends. These datasets consist of both original Trojan-free QAOA circuits and their corresponding Trojan-inserted counterparts. The generated datasets are then utilized for training and evaluating the TrojanNet model. Experimental results showcase an average accuracy of 98.80% and an average F1-score of 98.53% in effectively detecting and classifying Trojan-inserted QAOA circuits. Finally, we conduct a performance comparison between TrojanNet and existing machine learning-based Trojan detection methods specifically designed for conventional netlists.

Abstract: Neural network quantum state (NNQS) has emerged as a promising candidate for quantum many-body problems, but its practical applications are often hindered by the high cost of sampling and local energy calculation. We develop a high-performance NNQS method for \textit{ab initio} electronic structure calculations. The major innovations include: (1) A transformer based architecture as the quantum wave function ansatz; (2) A data-centric parallelization scheme for the variational Monte Carlo (VMC) algorithm which preserves data locality and well adapts for different computing architectures; (3) A parallel batch sampling strategy which reduces the sampling cost and achieves good load balance; (4) A parallel local energy evaluation scheme which is both memory and computationally efficient; (5) Study of real chemical systems demonstrates both the superior accuracy of our method compared to state-of-the-art and the strong and weak scalability for large molecular systems with up to $120$ spin orbitals.

Abstract: In a recent paper, Robert Griffiths [Phys. Rev. A 107, 062219 (2023)] analyzed a protocol for transmission of information between two parties introduced by Salih et al. [Phys. Rev. Lett. 110, 170502 (2013)]. There is a considerable controversy about the counterfactuality of this protocol, and Griffiths suggested to resolve it by introducing a new measure of channel usage, which he called "Cost". I argue that this measure is not appropriate because the original interaction-free measurement protocol which triggered the definition of the concept of counterfactuality is not counterfactual according to this measure.

Abstract: We analyze the anisotropic Dicke model in the presence of a periodic drive and under a quasiperiodic drive. The study of drive-induced phenomena in this experimentally accesible model is important since although it is simpler than full-fledged many-body quantum systems, it is still rich enough to exhibit many interesting features. We show that under a quasiperiodic Fibonacci (Thue-Morse) drive, the system features a prethermal plateau that increases as an exponential (stretched exponential) with the driving frequency before heating to an infinite-temperature state. In contrast, when the model is periodically driven, the dynamics reaches a plateau that is not followed by heating. In either case, the plateau value depends on the energy of the initial state and on the parameters of the undriven Hamiltonian. Surprisingly, this value does not always approach the infinite-temperature state monotonically as the frequency of the periodic drive decreases. We also show how the drive modifies the quantum critical point and discuss open questions associated with the analysis of level statistics at intermediate frequencies.

Abstract: Quantum computing offers potential solutions for finding ground states in condensed-matter physics and chemistry. However, achieving effective ground state preparation is also computationally hard for arbitrary Hamiltonians. It is necessary to propose certain assumptions to make this problem efficiently solvable, including preparing a trial state of a non-trivial overlap with the genuine ground state. Here, we propose a classical-assisted quantum ground state preparation method for quantum many-body systems, combining Tensor Network States (TNS) and Monte Carlo (MC) sampling as a heuristic method to prepare a trial state with a non-trivial overlap with the genuine ground state. We extract a sparse trial state by sampling from TNS, which can be efficiently prepared by a quantum algorithm on early fault-tolerant quantum computers. Our method demonstrates a polynomial improvement in scaling of overlap between the trial state and genuine ground state compared to random trial states, as evidenced by numerical tests on the spin-$1/2$ $J_1$-$J_2$ Heisenberg model. Furthermore, our method is a novel approach to hybridize a classical numerical method and a quantum algorithm and brings inspiration to ground state preparation in other fields.

Abstract: We consider quantum variants of Parrondo games on low-dimensional Hilbert spaces. The two games which form the Parrondo game are implemented as quantum walks on a small cycle of length $M$. The dimension of the Hilbert space is $2M$. We investigate a random sequence of these two games which is realized by a quantum coin, so that the total Hilbert space dimension is $4M$. We show that in the quantum Parrondo game constructed in this way a systematic win or loss occurs in the long time limit. Due to entaglement and self-interference on the cycle, the game yields a rather complex structure for the win or loss depending on the parameters.

Abstract: Information is instrumental in our understanding of thermodynamics. Their interplay has been studied through completely degenerate Hamiltonians whereby the informational contributions to thermodynamic transformations can be isolated. In this setting, all states other then the maximally mixed state are considered to be in informational non-equilibrium. An important yet still open question is: how to characterise the ability of quantum dynamics to maintain informational non-equilibrium? Here, the dynamical resource theory of informational non-equilibrium preservability is introduced to begin providing an answer to this question. A characterisation of the allowed operations is given for qubit channels and the n dimensional Weyl-covariant channels - a physically relevant subset of the general channels. An operational interpretation of a state discrimination game with Bell state measurements is given. Finally, an explicit link between a channels classical capacity and its ability to maintain informational non-equilibrium is made.

Abstract: Quantum metrology has emerged as a promising avenue for surpassing the limitations of classical mechanics in high-precision measurements. However, the practical implementation of quantum metrology is hindered by the challenges of manipulating exotic quantum states in large systems. Here, we propose and demonstrate a hardware-efficient approach to achieve Heisenberg-limited quantum metrology using large photon-number Fock states. We have developed a programmable photon number filter that efficiently generates Fock states with up to 100 photons in a high-quality superconducting microwave cavity. Using these highly nontrivial states in displacement and phase measurements, we demonstrate a precision scaling close to the Heisenberg limit and achieve a maximum metrological gain of up to 14.8 dB. Our hardware-efficient quantum metrology can be extended to mechanical and optical systems and provides a practical solution for high metrological gain in bosonic quantum systems, promising potential applications in radiometry and the search for new particles.

Abstract: We describe a numerical time-domain approach for high-accuracy calculations of Casimir-Polder forces near micro-structured materials. The use of a time-domain formulation enables the investigation of a broad range of materials described by advanced material models, including nonlocal response functions. We validate the method by a number of example calculations for which we thoroughly investigate the convergence properties of the method, and comparing to analytical reference calculations, we find average relative errors as low as a few parts in a million. As an application example, we investigate the anisotropy-induced repulsive behavior of the Casimir-Polder force near a sharp gold wedge described by a hydrodynamic Drude model.

Abstract: Cold atoms in an optical cavity have been widely used for quantum simulations of many-body physics, where the quantum control capability has been advancing rapidly in recent years. Here, we show the atom cavity system is universal for quantum optimization with arbitrary connectivity. We consider a single-mode cavity and develop a Raman coupling scheme by which the engineered quantum Hamiltonian for atoms directly encodes number partition problems (NPPs). The programmability is introduced by placing the atoms at different positions in the cavity with optical tweezers. The NPP solution is encoded in the ground state of atomic qubits coupled through a photonic cavity mode, that can be reached by adiabatic quantum computing (AQC). We construct an explicit mapping for the 3-SAT and vertex cover problems to be efficiently encoded by the cavity system, which costs linear overhead in the number of atomic qubits. The atom cavity encoding is further extended to quadratic unconstrained binary optimization (QUBO) problems. The encoding protocol is optimal in the cost of atom number scaling with the number of binary degrees of freedom of the computation problem. Our theory implies the atom cavity system is a promising quantum optimization platform searching for practical quantum advantage.

Abstract: Enhancing the capabilities of superconducting quantum hardware, requires higher gate fidelities and lower crosstalk, particularly in larger scale devices, in which qubits are coupled to multiple neighbors. Progress towards both of these objectives would highly benefit from the ability to fully control all interactions between pairs of qubits. Here we propose a new coupler model that allows to fully decouple dispersively detuned Transmon qubits from each other, i.e. ZZ-crosstalk is completely suppressed while maintaining a maximal localization of the qubits' computational basis states. We further reason that, for a dispersively detuned Transmon system, this can only be the case if the anharmonicity of the coupler is positive at the idling point. A simulation of a 40ns CZ-gate for a lumped element model suggests that achievable process infidelity can be pushed below the limit imposed by state-of-the-art coherence times of Transmon qubits. On the other hand, idle gates between qubits are no longer limited by parasitic interactions. We show that our scheme can be applied to large integrated qubit grids, where it allows to fully isolate a pair of qubits, that undergoes a gate operation, from the rest of the chip while simultaneously pushing the fidelity of gates to the limit set by the coherence time of the individual qubits.

Abstract: This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded linear operators on a Hilbert space. We extensively explore the significance of understanding the behavior of linear operators and the existence of invariant subspaces, as well as their profound connections to spectral theory, operator algebras, quantum mechanics, dynamical systems and accelerator physics . By thoroughly exploring these applications, we aim to highlight the wide-ranging impact and relevance of the invariant subspace problem in mathematics and physics.

Abstract: We develop a paradigm for building quantum models in the orthonormal space of Chebyshev polynomials. We show how to encode data into quantum states with amplitudes being Chebyshev polynomials with degree growing exponentially in the system size. Similar to the quantum Fourier transform which maps computational basis space into the phase (Fourier) basis, we describe the quantum circuit for the mapping between computational and Chebyshev spaces. We propose an embedding circuit for generating the orthonormal Chebyshev basis of exponential capacity, represented by a continuously-parameterized shallow isometry. This enables automatic quantum model differentiation, and opens a route to solving stochastic differential equations. We apply the developed paradigm to generative modeling from physically- and financially-motivated distributions, and use the quantum Chebyshev transform for efficient sampling of these distributions in extended computational basis.

Abstract: We present a novel formalism to both understand and construct mixers that preserve a given subspace. The method connects and utilizes the stabilizer formalism that is used in error correcting codes. This can be useful in the setting when the quantum approximate optimization algorithm (QAOA), a popular meta-heuristic for solving combinatorial optimization problems, is applied in the setting where the constraints of the problem lead to a feasible subspace that is large but easy to specify. The proposed method gives a systematic way to construct mixers that are resource efficient in the number of controlled not gates and can be understood as a generalization of the well-known X and XY mixers. The numerical examples provided show a dramatic reduction of CX gates when compared to previous results. Overall, we hope that this new perspective can lead to further insight into the development of quantum algorithms.

Abstract: Hypergraph product codes are a promising avenue to achieving fault-tolerant quantum computation with constant overhead. When embedding these and other constant-rate qLDPC codes into 2D, a significant number of nonlocal connections are required, posing difficulties for some quantum computing architectures. In this work, we introduce a fault-tolerance scheme that aims to alleviate the effects of implementing this nonlocality by measuring generators acting on spatially distant qubits less frequently than those which do not. We investigate the performance of a simplified version of this scheme, where the measured generators are randomly selected. When applied to hypergraph product codes and a modified small-set-flip decoding algorithm, we prove that for a sufficiently high percentage of generators being measured, a threshold still exists. We also find numerical evidence that the logical error rate is exponentially suppressed even when a large constant fraction of generators are not measured.

Abstract: One of the fundamental challenges in enabling fault-tolerant quantum computation is realising fast enough quantum decoders. We present a new two-stage decoder that accelerates the decoding cycle. In the first stage, a partial decoder based on belief propagation is used to correct errors that occurred with high probability. In the second stage, a conventional decoder corrects any remaining errors. We study the performance of our two-stage decoder with simulations using the surface code under circuit-level noise. When the conventional decoder is minimum-weight perfect matching, adding the partial decoder decreases bandwidth requirements, increases speed and improves logical accuracy. Specifically, we observe partial decoding consistently speeds up the minimum-weight perfect matching stage by between 2x-4x on average depending on the parameter regime, and raises the threshold from 0.94 to 1.01.

Abstract: Electronic spin defects in the environment of an optically-active spin can be used to increase the size and hence the performance of solid-state quantum registers, especially for applications in quantum metrology and quantum communication. Although multi-qubit electronic-spin registers have been realized using dark spins in the environment of a Nitrogen-Vacancy (NV) center in diamond, these registers have only included spins directly coupled to the NV, significantly restricting their maximum attainable size. To address this problem, we present a scalable approach to increase the size of electronic-spin registers. Our approach exploits a weakly-coupled probe spin together with double-resonance control sequences to mediate the transfer of spin polarization between the central NV spin and an environmental spin that is not directly coupled to it. We experimentally realize this approach to demonstrate the detection and coherent control of an unknown electronic spin outside the coherence limit of a central NV. Our work paves the way for engineering larger quantum spin registers, which have the potential to advance nanoscale sensing, enable correlated noise spectroscopy for error correction, and facilitate the realization of spin-chain quantum wires for quantum communication.

Abstract: Hybrid quantum-classical algorithms hold the potential to outperform classical computing methods for simulating quantum many-body systems. Adaptive Variational Quantum Eigensolvers (VQE) in particular have demonstrated an ability to generate highly accurate ansatz wave-functions using compact quantum circuits. However, the practical implementation of these methods on current quantum processing units (QPUs) faces significant challenges: the requirement to measure a polynomially scaling number of observables during the operator selection step, followed by the need to optimize a high-dimensional, noisy cost-function. In this study, we introduce new techniques to overcome these difficulties and execute hybrid adaptive algorithms on a 25-qubit error-mitigated quantum hardware coupled to a high performance GPU-accelerated quantum simulator. As a physics application, we compute the ground state of a 25-body Ising model using a novel greedy ADAPT-VQE procedure that requires only five circuit measurements for each iteration, regardless of the number of qubits and the size of the operator pool. As a chemistry application, we combine this greedy approach with the Overlap-ADAPT-VQE algorithm to approximate the ground state of a molecular system. The successful implementation of these hybrid QPU/simulator computations enhances the applicability of adaptive VQE algorithms on QPUs and instills further optimism regarding the near-term advantages of quantum computing.

Abstract: The dynamics of open quantum systems can be simulated by unraveling it into an ensemble of pure state trajectories undergoing non-unitary monitored evolution, which has recently been shown to undergo measurement-induced entanglement phase transition. Here, we show that, for an arbitrary decoherence channel, one can optimize the unraveling scheme to lower the threshold for entanglement phase transition, thereby enabling efficient classical simulation of the open dynamics for a broader range of decoherence rates. Taking noisy random unitary circuits as a paradigmatic example, we analytically derive the optimum unraveling basis that on average minimizes the threshold. Moreover, we present a heuristic algorithm that adaptively optimizes the unraveling basis for given noise channels, also significantly extending the simulatable regime. When applied to noisy Hamiltonian dynamics, the heuristic approach indeed extends the regime of efficient classical simulation based on matrix product states beyond conventional quantum trajectory methods. Finally, we assess the possibility of using a quasi-local unraveling, which involves multiple qubits and time steps, to efficiently simulate open systems with an arbitrarily small but finite decoherence rate.