Henry P. Stapp
Contents: 1. Introduction: Philosophical Setting 2. Quantum Model of the Mind/Brain 3. Person and Self 4. Meeting Baars's Criteria for Consciousness 5. Qualia 6. Free-Will
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It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation. This result is achieved by showing that the complexity class NQP of Adleman, Demarrais, and Huang, a quantum analog of NP, is equal to the counting class coC$_=$P.
Hard Quantum Extrapolations in Quantum Cryptography
本文提出经典→量子外推任务，研究其困难性与量子承诺、量子公钥密码学和量子密钥分发等原语之间的等价或蕴含关系，并进一步提出完全量子类比，为理解量子密码学的最小假设提供新视角。
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground state problems from quantum chemistry and binary optimization problems, respectively. They are based on the idea of using a classical computer to train a parameterized quantum circuit. We show that the corresponding classical optimization problems are NP-hard. Moreover, the hardness is robust in the sense that, for every polynomial time algorithm, there are ins…
In this paper we give the first proof that, under reasonable assumptions, a problem related to counterfeiting quantum money from knots [Farhi et al. 2010] is hard. Along the way, we introduce the concept of a component mixer, define three new classical query problems and associated complexity classes related to graph isomorphism and group membership, and conjecture an oracle separating QCMA from QMA.
Quantum Simulation of Molecular Dynamics Processes -- A Benchmark Study Using Classical Simulator and Present-Day Quantum Hardware
本文针对自由波包传播、谐振子振动和势垒隧穿，提出浅电路制备类高斯初始波包并实现时间演化，经经典仿真验证算法准确，但当代 IBM 与 IonQ 硬件仍受噪声限制。
Although quantum control typically relies on greedy (local) optimization, traps (irregular critical points) in the control landscape can make optimization hard by foiling local search strategies. We demonstrate the failure of greedy algorithms to realize two fast quantum computing gates: a qutrit phase gate and a controlled-not gate. Then we show that our evolutionary algorithm circumvents the trap to deliver effective quantum control in both instances. Even when greedy algorithms succeed, our evolutionary algorithm delivers a superior control procedure because less time resolution is required…
Quantum Optimization of the Color-of-Money Problem on IBM Quantum Hardware: A Proof-of-Concept Study
本研究在IBM量子硬件上实现了货币颜色问题的概念验证，通过QUBO转换和变分量子算法，成功复现了经典最优解，验证了量子优化在资金管理中的可行性。
Solving an Industrially Relevant Quantum Chemistry Problem on Quantum Hardware
本研究在 trapped ion 量子硬件上计算工业相关强相关金属螯合物的活性空间哈密顿量基态能量，通过变分量子算法训练与经典子空间对角化实现化学精度，并以高效测量和后处理集成到工业量子化学流程中。
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the decoding problem consists of determining the most likely recovery given the syndrome. The corresponding classical problem is known to be NP-complete, and a similar decoding problem for quantum codes is also known to be NP-complete. However, this decoding strategy is not optimal in the quantum setting as it does not take into account error degeneracy, which causes d…
Scalable embedding of parity constraints in quantum annealing hardware
本文提出固定、模块化且可扩展的奇偶映射嵌入方法，用于将任意伊辛哈密顿量表示的组合优化问题嵌入量子退火硬件，并验证嵌入后哈密顿量的物理性质与原问题一致。
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the non-collapse of the polynomial hierarchy that approximating the output probabilities of random quantum circuits to within $\exp(-Ω(m\log m))$ additive error is hard for any classical computer, where $m$ is the number of gates in the quantum computation. More precisely, we show that the above problem is $\#\mathsf{P}$-hard under $\mathsf{BPP}^{\mathsf{NP}}$ reduction. I…
Application of Power Flow problem to an open quantum neural hardware
针对量子硬件上的现实问题求解需求，研究将 Newton-Raphson 潮流计算应用于新型耗散量子神经网络硬件，并分析网络参数对4母线电力系统求解性能的影响。
Gate-based universal quantum computers form a rapidly evolving field of quantum computing hardware technology. In previous work, we presented a quantum algorithm for lattice protein folding on a cubic lattice, tailored for quantum annealers. In this paper, we introduce a novel approach for solving the lattice protein folding problem on universal gate-based quantum computing architectures. Lattice protein models are coarse-grained representations of proteins that have been used extensively over the past thirty years to examine the principles of protein folding and design.These models can be use…
Application-Driven Benchmarking of the Traveling Salesperson Problem: a Quantum Hardware Deep-Dive
本文以旅行商问题为例，对中性原子、离子阱和超导等多种量子硬件进行应用驱动的基准评测，揭示运行实际应用所需步骤及各技术相对效率，为从应用角度理解量子计算能力提供依据。
QAHAN: A Quantum Annealing Hard Attention Network
本文提出量子退火硬注意力机制与网络QAHAN，利用量子隧穿效应实现无梯度全局优化，在MNIST和CIFAR-10上收敛更快、曲线更平滑且噪声鲁棒性更强，推动量子机器视觉发展。
Hard-core Bosons in Action: Applications to Quantum Circuits
本文回顾并扩展了基于硬核玻色子的代数框架用于量子电路模拟，提出高效实现，与IBM Qiskit相比显著提升模拟速度，并引入与遗传算法结合的新应用用于量子电路综合。
Quantum Dropout: On and Over the Hardness of Quantum Approximate Optimization Algorithm
针对QAOA在崎岖能量景观中性能下降的问题，提出量子丢弃方法，通过选择性移除电路子句而不影响解，数值实验验证了其性能提升。
Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum eigensolvers. We show that such an optimization can be improved substantially by using an approximation rather than the exact expectation. Together with efficient classical sampling algorithms, a quantum algorithm with minimal gate count can thus improve the efficiency of general integer-value problems, such as the shortest vector problem (SVP) investigated in this wo…
Evaluating the Quantum Approximate Optimization Algorithms for QUBO problems Across Quantum Hardware Platforms: Performance Analysis, Challenges, and Strategies
本文评估标准QAOA与ADAPT-QAOA在不同量子硬件平台求解金融特征选择类QUBO问题的性能，发现ADAPT-QAOA在高难度问题上更优，超导硬件求解时间短、离子阱硬件错误率佳，为相关部署提供策略参考。
The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurem…
Benchmarking the Lights Out Problem on Real Quantum Hardware
研究在真实量子硬件上实现灯灭问题并评估Grover搜索性能，发现IBM硬件改进和IQM设备校准质量对结果影响显著。
Hardness-dependent quantum adiabatic schedules for the maximum-independent-set problem
针对最大独立集问题与中性原子量子计算平台，提出一种依赖问题难度而非规模的高效绝热调度数值方法，性能优于基准且易硬件实现，已在256量子比特Aquila计算机上验证，扩展至混合算法有望用现有技术求解更难实例。
QC-Adviser: Quantum Hardware Recommendations for Solving Industrial Optimization Problems
本文提出QC-Adviser原型，帮助非专家用户在无需量子计算知识的情况下选择合适的量子退火硬件，以解决工业优化问题中的硬件选择难题。
Quantum hard disks on a lattice
本文提出晶格量子硬盘模型并以里德伯原子实现，揭示其一维弹道熔化与二维抗缺陷晶体结构，并归因于量子多体伤痕。
We present a hybrid classical-quantum algorithm to solve optimization problems in current quantum computers, whose basic idea is to assist variational quantum eigensolvers (VQE) with adiabatic change of the Hamiltonian. The rational for this new algorithm is to circumvent the problem of facing very small gradients in the classical optimization piece of a VQE, while being able to run in current hardware efficient devices. A discrete concatenation of VQEs adapted to interpolating Hamiltonians provides a method to keep the quantum state always close to a path faithfully directed to find the final…
NP-hard but no longer hard to solve? Using quantum computing to tackle optimization problems
本文展望了量子优化领域，通过用例展示NISQ设备解决(NP-)hard优化问题的潜力，强调比较量子和经典方法需使用恰当指标，并讨论了近期突破与未来方向。
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells. These methods extend with fabric growth while scaling linearly in time and quadratically in footprint. We also provide methods for handling hard faults in the logical fabric without invoking approximations to the origin…
Reinforcement learning with learned gadgets to tackle hard quantum problems on real hardware
本文提出gadget reinforcement learning方法，通过学习合成程序自动构建复合门，提升量子电路设计的准确性、兼容性和可扩展性，应用于Ising模型和量子化学问题。
The entanglement entropy and quantum fidelity in a hard-core-boson model with nearest- and next-nearest-neighbor interactions are studied numerically. By using exact diagonalization and the density matrix renormalization group, the effects of interactions on entanglement entropy and fidelity susceptibility in the model are investigated. We focus our attention on looking for three quantum phase transitions. It is found that the first derivative of the entanglement entropy can indicate all of three phase transitions, while the fidelity susceptibility cannot predict the transition from superfluid…
A quantum channel is said to be a mixed-unitary channel if it can be expressed as a convex combination of unitary channels. We prove that, given the Choi representation of a quantum channel, it is NP-hard with respect to polynomial-time Turing reductions to determine whether or not that channel is a mixed-unitary channel. This hardness result holds even under the assumption that the channel is not within an inverse-polynomial distance (in the dimension of the space upon which it acts) of the boundary of the mixed-unitary channels.
Dynamics of defects and interfaces for interacting quantum hard disks
研究量子硬盘问题中缺陷和界面的稳定性，发现其在短程软芯相互作用下仍保持稳定，揭示量子动力学的鲁棒性。
Due to several physical limitations in the realisation of quantum hardware, today's quantum computers are qualified as Noisy Intermediate-Scale Quantum (NISQ) hardware. NISQ hardware is characterized by a small number of qubits (50 to a few hundred) and noisy operations. Moreover, current realisations of superconducting quantum chips do not have the ideal all-to-all connectivity between qubits but rather at most a nearest-neighbour connectivity. All these hardware restrictions add supplementary low-level requirements. They need to be addressed before submitting the quantum circuit to an actual…
On melting of Boltzmann system of quantum hard spheres
本文研究量子硬球玻尔兹曼系统的熔化，发现量子熔化线在有限温度下始终偏离经典线，经典极限不可达。
The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time quantum walks on a variety of graphs, it is not known if PST persists for many particles in the presence of interactions. We show that if single-particle PST occurs on one-dimensional weighted path graphs, then systems of hard-core bosons undergoing quantum walks on these paths also undergo PST. The analysis extends the Tonks-Girardeau ansatz to weighted graphs…
The necessary conditions to derive the quantum VdW EoS with hard-core repulsion from the quantum partition are discussed. On a plausible example it is shown that an alternative way to account correctly for the 3-rd virial coefficient of classical hard spheres leads to inconsistencies. The multicomponent formulation of the quantum VdW EoS with hard-core repulsion is derived within a self-consisting approximation. For practical applications it is simplified, extended to higher densities and generalized to the case of hard convex bodies of any dimension $D\ge 2$.
The Quantum Overlap Gap Property and Algorithmic Hardness for the Quantum Hypergraph Max-Cut Problem
本文利用量子重叠间隙性质框架，证明稳定与局部量子算法在平均情况下难以近似量子超图最大割问题，并给出量子算法深度下界。
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the second level of this quantum hierarchy, but that these problems are in fact hard to approximate. Using these techniques, we also obtain hardness of approximation for the class QCMA. Our approach is based on the use of dispersers, and is inspired by the classical results of Umans regarding hardness of approximation for the second level of the classical polynomi…
A critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB team, is sampling from the probability distributions of randomly chosen quantum circuits, which we call Random Circuit Sampling (RCS). In this paper we study both the hardness and verification of RCS. While RCS was defined with experimental realization in mind, we show complexity theoretic evidence of hardness that is on par with the strongest theoretical propo…
Quantum pricing-based column-generation framework for hard combinatorial problems
本文提出一种基于中性原子量子采样器的混合经典-量子列生成算法，在最小顶点着色问题上以较少迭代获得良好解，并与先进经典及量子方法对比。
Exact solution of the Schrödinger equation is given for a particle inside a hard sphere whose wall is moving with a constant velocity. Numerical computations are presented for both contracting and expanding spheres. The propagator is constructed and compared with the propagator of a particle in an infinite square well with one wall in uniform motion.
Optimizing the depth of variational quantum algorithms is strongly QCMA-hard to approximate
本文证明近似变分量子算法ansatz的最优深度在乘法因子N^{1-ε}内是QCMA难的，且该困难性在QAOA型设置中依然存在，首次给出自然的QCMA难近似问题。
As quantum hardware increases in complexity, successful algorithmic execution relies more heavily on awareness of existing device constraints. In this work we focus on the problem of routing quantum information across the machine to overcome the limited connectivity of quantum hardware. Previous approaches address the problem for each two-qubit gate separately and then impose the compatibility of the different routes. Here we shift the focus onto the set of all routing operations that are possible at any given time and favor those that most benefit the global pattern of two-qubit gates. We ben…
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, named `D-Wave' chips, promise to solve practical optimization problems potentially faster than conventional `classical' computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of quantum annealers from their classical thermal counterparts. Here, we…
Generating Hard Ising Instances With Planted Solutions Using Post-Quantum Cryptographic Protocols
本文提出基于McEliece后量子密码协议生成具有植入解的困难Ising实例的新方法，通过私钥大小调节难度并保证唯一基态，有效防止后门利用，适用于安全评估量子设备。
Quantum Hard Spheres with Affine Quantization
本文通过仿射量化方法研究量子硬球流体的热力学性质，采用路径积分蒙特卡罗方法求解其热力学性质。
We study the out-of-equilibrium evolution of a strongly interacting quantum spin chain which is mapped on a system of hard rods that are coherently deposited on and removed from a lattice. We show that this closed quantum system approaches an equilibrium steady state which strongly resembles a microcanonical ensemble of classical hard rods. Starting from the fully coherent evolution equation we derive a Master equation for the evolution of the number of hard rods on the lattice. This equation does not only capture properties of the equilibrium state but also describes the dynamical non-equilib…
A fundamental pursuit in complexity theory concerns reducing worst-case problems to average-case problems. There exist complexity classes such as PSPACE that admit worst-case to average-case reductions. However, for many other classes such as NP, the evidence so far is typically negative, in the sense that the existence of such reductions would cause collapses of the polynomial hierarchy(PH). Basing cryptographic primitives, e.g., the average-case hardness of inverting one-way permutations, on NP-completeness is a particularly intriguing instance. As there is evidence showing that classical re…
We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wave length, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of…
The computational complexity conjecture of NP $\nsubseteq$ BQP implies that there should be an exponentially small energy gap for Quantum Annealing (QA) of NP-hard problems. We aim to verify how this computation originated gapless point could be understood based on physics, using the quantum Monte Carlo method. As a result, we found a phase transition detectable only by the divergence of fidelity susceptibility. The exponentially small gapless points of each instance are all located in the phase found in this study, which suggests that this phase transition is the physical cause of the failure…
NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp's 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers can search for the optimum value of such NP-hard optimization problems, given the problem can be embedded on their hardware. However, this is often not possible due to certain limitations of the hardware connectivity structure of the annealer. This paper studies a general framework for a decomposition algorithm for NP-hard graph problems aiming to identify an…
Measurement-based quantum computing enables universal quantum computing with only adaptive single-qubit measurements on certain many-qubit states, such as the graph state, the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, and several tensor-network states. Finding new resource states of measurement-based quantum computing is a hard task, since for a given state there are exponentially many possible measurement patterns on the state. In this paper, we consider the problem of deciding, for a given state and a set of unitary operators, whether there exists a way of measurement-based quantum computing…
On the Hardness of the Minimum Distance Problem of Quantum Codes
本研究通过将经典最小距离问题归约到量子问题，结合无4环图图态距离下界的技术工具，证明精确或近似求解稳定子量子码及CSS码的最小距离均为NP难，填补了量子码距离问题难度研究的空白。
We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show that the problem hardness is mainly due to entropic barriers. We study, both analytically and numerically, several optimization algorithms, finding that entropic barriers affect in a similar way classical local algorithms and quantum annealing. For the adiabatic algorithm, the difficulty we identify is distinct from that of tunnelling under large barriers, but …
Enhancing variational quantum algorithms by balancing training on classical and quantum hardware
本文提出结合经典增强 g-sim 方法与量子参数平移规则的 HELIA 训练方法，通过经典与量子硬件协同分担梯度估计资源，显著提升 VQE 和量子神经网络在基态估计与相位分类中的精度和成功率，并缓解贫瘠高原问题。
We classify the time complexities of three important decoding problems for quantum stabilizer codes. First, regardless of the channel model, quantum bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece and Tilborg did for classical binary linear codes in 1978. Then over the depolarizing channel, the decoding problems for finding a most likely error and for minimizing the decoding error probability are also shown to be NP-hard. Our results indicate that finding a polynomial-time decoding algorithm for general stabilizer codes may be impossible, but this, on the other …
We show that the condition for the appearance of quantum chaos (Wigner-Dyson distribution of energy eigenvalues, gaussian-random energy eigenfunctions) in a dilute gas of many hard spheres is $λ\ll \ell$, where $λ$ is the wavelength of a typical particle and $\ell$ is the mean free path between collisions. For fermions with Fermi wavelength $λ_F \ll \ell$, this implies that all energy eigenstates, including the ground state, are chaotic. Physical implications are discussed.
Quantum Compilation Toolkit for Rydberg Atom Arrays with Implications for Problem Hardness and Quantum Speedups
本研究提出并实现了面向里德堡原子阵列的三模块端到端量子编译工具包，用于求解MIS问题，可高效约简问题规模、检查硬件兼容性、实现可控开销的图嵌入，并在QuEra Aquila设备上验证，拓展了近期里德堡原子阵列的可解问题范围。
Recent proposals of topological flat band (TFB) models have provided a new route to realize the fractional quantum Hall effect (FQHE) without Landau levels. We study hard-core bosons with short-range interactions in two representative TFB models, one of which is the well known Haldane model (but with different parameters). We demonstrate that FQHE states emerge with signatures of even number of quasi-degenerate ground states on a torus and a robust spectrum gap separating these states from higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrat…
Compiling quantum circuits to realistic hardware architectures using temporal planners
本文研究了将量子电路编译到新兴量子硬件的时空规划方法，重点探讨了超导架构的最近邻约束，并通过QAOA电路的实验验证了时间规划在编译优化中的可行性。
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