Physics and Computation: A Perspective From Non-Hermitian Quantum Computer

• URL: http://arxiv.org/abs/2506.18012v2
• Date: Thu, 28 Aug 2025 12:23:01 GMT
• Title: Physics and Computation: A Perspective From Non-Hermitian Quantum Computer
• Authors: Qi Zhang, Biao Wu,
• Abstract summary: We show that NQC is extraordinarily powerful, capable of solving not only all NP problems but also all problems within the complexity class $textPsharpP$ in time.<n>We investigate two physical schemes for implementing the non-unitary gate $G$ and find that the remarkable computational power of NQC originates from the exponentially large physical resources required.
• Score: 8.73778121120948
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We elucidate the profound connection between physics and computation by proposing and examining the model of the non-Hermitian quantum computer (NQC). In addition to conventional quantum gates such as the Hadamard, phase, and CNOT gates, this model incorporates a non-unitary quantum gate $G$. We show that NQC is extraordinarily powerful, capable of solving not only all NP problems but also all problems within the complexity class $\text{P}^{\sharp\text{P}}$ in polynomial time. We investigate two physical schemes for implementing the non-unitary gate $G$ and find that the remarkable computational power of NQC originates from the exponentially large physical resources required.

Related papers

• Quantum Resource Management in the NISQ Era: Implications and Perspectives from Software Engineering [44.99833362998488]
  We analyze the role of resources in current uses of NISQ devices, identifying their relevance and implications for quantum software engineering.<n>We aim to strengthen the field of Quantum Resource Estimation (QRE) and move toward scalable and reliable quantum software development.
  arXiv  Detail & Related papers  (2025-08-06T19:15:57Z)
• Robust Fitting on a Gate Quantum Computer [22.0076458961442]
  We propose a quantum circuit to solve the $ell_infty$ feasibility test in the 1D case, which allows to demonstrate for the first time quantum robust fitting on a real gate quantum computer. We also show how 1D Boolean influences can be accumulated to compute influences for higher-dimensional non-linear models.
  arXiv  Detail & Related papers  (2024-09-03T15:54:20Z)
• Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers [37.69303106863453]
  We propose a state preparation method based on coupled cluster (CC) theory, which is a pillar of quantum chemistry on classical computers. Our approach leads to a reduction of the classical computation overhead, and the number of CNOT and T gates by 28% and 57% on average.
  arXiv  Detail & Related papers  (2024-06-17T14:10:10Z)
• Universal quantum computation using quantum annealing with the transverse-field Ising Hamiltonian [0.0]
  We present a practical method for implementing universal quantum computation using the transverse-field Ising Hamiltonian.<n>Our proposal is compatible with D-Wave devices, opening up possibilities for realizing large-scale gate-based quantum computers.
  arXiv  Detail & Related papers  (2024-02-29T12:47:29Z)
• Full Quantum Process Tomography of a Universal Entangling Gate on an IBM's Quantum Computer [0.0]
  We conduct a thorough analysis of the SQSCZ gate, a universal two-qubit entangling gate, using real quantum hardware. Our analysis unveils commendable fidelities and noise properties of the SQSCZ gate, with process fidelities reaching $97.27098%$ and $88.99383%$, respectively.
  arXiv  Detail & Related papers  (2024-02-10T13:25:01Z)
• Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era [0.0]
  Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way. In FTQC, a quantum circuit is decomposed into universal gates that can be fault-tolerantly implemented. In this paper, we propose that the Clifford+$T$ decomposition error for a given quantum circuit can be modeled as the depolarizing noise.
  arXiv  Detail & Related papers  (2023-01-10T19:00:01Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Optimal Stochastic Resource Allocation for Distributed Quantum Computing [50.809738453571015]
  We propose a resource allocation scheme for distributed quantum computing (DQC) based on programming to minimize the total deployment cost for quantum resources. The evaluation demonstrates the effectiveness and ability of the proposed scheme to balance the utilization of quantum computers and on-demand quantum computers.
  arXiv  Detail & Related papers  (2022-09-16T02:37:32Z)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• Towards Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry [12.724648200604134]
  We introduce a framework of equi convolutional quantum algorithms which is tailored for a number of machine-learning tasks.<n>It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) -- and define a more powerful model: PQC+.
  arXiv  Detail & Related papers  (2022-07-15T01:41:53Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Towards the real-time evolution of gauge-invariant $\mathbb{Z}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation [0.0]
  We benchmark the real-time dynamics of $mathbbZ$ and $U(1)$ gauge in plaquette models using noisy intermediate scale quantum (NISQ) hardware. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state, and locally conserved charges.
  arXiv  Detail & Related papers  (2021-09-30T12:22:21Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)
• Super-robust nonadiabatic geometric quantum control [0.0]
  Nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) have been proposed to reduce the run time of geometric quantum gates. We show that NGQC and NHQC scenarios have no advantage over standard dynamical gates in most cases. We propose a scheme of super-robust nonadiabatic geometric quantum control, in which the super-robust condition can guarantee both high speed and robustness.
  arXiv  Detail & Related papers  (2020-08-05T14:50:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.