This work aims to reproduce a quantum system composed of a charged spin - $1/2$ fermion interacting with a dyon with an opposite electrical charge (charge-dyon system), utilizing a position-dependent effective mass (PDM) background in the non-relativistic regime via the PDM free Pauli equation. To investigate whether there is a PDM quantum system with the same physics (analogous model) that a charge-dyon system (target system), we resort to the PDM free Pauli equation itself. We proceed with replacing the exact bi-spinor of the target system into this equation, obtaining an uncoupled system of non-linear partial differential equations for the mass distribution $M$. We were able to solve them numerically for $M$ considering a radial dependence only, i.e., $M=M(r)$, fixing $θ_0$, and considering specific values of $μ$ and $m$ satisfying a certain condition. We present the solutions graphically, and from them, we determine the respective effective potentials, which actually represent our analogous models. We study the mapping for eigenvalues starting from the minimal value $j = μ- 1/2$.
We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an $n$-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on $\lceil \log_3(2n+1)\rceil$ qubits. The mapping has a simple structure and is optimal in the sense that it is impossible to construct Pauli operators in any fermion-to-qubit mapping acting nontrivially on less than $\log_3(2n)$ qubits on average. We apply it to the problem of learning $k$-fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show tha…
Hardware-Aware Fermion-to-Qubit Mappings for Simulating the 2D Hubbard Model on Heavy-Hexagon Quantum Processors
University of Milano-Bicocca（米兰比可卡大学）；INFN Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）；Bicocca Quantum Technologies (BiQuTe) Centre（比可卡量子技术中心）；University of Helsinki（赫尔辛基大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络维格纳物理研究中心）；Algorithmiq Ltd（算法有限公司）；University of Florence（佛罗伦萨大学）；INFN Firenze（意大利国家核物理研究所佛罗伦萨分部）
Spatiotemporal Pauli processes: Quantum combs for modeling correlated noise in quantum error correction
Monash University（莫纳什大学）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局（A*STAR））；CSIRO（澳大利亚联邦科学与工业研究组织）；The University of Melbourne（墨尔本大学）；Singapore University of Technology and Design（新加坡科技设计大学）；National University of Singapore（新加坡国立大学）
Noisy Intermediate-Scale Quantum (NISQ) algorithms, which run on noisy quantum computers should be carefully designed to boost the output state fidelity. While several compilation approaches have been proposed to minimize circuit errors, they often omit the detailed circuit structure information that does not affect the circuit depth or the gate count. In the presence of spatial variation in the error rate of the quantum gates, adjusting the circuit structure can play a major role in mitigating errors. In this paper, we exploit the freedom of gate reordering based on the commutation rules to s…
Quantum simulation of chemical Hamiltonians enables the efficient calculation of chemical properties. Mapping is one of the essential steps in simulating fermionic systems on quantum computers. In this work, a unified framework of transformations mapping fermionic systems to qubit systems is presented, and many existing transformations, such as Jordan-Wigner, Bravyi-Kitaev, and parity transformations, are included in this framework. Based on this framework, the Multilayer Segmented Parity (MSP) transformation is proposed. The MSP transformation is a general mapping with an adjustable parameter…
Symplectic Pauli-Schrödinger Equation for the Quark-Antiquark Interaction System
International Center for Physics, Instituto de Física, Universidade de Brasília（巴西利亚大学物理研究所国际物理中心）；Departamento de Física, Universidade Estadual do Maranhão（马拉尼昂州立大学物理系）；FCTE/Universidade de Brasília（巴西利亚大学FCTE）；Universidade Federal do Pará（帕拉联邦大学）；Canadian Quantum Research Center（加拿大量子研究中心）
We analyze phase transitions induced by forbidding charges and fluxes in $\mathcal{D}(S_3)$, the simplest non-Abelian model among quantum doubles, a class of 2D spin lattice topological models introduced by Kitaev. Contrary to a topological quantum field theory, the lattice degrees of freedom allow to forbid charges and fluxes independently, resulting in a non-trivial effect on dyons. Forbidding charges and fluxes leads to only a subset of the original anyons remaining, forming a new theory. We interpret the processes the theory undergoes in terms of condensation, spontaneous symmetry breaking…
Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the Auxiliary Fermion transformation. The Bravyi-Kitaev transform is reformulated in terms of a classical …
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or subsystem codes subject to correlated Pauli noise models, including models of fault tolerance. This mapping connects the error correction threshold of the quantum code to a phase transition in the statistical mechanical model. Thus, any existing method for finding phase transitions, such as Monte Carlo simulations, can be applied to approximate the threshold…
An invaluable method for probing the physics of a quantum many-body spin system is a mapping to noninteracting effective fermions. We find such mappings using only the frustration graph $G$ of a Hamiltonian $H$, i.e., the network of anticommutation relations between the Pauli terms in $H$ in a given basis. Specifically, when $G$ is (even-hole, claw)-free, we construct an explicit free-fermion solution for $H$ using only this structure of $G$, even when no Jordan-Wigner transformation exists. The solution method is generic in that it applies for any values of the couplings. This mapping general…
Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem color codes. They are known to exhibit projective non-Abelian statistics which is exploited to perform encoded gates. In this paper, we initiate the study of twists in qudit color codes over odd prime alphabet. To the best of our knowledge, this is the first study of twists in qudit color codes. Specifically, we present a systematic construction of twists in qud…
Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions
Qclairvoyance Quantum Labs（Qclairvoyance量子实验室）；Indian Institute of Technology Bombay（孟买印度理工学院）；The University of Arizona（亚利桑那大学）；SRM Institute of Science and Technology（SRM科学与技术学院）
In our recent work, we have examined various fermion to qubit mappings in the context of quantum simulation including the original Bravyi-Kitaev Superfast encoding (OSE) as well as a generalized version (GSE). We return to OSE and compare it against the Jordan-Wigner (JW) transform for quantum chemistry considering the number of qubits required, the Pauli weight of terms in the transformed Hamiltonians, and the $L_1$ norm of the Hamiltonian. We considered a test set of molecular systems known as the Atomization Energy 6 (AE6) as well as Hydrogen lattices. Our results showed that the resource e…
Quantum simulation of strong charge-parity violation and Peccei-Quinn mechanism
Frontier Research Institute for Interdisciplinary Sciences, Tohoku University（东北大学前沿跨学科研究院）；Department of Applied Physics, Graduate School of Engineering, Tohoku University（东北大学工学研究科应用物理系）
We study stabilizer quantum error correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a subregion to its entanglement properties, and 2) a previously established mapping between entanglement entropies and domain wall free energies of an underlying spin model, we propose a statistical mechanical description of the QECC in terms of "entanglement domain walls". Free energies of such domain walls generically feature a leading volume law term coming …
Queen Mary University of London（伦敦大学玛丽女王学院）；qBraid Co.（qBraid公司）；RIKEN Wako（理化学研究所和光）；University of British Columbia（不列颠哥伦比亚大学）；University of Regensburg（雷根斯堡大学）；National Taiwan University（台湾大学）；Interdisciplinary Theoretical & Mathematical Science Program (iTHEMS), RIKEN Wako（理化学研究所和光跨学科理论与数学科学项目）
