Fermionic quantum computation

Abstract

We define a model of quantum computation with local fermionic modes (LFMs) -- sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of $m$ LFMs and the Hilbert space of $m$ qubits, simulation of one fermionic gate takes $O(m)$ qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to $O(\log m)$ and a constant, respectively. Nearest-neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.

18 pages, Latex; one reference added

References in corpus (3)

• Unpaired Majorana fermions in quantum wires
• Simulation of topological field theories by quantum computers
• Unconventional Quantum Computing Devices

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• A Full Quantum Eigensolver for Quantum Chemistry Simulations
• Fermihedral: On the Optimal Compilation for Fermion-to-Qubit Encoding
• Exploring Ground States of Fermi-Hubbard Model on Honeycomb Lattices with Counterdiabaticity
• Quantum computing quantum Monte Carlo algorithm
• Realizing Universal Majorana Fermionic Quantum Computation
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Vortices observed and to be observed
• Excited state search using quantum annealing
• Exact block encoding of imaginary time evolution with universal quantum neural networks
• Estimating molecular thermal averages with the quantum equation of motion and informationally complete measurements
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Boltzmann machines and quantum many-body problems
• Volichenko-type metasymmetry of braided Majorana qubits
• Universal Translationally-Invariant Hamiltonians
• Ladder Operator Block-Encoding
• Quantum simulation by qubitization without Toffoli gates
• Universal Signatures of Majorana-like Quasiparticles in Strongly Correlated Landau-Fermi Liquids
• A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Refining resource estimation for the quantum computation of vibrational molecular spectra through Trotter error analysis
• Hamiltonian-based graph-state ansatz for variational quantum algorithms
• The Role of Quantum Computing in Advancing Scientific High-Performance Computing: A perspective from the ADAC Institute
• Computing Electronic Correlation Energies using Linear Depth Quantum Circuits
• Quantum Computing in Pharma: A Multilayer Embedding Approach for Near Future Applications
• Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits
• Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques
• A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians
• A representation of complex rational numbers in quantum mechanics
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Local Jordan-Wigner transformations on the torus
• Topological quantum phase transitions in a Majorana chain with spatial modulation
• Sequence of penalties method to study excited states using VQE
• Calculation of the moscovium ground-state energy by quantum algorithms
• Local quantum overlapping tomography
• Matchgate circuits deeply thermalize
• A Method of Determining Excited-States for Quantum Computation
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• A Generalized Circuit for the Hamiltonian Dynamics Through the Truncated Series
• Multireference error mitigation for quantum computation of chemistry
• Fermionic quantum computation with Cooper pair splitters
• Approximate Quantum Codes From Long Wormholes
• Reducing circuit depth with qubitwise diagonalization
• The Yang-Baxter integrability of the critical Ising chain
• Hardware-efficient quantum phase estimation via local control
• Altermagnet-Superconductor Heterostructure: a Scalable Platform for Braiding of Majorana Modes
• Parallelization techniques for quantum simulation of fermionic systems
• A massless interacting Fermionic Cellular Automaton exhibiting bound states
• The Electronic Structure of the Hydrogen Molecule: A Tutorial Exercise in Classical and Quantum Computation
• Optimizing Electronic Structure Simulations on a Trapped-ion Quantum Computer using Problem Decomposition
• Gauged cooling of topological excitations and emergent fermions on quantum simulators
• Topological obstructions to quantum computation with unitary oracles
• Simulating polaritonic ground states on noisy quantum devices
• Entanglement spectrum of matchgate circuits with universal and non-universal resources
• Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
• Exterior calculus and fermionic quantum computation
• On the locality of qubit encodings of local fermionic modes
• Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers
• Basis set generation and optimization in the NISQ era with Quiqbox.jl
• Quantum nuclear dynamics on a distributed set of ion-trap quantum computing systems
• Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms
• Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits
• From Majorana fermions to topological quantum computation in semiconductor/superconductor heterostructures
• QForte: an efficient state simulator and quantum algorithms library for molecular electronic structure
• Exotic quantum statistics and thermodynamics from a number-conserving theory of Majorana fermions
• Towards solving the BCS Hamiltonian gap in Near-Term Quantum Computers
• Conformal Field Theories as Scaling Limit of Anyonic Chains
• Analyzing the spectral density of a perturbed analog quantum simulator using Keldysh formalism
• Transforming Collections of Pauli Operators into Equivalent Collections of Pauli Operators over Minimal Registers
• Expanding variational quantum eigensolvers to larger systems by dividing the calculations between classical and quantum hardware
• Clifford circuit based heuristic optimization of fermion-to-qubit mappings
• Topological Computation by non-Abelian Braiding in Classical Metamaterials
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Discontinuous Galerkin discretization for quantum simulation of chemistry
• Shannon theory for quantum systems and beyond: information compression for fermions
• On braid statistics versus parastatistics
• A diagrammatic calculus of fermionic quantum circuits
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Simplified projection on total spin zero for state preparation on quantum computers
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations
• Quantum permutation puzzles with indistinguishable particles
• Hot-Start Optimization for Variational Quantum Eigensolver
• Stabilizer configuration interaction: Finding molecular subspaces with error detection properties
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Majorana braiding simulations with projective measurements
• Classical simulation of dissipative fermionic linear optics
• High-Quality Protein Force Fields with Noisy Quantum Processors
• Crosstalk-Based Parameterized Quantum Circuit Approximation
• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Almost optimal measurement scheduling of molecular Hamiltonian via finite projective plane
• Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer
• Effective simulation of state distribution in qubit chains
• GHZ transform (I): Bell transform and quantum teleportation
• Digital Quantum Simulation of Scalar Yukawa Coupling
• Time-resolved tomography of a driven adiabatic quantum simulation
• Lattice Gauge Theory for a Quantum Computer
• Permanents, Bosons and Linear Optics
• Quantum Simulation of Molecules without Fermionic Encoding of the Wave Function
• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Basis set convergence of Wilson basis functions for electronic structure
• The parastatistics of braided Majorana fermions
• On sets of commuting and anticommuting Paulis
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Interpolated Collision Model Formalism
• Weighted Quantum Channel Compiling through Proximal Policy Optimization
• HATT: Hamiltonian Adaptive Ternary Tree for Optimizing Fermion-to-Qubit Mapping
• Best-practice aspects of quantum-computer calculations: A case study of hydrogen molecule
• Mitigating the measurement overhead of ADAPT-VQE with optimised informationally complete generalised measurements
• Limits of Validity of Rashba Model in BiTeI: A High-field Magneto-optical Study
• Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model
• Excited state calculations using variational quantum eigensolver with spin-restricted ansätze and automatically-adjusted constraints
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• The Representation of Numbers in Quantum Mechanics
• Utilizing Quantum Processor for the Analysis of Strongly Correlated Materials
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Minimal operational theories: classical theories with quantum features
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory
• Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
• Local fermion-to-qudit mappings: a practical recipe for four-level systems
• Electronic Structure Theory with Molecular Point Group Symmetries on Quantum Annealers
• Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information
• Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization
• Improved Strategies for Fermionic Quantum Simulation with Global Interactions
• Solitonic Andreev spin qubits from Andreev states in Corbino Josephson junctions
• Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme
• Protected quantum gates using qubit doublons in dynamical optical lattices
• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph
• Three-qubit encoding in ytterbium-171 atoms for simulating 1+1D QCD
• Expanding the Class of Free Fermions via Twin-Collapse Methods
• Simulating Topological Order on Quantum Processors
• Twisted Interferometry
• An Eigenvalue Problem for a Fermi System and Lie Algebras
• Quantum science with arrays of metastable helium-3 atoms
• Optimal fermionic swap networks for Hubbard models
• Sparse SYK and traversable wormholes
• Benchmarking Quantum Simulation of Chemical Hamiltonians using the Sorted-List Encoding
• Engineering quasi-steady-state correlations in uncorrelated thermal states using stochastic driving
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions
• Many-Fermion Simulation from the Contracted Quantum Eigensolver without Fermionic Encoding of the Wave Function
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing
• Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems
• PHOENIX: Pauli-Based High-Level Optimization Engine for Instruction Execution on NISQ Devices
• On sampling determinantal and Pfaffian point processes on a quantum computer
• Constrained Shadow Tomography for Molecular Simulation on Quantum Devices
• Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions
• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
• Fast collisional $\sqrt{\mathrm{SWAP}}$ gate for fermionic atoms in an optical superlattice
• Realizing Majorana Kramers pairs in two-channel InAs-Al nanowires with highly misaligned electric fields
• Quantum solver for single-impurity Anderson models with particle-hole symmetry
• Extension of the Jordan-Wigner mapping to nonorthogonal spin orbitals for quantum computing application to valence bond approaches
• Accelerating Fermionic System Simulation on Quantum Computers
• Near-Term Fermionic Simulation with Subspace Noise Tailored Quantum Error Mitigation
• Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition
• Designing a Machine Learning-Driven, Cross-Hardware Emulator for Noisy Quantum Computers with Gate-Based Protocols
• Dynamical complexity of non-Gaussian many-body systems with dissipation
• Creation of Wave Packets for Quantum Chromodynamics on Quantum Computers
• A simple quantum simulation algorithm with near-optimal precision scaling
• Grobner Bases for Finite-temperature Quantum Computing and their Complexity
• Complexity of Fermionic 2-SAT
• From Fermat's last theorem to the quantum computer
• Electronic Structure Calculatins and the Ising Machine
• Color codes with domino twists: Construction, logical measurements, and computation
• Ancillary entangling Floquet kicks for accelerating quantum algorithms
• Quantum operation of fermionic systems and process tomography using Majorana fermion gates
• Hyperspheres and control of spin chains
• Quantum information theory on sparse wavefunctions and applications for Quantum Chemistry
• Mutual information in interacting spin systems
• Resource-Optimized Grouping Shadow for Efficient Energy Estimation
• Evaluating Ground State Energies of Chemical Systems with Low-Depth Quantum Circuits and High Accuracy
• Electronic Structure Calculations and the Ising Hamiltonian
• Mapping quantum chemical dynamics problems onto spin-lattice simulators
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states
• Complex Rational Numbers in Quantum Mechanics
• Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation
• Effective non-local parity-dependent couplings in qubit chains
• Quantum-Classical Computing for Time-Dependent Ion-Atom Collision Dynamics: Applications to Charge Transfer Cross Section Simulations
• Optimizing Sparse SYK
• Toward Density Functional Theory on Quantum Computers?
• Scalable Simulation of Fermionic Encoding Performance on Noisy Quantum Computers
• Transversal architecture for megaquop-scale quantum simulation with neutral atoms
• Quantum Routing and Entanglement Dynamics Through Bottlenecks