Tree-Based Fermion-to-Qubit Mapping for Lower-Cost Quantum Encoding
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Solution Overview
Problem
Current quantum computing methods face challenges in efficiently encoding fermionic states due to limited qubit connectivity and high computational costs, particularly in simulating many-body Fermionic quantum systems, which are crucial for applications in computational chemistry and drug discovery.
Innovation Solution
A method involving tree-based Fermion-to-qubit mappings is employed, where a plurality of tree-based mappings are derived and optimized based on a tree structure and instructions, minimizing computational cost by assigning fermionic mode operators, qubits, and Pauli operators to nodes and links, and identifying the target mapping that meets an optimization criterion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional Fermion-to-qubit mappings are used, then the fermionic state can be encoded in qubit state, but the computational cost becomes high and qubit connectivity requirements increase
Solution Approach 1:
The patent transforms the fermionic problem parameters by mapping fermionic mode operators to qubit operators through a systematic transformation process. This parameter transformation allows the fermionic Hamiltonian and state to be represented in qubit space with optimized computational properties, reducing the complexity of quantum circuit implementation while maintaining accuracy in representing fermionic anti-symmetry.
Solution Approach 2:
The patent segments the fermionic system into discrete mode operators that can be independently mapped to qubit operators. By dividing the many-body fermionic problem into manageable operator components and mapping them systematically to qubit space, the method reduces the overall computational complexity and makes the problem tractable on current quantum hardware.
2Reliability
If exact Fermionic anti-symmetry is maintained in the mapping, then physical accuracy is improved, but the number of CNOT gates increases
Solution Approach 1:
The patent changes the representation parameters of fermionic operators by mapping them to qubit operators through a transformation that preserves essential anti-symmetry properties. This parameter transformation allows the system to maintain physical accuracy while using a more efficient qubit representation that reduces the number of required two-qubit gates.
Solution Approach 2:
The patent extracts and isolates the essential anti-symmetry requirements from the full fermionic many-body problem. By identifying and maintaining only the critical anti-symmetry properties needed for physical accuracy while representing the rest of the system in an optimized qubit basis, the method reduces computational overhead without sacrificing essential physics.
3Quantity of substance
If more qubits are used to represent the fermionic system, then the system size that can be simulated increases, but the circuit depth and error accumulation increase
Solution Approach 1:
The patent transforms the system representation parameters by mapping fermionic modes to qubits in a way that optimizes the qubit count and circuit structure. This parameter transformation allows efficient representation of larger fermionic systems while minimizing circuit depth and the number of error-prone two-qubit gates, thereby maintaining higher circuit fidelity.
Solution Approach 2:
The patent employs a dynamic mapping approach where the assignment of fermionic modes to qubits can be optimized based on the specific problem structure and hardware connectivity. This dynamic optimization allows the system to adapt the qubit representation to minimize circuit depth and error accumulation while representing the required system size.
Data Source
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AI summary
The present invention relates to a method of encoding a fermionic state of a fermionic system described by a plurality of N fermionic mode operators in a qubit state of a plurality of n qubits of a quantum processing device according to a target Fermion-to-qubit mapping, wherein said method comprises: deriving a plurality of tree-based Fermion-to-qubit mappings for the encoding, wherein each mapping of the plurality is derived on the basis of a pair of a tree and an instruction for deriving the mapping on the basis of said tree, said tree comprising a plurality of nodes and a plurality of links, wherein a link is either an edge connecting two nodes or a leg connected only to one node, wherein said instruction comprises a first instruction of assigning the fermionic mode operators, the qubits, and a plurality of Pauli operators, each Pauli operator being associated with a Hilbert space of a qubit of the quantum processing device, to the nodes and links of said tree to thereby obtain a labeled tree, and said instruction further comprises a second instruction for deriving the mapping on the basis of said labeled tree; estimating, for each of the Fermion-to-qubit mappings, a computational cost of encoding the fermionic state in the qubit state of the qubits of the quantum processing device according to said mapping; identifying the target fermion-to-qubit mapping as the mapping among the Fermion-to-qubit mappings of the plurality for which the computational cost fulfills an optimization criterion.