RUS Quantum Arithmetic Circuits With Fewer Ancilla Qubits
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Solution Overview
Problem
Existing quantum computer algorithms for arithmetic operations, such as the quantum linear-systems algorithm, require numerous ancillary qubits due to their reliance on classical reversible logic and phase-kickback approaches, leading to inefficiencies in resource usage.
Innovation Solution
The implementation of quantum repeat-until-success (RUS) multiplication circuits coupled with ancilla qubits, utilizing gearbox and programmable ancilla rotation circuits to perform arithmetic operations efficiently, allowing for error correction within selected limits, and enabling the evaluation of functions through Taylor series representations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If classical reversible logic and phase-kickback approaches are used for quantum arithmetic operations, then the algorithms can be implemented with standard quantum gates, but the number of ancillary qubits required increases substantially
Solution Approach 1:
The patent extracts the multiplication operation from the traditional phase-kickback approach and implements it using a dedicated RUS multiplication circuit that directly computes the product phase on the target qubit. This separates the multiplication function from the general reversible logic framework, eliminating the need for numerous ancillary qubits that would otherwise be required to implement multiplication through classical reversible logic gates.
Solution Approach 2:
The patent introduces an intermediary measurement and correction mechanism in the RUS circuit. The measurement circuit measures the ancilla qubit state, and based on the measurement outcome, a correction circuit applies conditional phase corrections to the target qubit. This intermediary measurement-correct ion process enables accurate multiplication with far fewer ancillary qubits than direct reversible logic implementation.
2Productivity
If quantum linear-systems algorithm is implemented with classical arithmetic, then exponential speedup is achieved, but hundreds of ancillary qubits are needed for reversible arithmetic operations
Solution Approach 1:
The patent extracts the arithmetic operations from the classical reversible logic framework and replaces them with specialized RUS circuits that perform multiplication and function evaluation directly in the quantum domain. This extraction eliminates the need for hundreds of ancillary qubits while preserving the exponential speedup of the quantum linear-systems algorithm.
Solution Approach 2:
The patent changes the operational parameters of arithmetic operations by using RUS circuits that compute products through phase rotations and measurements rather than through sequences of reversible logic gates. This parameter change in the computational approach dramatically reduces the ancillary qubit requirement from hundreds to a manageable number.
3Quantity of substance
If RUS multiplication circuits are used to reduce ancillary qubits, then the number of qubits is reduced, but error terms require correction within selected error limits
Solution Approach 1:
The patent implements feedback through the measurement and correction circuit in the RUS architecture. The measurement circuit measures the ancilla qubit state, and the correction circuit applies conditional phase corrections based on the measurement outcome. This feedback mechanism ensures that error terms are corrected within selected error limits, maintaining reliability while using fewer ancillary qubits.
Solution Approach 2:
The patent applies beforehand cushioning by pre-calculating and applying correction phases in the RUS circuit. The correction circuit is designed to compensate for known error terms before they accumulate, ensuring that the final result remains within acceptable error bounds without requiring excessive ancillary qubits for error prevention.
4Productivity
If gearbox and programmable ancilla rotation circuits are used for multiplication, then arithmetic operations become more efficient, but circuit complexity increases
Solution Approach 1:
The patent achieves universality by designing the RUS multiplication circuit to handle multiple arithmetic operations (multiplication, function evaluation) through a single unified architecture. The gearbox and programmable ancilla rotation circuits are configured to perform different operations by adjusting parameters rather than requiring separate dedicated circuits for each operation, thus improving efficiency without proportionally increasing complexity.
Solution Approach 2:
The patent applies dynamics by making the ancilla rotation angles programmable and adjustable. The programmable ancilla rotation circuits allow the same physical circuit to adapt to different computational requirements by changing rotation parameters, thereby achieving efficient arithmetic operations without permanently increasing the structural complexity of the quantum circuit.
Data Source
AI summary
Quantum circuits and associated methods use Repeat-Until-Success (RUS) circuits to perform approximate multiplication and approximate squaring of input values supplied as rotations encoded on ancilla qubits. So-called gearbox and programmable ancilla circuits are coupled to encode even or odd products of input values as a rotation of a target qubit. In other examples, quantum RUS circuits provide target qubit rotations that are associated with reciprocals using series expansion representations.