Quantum Computation Method Using Constraint Hamiltonians
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Solution Overview
Problem
Current quantum computing methods face challenges in performing arbitrary quantum computations due to difficulties in realizing long-range interactions, which are either impractical or lead to increased runtime and reduced scalability.
Innovation Solution
The method involves encoding a computational problem into a problem Hamiltonian and a constraint Hamiltonian, using a quantum system with constituents like qubits. It performs N rounds of operations, applying sequences of unitary operators that include problem-encoding, constraint-enforcing, and unitary driver operators, followed by measurements to output the result.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If long-range interactions are used to perform arbitrary quantum computations, then programmability is improved, but device complexity and difficulty of realization worsen
Solution Approach 1:
The patent introduces a classical computer as an intermediary that generates control signals to mediate between the quantum computer's qubits. This classical controller handles the complexity of coordinating long-range interactions, allowing the quantum system to achieve arbitrary programmability without directly implementing complex long-range coupling mechanisms between all qubit pairs.
Solution Approach 2:
The patent segments the quantum computation into discrete rounds of operations, where each round applies specific unitary operators (problem-encoding, constraint-enforcing, and driver operators) to the quantum state. This segmentation allows complex arbitrary computations to be broken down into manageable sequential steps that can be implemented using available quantum hardware with limited connectivity.
2Device complexity
If sequences of short-range interactions are used to replace long-range interactions, then device complexity is reduced, but productivity worsens due to sequential execution
Solution Approach 1:
The patent employs periodic action by structuring the computation as N rounds of operations, where each round consists of alternating applications of problem-encoding unitary operators and constraint-enforcing unitary operators. This periodic structure allows the system to systematically build up the quantum state toward the ground state encoding the solution, achieving convergence through repeated cycles rather than a single long sequential process.
3Productivity
If quantum computation is parallelized, then productivity is improved, but loss of information worsens due to reduced efficiency and increased runtime
Solution Approach 1:
The patent ensures continuity of useful action by designing each round of operations to continuously evolve the quantum state closer to the ground state. The unitary operators are specifically chosen to maintain progress toward the solution, with problem-encoding operators incorporating problem-specific information and constraint-enforcing operators maintaining validity, ensuring that each successive round contributes meaningfully to reaching the final solution without wasting computational effort.
Data Source
AI summary
A method of performing a quantum computation includes providing a quantum system comprising constituents; encoding a computational problem into a problem Hamiltonian of the quantum system; determining a constraint Hamiltonian of the quantum system; the constraint Hamiltonian a sum of summand constraint Hamiltonians; a ground state of a total Hamiltonian encodes a solution to the computational problem, the total Hamiltonian includes a sum of the problem Hamiltonian and the constraint Hamiltonian; determining a first subset S1 of the summand constraint Hamiltonians of the constraint Hamiltonian and a second subset S2 of the summand constraint Hamiltonians of the constraint Hamiltonian; performing N rounds of operations, wherein N≥2, each round includes preparing an initial quantum state and evolving the quantum system according to a sequence of unitary operators where the sequence includes problem-encoding unitary operators, constraint-enforcing unitary operators and unitary driver operators; and outputting a result of the quantum computation.