Quantum Circuit Iteration for Finite-Temperature Expectation Values
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Solution Overview
Problem
Conventional systems face inefficiencies in calculating thermal equilibrium expectation values at finite temperatures due to the need to randomly sample and calculate from a large number of states exponentially, leading to poor computer hardware utilization.
Innovation Solution
A quantum calculation support program that expands imaginary-time evolution expressions into multiple orders, generates quantum circuits for partial calculations, and repeatedly executes these circuits until convergence, using a statistical ensemble suitable for each partial circuit to improve efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional systems calculate thermal equilibrium expectation values by randomly sampling from a large number of exponentially growing states, then calculation completeness is improved, but calculation efficiency and hardware utilization deteriorate
Solution Approach 1:
The patent divides the calculation process into two distinct phases: (1) a classical preprocessing phase that generates an expanded operator product expression and identifies important terms, and (2) a quantum execution phase that only evaluates the identified important terms. This segmentation allows the classical computer to handle the combinatorial explosion of terms analytically, while the quantum computer focuses only on evaluating specific matrix elements, thereby resolving the contradiction between calculation completeness and efficiency
Solution Approach 2:
The patent performs preliminary classical computation to expand the operator product into normal-ordered form and identify important terms before quantum calculation begins. By pre-processing the Hamiltonian and operator expressions classically, the system eliminates the need for the quantum computer to randomly sample through all exponentially many states, achieving both completeness (through systematic expansion) and efficiency (through selective quantum evaluation)
2Reliability
If the number of qubits is increased to enable quantum error correction (from several hundred to about 1 million), then calculation reliability is improved, but device complexity and implementation difficulty worsen
Solution Approach 1:
The patent applies partial action by having the quantum computer execute only specific important terms identified through classical preprocessing, rather than performing complete thermal equilibrium calculations. This partial execution reduces the quantum circuit depth and qubit requirements, making the calculation feasible on near-term quantum devices with several hundred qubits while still obtaining meaningful results for the physical quantity of interest
3Measurement precision
If imaginary-time evolution is implemented using linear combination of unitaries (LCU) with polynomial expansion, then calculation accuracy is improved, but the number of required quantum circuits and calculation time increase
Solution Approach 1:
The patent extracts and evaluates only the important terms from the full operator product expansion using quantum computation, while handling the remaining combinatorial structure classically. This extraction approach maintains calculation accuracy by systematically identifying all important contributions through classical preprocessing, while dramatically reducing calculation time by limiting quantum circuit execution to only the essential terms
Data Source
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AI summary
A quantum calculation support program for causing a computer to execute processing including: expanding an imaginary-time evolution expression into multiple expressions for multiple orders; generating sets of orders obtained by extracting an order twice from the multiple orders; performing, for each set, generating a quantum circuit indicating quantum calculation of the physical quantity obtained by partial imaginary-time evolution using expressions of orders in the set, and causing a quantum computer to repeatedly execute the quantum calculation using the quantum circuit for the set until the physical quantity obtained from the quantum calculation converges such that an output state obtained by the quantum calculation using the quantum circuit for the set is used as an input state in the subsequent quantum calculation; and calculating the thermal equilibrium expectation value at the finite temperature of the physical quantity using a value of the physical quantity after convergence for each set.