Quantum Basis Transformation for Low-Noise Observable Measurement
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Solution Overview
Problem
Existing quantum computation methods face inefficiencies in simultaneous measurement of observables due to high noise levels from two-qubit gates and increased computational complexity from partitioning under general commutativity, leading to errors and reduced computational efficiency.
Innovation Solution
A method to create a basis transformation circuit that reduces the number of two-qubit gates by selecting observables with fewer non-identity characters in their Pauli strings, allowing for efficient simultaneous measurement of observables with minimal noise and error.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If partitioning is performed under general commutativity to enable simultaneous measurement of observables, then the ability to simultaneously measure more observables is improved, but the computational complexity and noise from two-qubit gates increase
Solution Approach 1:
The patent segments the set of observables into multiple partitions based on qubit-wise commutativity. Each partition contains observables that can be simultaneously measured with minimal two-qubit gates. This segmentation approach allows the system to handle general commutativity requirements while avoiding the complexity of treating all observables uniformly, thus resolving the contradiction between measurement versatility and computational complexity.
Solution Approach 2:
The patent changes the parameter of commutativity assessment from general commutativity to qubit-wise commutativity. By using qubit-wise commutativity as the selection criterion for partitioning, the system achieves a balance that enables simultaneous measurement of observables while significantly reducing the number of two-qubit gates required, thereby lowering computational complexity and noise levels.
2Adaptability or versatility
If partitioning is performed under general commutativity to enable simultaneous measurement of observables, then the ability to simultaneously measure more observables is improved, but the noise level from two-qubit gates increases leading to errors
Solution Approach 1:
The patent segments observables into partitions where each partition is measured using a dedicated basis transformation circuit with minimized two-qubit gates. This segmentation ensures that simultaneous measurement capability is maintained while the noise from two-qubit gates is confined to minimal necessary operations within each partition, preserving measurement accuracy.
Solution Approach 2:
The patent changes the commutativity parameter from general to qubit-wise, which directly reduces the number of two-qubit gates required in basis transformation circuits. This parameter change lowers noise levels and improves measurement reliability while still enabling simultaneous measurement of multiple observables through partitioning.
3Reliability
If the number of two-qubit gates is reduced in basis transformation circuits, then noise and errors are reduced, but the ability to handle general commutativity cases is limited
Solution Approach 1:
The patent segments the full set of observables into multiple partitions, each handled by a simplified basis transformation circuit with reduced two-qubit gates. This segmentation allows the system to maintain high measurement accuracy within each partition while collectively handling a broad range of observable types through the combination of multiple partitions, thus preserving adaptability.
Solution Approach 2:
The patent applies partial action by using qubit-wise commutativity checks instead of full general commutativity analysis for each observable pair. This partial approach reduces the computational overhead and two-qubit gate requirements while still achieving sufficient measurement flexibility through the partitioning strategy that covers multiple observable groups.
Data Source
AI summary
An information processing apparatus calculates, for each of a plurality of simultaneously measurable observables included in an observable group, an index value based on the number of characters other than I included in a Pauli string representing the observable. The information processing apparatus selects a predetermined number of observables from the observable group, based on the index values. The information processing apparatus then creates a basis transformation circuit that transforms an expectation value of each of the predetermined number of selected observables, included in an execution result of a quantum circuit that performs quantum computation based on a problem to be solved, into a measurement result of a single qubit.