Scalable Quantum Error Mitigation via Truncated Assignment Matrices
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Solution Overview
Problem
Current error mitigation techniques in quantum computing, such as those employing assignment matrices, are inefficient and non-scalable for large-qubit systems, requiring excessive memory and time, and are not feasible for processing increased bitstring and qubit quantities.
Innovation Solution
A scalable and matrix-free approach that calculates a truncated set of assignment matrix elements using only observed bitstring data, allowing for error mitigation without constructing a full assignment matrix, thereby reducing memory and computational power requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a full assignment matrix is constructed for error mitigation, then error mitigation accuracy is improved, but memory requirements and computational time increase exponentially
Solution Approach 1:
The patent extracts only the necessary elements from the full assignment matrix - specifically, only the columns corresponding to observed bitstrings are retained and stored. This selective extraction eliminates the need to store and process the complete exponential-size matrix, reducing memory requirements from O(2^n) to O(m) where m is the number of observed bitstrings.
Solution Approach 2:
Instead of computing the complete assignment matrix, the patent performs partial computation by calculating only the necessary matrix elements corresponding to observed bitstrings. This partial action approach provides sufficient error mitigation accuracy while avoiding the exponential resource costs of full matrix construction.
2Measurement precision
If a full assignment matrix is constructed for error mitigation, then error mitigation accuracy is improved, but computational time increases exponentially
Solution Approach 1:
The patent extracts and processes only the relevant portion of the assignment matrix corresponding to observed bitstrings. This eliminates the need to compute and process the entire exponential-size matrix, reducing computational time from exponential to linear scaling with the number of observations.
Solution Approach 2:
The patent performs partial computation of the assignment matrix by calculating only the necessary elements for observed bitstrings. This partial action provides adequate error mitigation while avoiding the excessive computational time required for full matrix construction.
3Reliability
If current error mitigation approaches are used, then error mitigation is feasible for small qubit counts, but scalability to large qubit systems is lost
Solution Approach 1:
The patent implements a dynamic approach where the assignment matrix size adapts to the actual number of observed bitstrings rather than being fixed at the exponential maximum. This dynamic sizing enables the system to scale efficiently with qubit count by processing only the necessary subset of matrix elements.
Solution Approach 2:
The patent changes the fundamental parameter of matrix size from the theoretical maximum (2^n) to the actual observed count (m). This parameter change enables scalability to large qubit systems by making the computational burden proportional to actual data rather than potential data space.
4Reliability
If a full assignment matrix is constructed, then complete error correction coverage is achieved, but memory and computing power requirements become infeasible
Solution Approach 1:
The patent extracts only the essential columns from the full assignment matrix that correspond to actually observed bitstrings. This extraction maintains complete error correction coverage for observed outcomes while eliminating the impossible-to-store and process remaining matrix elements.
Data Source
AI summary
Systems, computer-implemented methods and/or computer program products are provided for facilitating error mitigation for classical data output from a classical system and/or for qubit data output from a quantum system. A system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a computation component that performs error mitigation employing less than a full set of assignment matrix elements. In one or more embodiments, the error mitigation can be performed without constructing an assignment matrix. Additionally and/or alternatively, the computer executable components can comprise a computation component that performs error mitigation employing an iterative solver using the less than a full set of assignment matrix elements as the initial input set for the iterative solver.