Pairwise Quantum Process Tomography Beyond Exponential Scaling
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Solution Overview
Problem
Current methods for quantum process tomography, such as naive quantum state tomography and quantum process tomography, face challenges due to exponential scaling with the number of qubits, limiting their application to small system sizes and being prone to errors from state-preparation and measurement (SPAM) operations, which hinder the characterization of high-fidelity quantum processes.
Innovation Solution
The method involves performing characterization measurements to form process maps that exclude state-preparation and measurement errors, using a composition of K-qubit processes, where K is greater than 1 and less than N, and applying gate set tomography to characterize an N-qubit process by preparing K qubits of interest and N-K spectator qubits in specific states, applying circuits, and measuring the state of the K qubits of interest.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If naive quantum state tomography or quantum process tomography is used to characterize quantum processes, then complete characterization of the quantum process is achieved, but the experimental effort scales exponentially with the number of qubits
Solution Approach 1:
The patent divides the N-qubit system into K qubits of interest and N-K spectator qubits. By focusing measurements only on the K qubits and tracing out the spectator qubits, the method segments the characterization task to reduce complexity from exponential scaling with N to exponential scaling with K only, where K < N.
Solution Approach 2:
The patent extracts and removes the spectator qubits from the measurement process by preparing them in a maximally mixed state and tracing them out mathematically. This extraction eliminates the exponential complexity associated with characterizing all N qubits while preserving the essential dynamics of the K qubits of interest.
2Measurement precision
If standard quantum process tomography is used to characterize high-fidelity quantum processes, then detailed process information is obtained, but state-preparation and measurement errors overwhelm the intrinsic error
Solution Approach 1:
The patent extracts and eliminates SPAM errors by using measurement protocols that are insensitive to state-preparation and measurement inaccuracies. The method formulates process characterization in terms of process maps that can be obtained through error-mitigated measurement schemes, effectively removing the dominant error sources while preserving the ability to characterize high-fidelity quantum processes.
3Device complexity
If randomized benchmarking is used to overcome exponential scaling, then a single number characterizing the quantum process is obtained, but detailed process information is lost
Solution Approach 1:
The patent segments the quantum process into K-qubit subsystems that can be characterized individually through process maps. This segmentation allows the method to achieve polynomial scaling similar to randomized benchmarking while recovering detailed process information about each subsystem, rather than losing all detail information as in standard randomized benchmarking.
Solution Approach 2:
The patent transitions from the single-number output of randomized benchmarking to process maps that capture the full quantum dynamical behavior. By using process maps with appropriate error mitigation and segmentation, the method recovers the dimensional information lost in randomized benchmarking while maintaining improved scaling properties.
Data Source
AI summary
A method for characterizing an N-qubit process, for N an integer greater than 1. In some embodiments, the method includes performing a plurality of characterization measurements of the N-qubit process to form a plurality of process maps, and fitting the plurality of process maps with a composition of K-qubit processes, K being an integer greater than 1 and less than N.