Hybrid Quantum-Classical Trace Estimation With Informationally Complete POVMs
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Solution Overview
Problem
Complex computational problems, such as simulating quantum-mechanical systems, are resource-intensive for classical computers and challenging for quantum computers due to errors in state preparation and measurement, making efficient estimation of trace values intractable.
Innovation Solution
A hybrid quantum-classical computing system uses a quantum computing unit and a classical computer to estimate the trace of a density operator through a method involving repeated quantum measurements, linear maps, and classical post-processing to overcome noise and error issues, allowing efficient calculation of trace values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quantum error correction is used to correct errors from noisy gates, then the reliability of quantum state preparation is improved, but the device complexity increases due to additional qudits and increased runtime
Solution Approach 1:
The patent introduces a classical post-processing step as an intermediary between quantum measurement and final result interpretation. The classical computer processes measurement outcomes to estimate trace values, effectively mediating the connection between noisy quantum measurements and reliable computational results without requiring additional quantum resources for error correction
Solution Approach 2:
The patent replaces the quantum mechanical error correction mechanism with a classical computational approach. Instead of using quantum gates and additional qudits to correct errors, the system uses classical algorithms to process measurement data and extract accurate trace estimates, substituting quantum error correction with classical data processing
2Productivity
If the dimension of quantum systems increases to solve more complex problems, then the productivity of quantum computing is improved, but the memory requirements for classical computers become prohibitive
Solution Approach 1:
The patent extracts only the necessary measurement outcomes from quantum systems and processes only the essential data needed for trace estimation on classical computers. By taking out and processing only the relevant information rather than full quantum state representations, the method avoids the exponential memory growth that would otherwise be required
Solution Approach 2:
The patent segments the computational task into quantum measurement phase and classical post-processing phase. The quantum system handles state preparation and measurement, while the classical system handles trace estimation through structured algorithms that process measurement outcomes in a memory-efficient manner, dividing the overall computation to avoid prohibitive memory requirements
3Measurement precision
If quantum detector tomography is used to calibrate detectors and reduce readout error, then the measurement precision is improved, but the loss of time increases due to requirement of prepared trial states for calibration
Solution Approach 1:
The patent performs detector calibration and characterization in advance through quantum detector tomography, storing the obtained calibration data for reuse. By performing the time-consuming calibration action beforehand and reusing the results across multiple measurements, the method achieves high measurement precision without repeating the calibration process for each measurement task
Solution Approach 2:
The patent changes the operational parameters of the quantum system by operating in a regime where calibration is performed once and then the system operates with stored calibration characteristics. This parameter change from repeated calibration to single calibration with reuse reduces the time loss while maintaining measurement precision through the use of stored calibration data
Data Source
AI summary
The invention is related to a method for performing computation using a hybrid quantum-classical computing system comprising a quantum computing unit and a classical computer, said quantum computing unit comprising a quantum system defined by a set Q of N qudits, preferably a set Q of N qubits, and control means, said control means being operative to prepare a quantum state of said quantum system, said quantum state being described by a density operator σ acting on a Hilbert space H associated with said quantum system, to perform a quantum measurement defined by an informationally complete Positive Operator Valued Measure on said prepared quantum state, said informationally complete Positive Operator Valued Measure being described by an integer number NM of effects Πm, m=1, . . . , NM, the effects being preferably K-producible, K≥1, the effect Πm having a measurement outcome m, and to output the measurement outcome of said quantum measurement. The invention is further related to a hybrid quantum-classical computing system and to a computer program for execution by a classical computer of a hybrid quantum-classical computing system.