Algorithmiq’s Tensor-Network Error Mitigation (TEM) Qiskit Function.
Summary
A hybrid quantum-classical algorithm, Algorithmiq’s Tensor-network Error Mitigation (IBM TEM) technique is intended to handle noise mitigation solely at the classical post-processing step. TEM is a very appealing choice for both industry practitioners and quantum researchers because it allows the user to calculate the expectation values of observables with more precision and cost effectiveness while eliminating the unavoidable noise-induced mistakes that occur on quantum hardware.
In order to obtain unbiased estimators for the observables, the method entails building a tensor network that represents the inverse of the global noise channel affecting the quantum processor’s state. The map is then applied to informationally complete measurement outcomes obtained from the noisy state.
As a benefit, IBM TEM uses informationally full measurements to access a large collection of mitigated expectation values of observables and has optimal sampling overhead on quantum technology. as described in Filippov at al. (2023), and Filippov at al. (2024). A crucial component of the viability of quantum calculations, the measurement overhead is the quantity of extra measurements needed to carry out effective error mitigation. As a result, TEM may be able to provide quantum advantage in challenging situations, including simulations of tiny molecules, quantum chaos, many-body physics, and Hubbard dynamics.
Primary attributes and advantages of IBM TEM:
Optimal measurement overhead
There is no technique that can obtain a lower measurement overhead than IBM TEM, which is ideal in terms of theoretical limits. To put it another way, TEM needs the fewest extra measurements possible in order to mitigate errors. As a result, IBM TEM requires very little quantum runtime.
Cost-effectiveness
There is no need to add additional circuits to the quantum computer since IBM TEM takes care of noise reduction completely in the post-processing step. This reduces the possibility of adding more faults because of the flaws in quantum devices and also lowers the cost of computing.
Estimation of multiple observables
IBM TEM effectively estimates numerous observables using the same measurement data from the quantum computer because of informationally-complete measurements.
Measurement error mitigation
After a brief calibration run, the IBM TEM Qiskit Function’s patented measurement error mitigation technique may also greatly lower readout errors.
Accuracy
Digital quantum simulations are more accurate and reliable using IBM TEM, making quantum algorithms more reliable.
Description
With little sampling overhead, you can get error-mitigated expectation values for a number of observables on a quantum circuit using the IBM TEM function. An informationally complete positive operator-valued measure is used to measure the circuit, and a traditional computer is used to handle the measurement results. The tensor network techniques and the construction of a noise-inversion map are carried out using measurement. Tensor networks are used to represent the noisy layers in the function, which applies a map that completely inverts the noisy circuit.
The circuits are optimised to reduce the number of layers using two-qubit gates (the noisier gates on quantum devices) after being subjected to the function.
The noise model captures delicate aspects, such as qubit cross-talk, and accurately describes the noise on the device. Nevertheless, noise on the devices may drift and vary, and the learnt noise may not be precise when the estimation is made. This might lead to erroneous findings.
Does tensor network error mitigation increase quantum computation precision and efficacy over earlier noise reduction methods?
Tensor-network Error Mitigation (TEM) improves the accuracy and efficiency of quantum computations over conventional noise reduction methods by virtue of a number of important characteristics.
Improvements in Accuracy
By building a tensor network that depicts the inverse of the global noise channel influencing the state of the quantum processor, IBM TEM seeks to increase accuracy. In order to mitigate noise-induced errors, TEM provides unbiased estimators for the observables by applying this inverse map to informationally full measurement outputs.
The technique greatly increases digital quantum simulations’ accuracy and dependability, increasing the precision and dependability of quantum algorithms.
After a quick calibration run, the IBM TEM Qiskit Function’s innovative measurement error mitigation technique may significantly lower readout errors. A significant source of noise in quantum calculations is addressed here.
A sparse Pauli-Lindblad noise model, which is said to provide a realistic representation of the noise and able to capture delicate aspects like qubit cross-talk, is used in Qiskit Runtime to learn the noise impacting the layers of the quantum device. More efficient error mitigation is probably facilitated by this thorough noise modelling.
Improvements in Efficiency
According to theoretical constraints, IBM TEM achieves optimum measurement overhead, which means it needs the fewest extra measurements to carry out effective error mitigation. In contrast to techniques that call for more thorough sampling, this results in a minimal quantum runtime.
The addition of additional circuits to the quantum computer is not necessary since IBM TEM manages noise reduction completely at the classical post-processing step. When creating more complicated circuits for various error mitigation strategies, this not only lowers the computational cost but also lessens the possibility of adding further faults that might result from flaws in quantum devices.
TEM effectively estimates many observables using the same measurement data acquired from the quantum computer by using informationally-complete measurements. The computing process is more efficient overall when more information can be gleaned from a single set of measurements.
Circuits are transpiled and optimised to reduce the number of layers with two-qubit gates typically the noisier gates on quantum devices when they are exposed to the IBM TEM function. By lessening the effect of noise during the actual quantum computing, this pre-processing phase can improve the efficacy of the error mitigation that follows.
To summarise, IBM TEM sets itself apart by employing tensor networks and informationally complete measurements to classically invert the noise channel. This approach improves accuracy while minimising measurement overhead and reducing costs by obviating the need for additional quantum resources for mitigation.
