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Quantum process tomography: high fidelity methods

Станчо Станчев, Stancho G. Stanchev

Published Sep 17, 2024• 0 citations
OpenAlex

Abstract

The dissertation "Quantum Process Tomography: High Fidelity Methods" focuses on quantum tomographic methods using repeated (multi-pass) applications of quantum processes, which allows for the amplification of very small errors to measurable levels. The thesis is based on three studies that illustrate this approach. The first study introduces the Multi-pass Quantum Process Tomography (MQPT) method, which mitigates the measurement errors caused by state preparation and measurement (SPAM), readout errors, and statistical (shot noise) errors. The method employs some standard tomographic techniques applied to a multi-pass quantum gate or process, after which the single process is determined with significantly higher accuracy and precision through post-processing. The effectiveness of MQPT has been demonstrated through simulations and experiments on IBM Quantum processors, achieving substantial enhancement on accuracy and precision. The second study investigates the dynamics of quantum multi-level systems interacting with pulse sequences that exhibit Wigner-Majorana and Morris-Shore symmetries. Exact analytical formulas have been derived to describe these processes, revealing important characteristics of these interactions. The third study focuses on precision methods for characterization of high fidelity Raman qubit gates with Morris-Shore dynamic symmetry. By repeatedly applying the same gate, coherent errors are amplified to measurable levels, enabling more precise...

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The dissertation "Quantum Process Tomography: High Fidelity Methods" focuses on quantum tomographic methods using repeated (multi-pass) applications of quantum processes, which allows for the amplification of very small errors to measurable levels. The thesis is based on three studies that illustrate this approach. The first study introduces the Multi-pass Quantum Process Tomography (MQPT) method, which mitigates the measurement errors caused by state preparation and measurement (SPAM), readout errors, and statistical (shot noise) errors. The method employs some standard tomographic techniques applied to a multi-pass quantum gate or process, after which the single process is determined with significantly higher accuracy and precision through post-processing. The effectiveness of MQPT has been demonstrated through simulations and experiments on IBM Quantum processors, achieving substantial enhancement on accuracy and precision. The second study investigates the dynamics of quantum multi-level systems interacting with pulse sequences that exhibit Wigner-Majorana and Morris-Shore symmetries. Exact analytical formulas have been derived to describe these processes, revealing important characteristics of these interactions. The third study focuses on precision methods for characterization of high fidelity Raman qubit gates with Morris-Shore dynamic symmetry. By repeatedly applying the same gate, coherent errors are amplified to measurable levels, enabling more precise...
We introduce a method to enhance the precision and accuracy of Quantum Process Tomography (QPT) by mitigating the errors caused by state preparation and measurement (SPAM), readout and shot noise. Instead of performing QPT solely on a single gate, we propose performing QPT on a sequence of multiple applications of the same gate. The method involves the measurement of the Pauli transfer matrix (PTM) by standard QPT of the multipass process, and then deduce the single-process PTM by two alternative approaches: an iterative approach which in theory delivers the exact result for small errors, and a linearized approach based on solving the Sylvester equation. We examine the efficiency of these two approaches through simulations on IBM Quantum using ibmq_qasm_simulator. Compared to the Randomized Benchmarking type of methods, the proposed method delivers the entire PTM rather than a single number (fidelity). Compared to standard QPT, our method delivers PTM with much higher accuracy and precision because it greatly reduces the SPAM, readout and shot noise errors. We use the proposed method to experimentally determine the PTM and the fidelity of the CNOT gate on the quantum processor ibmq_manila (Falcon r5.11L).
We introduce a method to enhance the precision and accuracy of Quantum Process Tomography (QPT) by mitigating the errors caused by state preparation and measurement (SPAM), readout and shot noise. Instead of performing QPT solely on a single gate, we propose performing QPT on a sequence of multiple applications of the same gate. The method involves the measurement of the Pauli transfer matrix (PTM) by standard QPT of the multipass process, and then deduce the single-process PTM by two alternative approaches: an iterative approach which in theory delivers the exact result for small errors, and a linearized approach based on solving the Sylvester equation. We examine the efficiency of these two approaches through simulations on IBM Quantum using IBMQ_QASM_SIMULATOR. Compared to the Randomized Benchmarking type of methods, the proposed method delivers the entire PTM rather than a single number (fidelity). Compared to standard QPT, our method delivers PTM with much higher accuracy and precision because it greatly reduces the SPAM, readout and shot noise errors. We use the proposed method to experimentally determine the PTM and the fidelity of the CNOT gate on the quantum processor IBMQ_MANILA (Falcon r5.11L).
Accurate and robust quantum process tomography (QPT) is crucial for verifying quantum gates and diagnosing implementation faults in experiments aimed at building universal quantum computers. However, the reliability of QPT protocols is often compromised by faulty probes, particularly state preparation and measurement (SPAM) errors, which introduce fundamental inconsistencies in traditional QPT algorithms. We propose and investigate enhanced QPT for multiqubit systems by integrating the error matrix in a digital twin of the identity process matrix, enabling statistical refinement of SPAM error learning and improving QPT precision. Through numerical simulations, we demonstrate that our approach enables highly accurate and faithful process characterization. We further validate our method experimentally in superconducting quantum processors, achieving at least an order-of-magnitude fidelity improvement over standard QPT. Our results provide a practical and precise method for assessing quantum gate fidelity and enhancing QPT on a given hardware.
In the era of noisy intermediate-scale quantum computing, it is of crucial importance to verify quantum processes and extract information. Quantum process tomography is a typical approach, however, both resource-intensive and vulnerable to state preparation and measurement errors. Here, we propose an error-mitigated entanglement-assisted quantum process tomography (EM-EAPT) framework to address these limitations. By leveraging a maximally entangled state to reduce state preparation complexity and integrating error mitigation techniques, our method significantly enhances robustness against SPAM errors. Experimental validation on a superconducting processor demonstrates the efficacy of EM-EAPT for two-qubit and three-qubit quantum processes. Results show more accurate average gate fidelities close to the realistic estimation, achieving 98.1±\pm± 0.03% for a CNOT gate and 88.1%±\pm± 0.04% for a cascaded CNOT process after error mitigation, compared to non-mitigated implementations. This work advances practical quantum verification tools for NISQ devices, enabling higher-fidelity characterization of quantum processes under realistic noise conditions.
Raman qubits, represented by two ground or metastable quantum states coupled via an intermediate state, hold some advantages over directly coupled qubits, most notably much longer radiative lifetimes, shorter gate duration, and lower radiation intensity due to using electric-dipole allowed optical transitions. They are also relatively simple to implement and control, making them an attractive option for building quantum gates for quantum computers. In this work, we present a simple and fast tomographic method to measure the errors of Raman qubit gates possessing the Morris-Shore dynamic symmetry. The latter occurs when the qubit states are on two-photon resonance and the driving fields have the same time dependence. The method is based on repeating the same gate multiple times, which amplifies the small coherent errors to sufficiently large values, which can be measured with high accuracy and precision. Then the (small) gate errors can be determined from the amplified errors by using the analytical connections between them.
Abstract In quantum computation the target fidelity of the qubit gates is very high, with the admissible error being in the range from 10−3 to 10−4 and even less, depending on the protocol. The direct experimental determination of such a tiny error is very challenging by standard quantum-process tomography. Instead, the method of randomized benchmarking, which uses a random sequence of Clifford gates, has become a standard tool for determination of the average gate error as the decay constant in the exponentially decaying fidelity. In this paper, the task for determining a tiny error is addressed by sequentially repeating the same gate multiple times, which leads to the coherent amplification of the error, until it reaches large enough values to be measured reliably. If the transition probability is p = 1 − ϵ with ϵ ≪ 1 in the single process, then classical intuition dictates that the probability after N passes should be P N ≈ 1 − N ϵ . However, this classical expectation is misleading because it neglects interference effects. This paper presents a rigorous theoretical analysis based on the SU(2) symmetry of the qubit propagator, resulting in explicit analytic relations that link the N-pass propagator to the single-pass one in terms of Chebyshev polynomials. In particular, the relations suggest that in some special cases the N-pass transition probability degrades as P N = 1 − N 2 ϵ , i.e. dramatically faster than the classical probability estimate. In the general case, however, the relation between the single-pass and N-pass propagators is much more involved. Recipes are proposed for unambiguous determination of the gate errors in the general case for both Clifford and non-Clifford gates.