[Paper Review] Establishing trust in quantum computations

Timothy Proctor, Stefan Seritan+5 more|arXiv (Cornell University)|Apr 15, 2022

Quantum Computing Algorithms and Architecture6 citations

TL;DR

This paper introduces Mirror Circuit Fidelity Estimation (MCFE), a scalable and efficient protocol to verify the fidelity of quantum circuit execution on noisy intermediate-scale quantum (NISQ) devices and future fault-tolerant systems. By leveraging motion reversal and randomized compilation on mirror circuits, MCFE estimates circuit fidelity with linear classical scaling and constant data requirements, avoiding exponential scaling issues of traditional tomography.

ABSTRACT

Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it is no longer always feasible to use classical simulations to directly check the correctness of quantum computations. Without practical methods for quantifying the accuracy with which a quantum algorithm has been executed, it is difficult to establish trust in the results of a quantum computation. Here we solve this problem, by introducing a simple and efficient technique for measuring the fidelity with which an as-built quantum computer can execute an algorithm. Our technique converts the algorithm's quantum circuits into a set of closely related ``mirror circuits'' whose success rates can be efficiently measured. It enables measuring the fidelity of quantum algorithm executions both in the near-term, with algorithms run on hundreds or thousands of physical qubits, and into the future, with algorithms run on logical qubits protected by quantum error correction.

Motivation & Objective

• To address the critical challenge of verifying the correctness and accuracy of quantum computations on noisy, non-simulatable quantum hardware.
• To develop a method that quantifies the fidelity of quantum algorithm execution without relying on classical simulation or special circuit properties.
• To enable trust in quantum advantage claims by providing a practical, scalable verification protocol for real-world quantum computers.
• To ensure fidelity estimation remains efficient and precise even as quantum circuits scale to hundreds or thousands of physical qubits.
• To extend verification capabilities to future logical qubit systems protected by quantum error correction.

Proposed method

• Constructs mirror circuits from the target quantum circuit using motion reversal (Loschmidt echo) to reverse the circuit's unitary evolution.
• Employs randomized compilation to isolate the fidelity of the original circuit from noise and errors in the implementation.
• Uses three distinct motion reversal circuits with randomized Pauli frames to estimate the average success probability of the mirror circuits.
• Applies a mean adjusted success probability function that approximates the product of constituent subcircuit fidelities, enabling direct estimation of the original circuit's fidelity.
• Relies on the Pauli twirl and unitary rotation properties of noise channels to ensure fidelity estimates are robust and accurate.
• Scales linearly with circuit depth and number of qubits, with data requirements independent of qubit count, avoiding exponential scaling of tomographic methods.

Experimental results

Research questions

• RQ1 How can the fidelity of a quantum circuit be efficiently estimated on a noisy, non-simulatable quantum computer?
• RQ2 Can a verification protocol be designed that scales efficiently with circuit size and remains robust to hardware noise?
• RQ3 To what extent can fidelity estimation be decoupled from the specific structure of the quantum algorithm being executed?
• RQ4 Can the method be applied to both NISQ devices and future fault-tolerant systems with logical qubits?
• RQ5 How accurately can the method estimate fidelity compared to exact simulations or known error models?

Key findings

• The MCFE protocol achieves linear classical computational complexity in the number of qubits and circuit depth, enabling scalability to large circuits.
• The amount of experimental data required to estimate fidelity to a given relative precision is independent of the number of qubits, avoiding exponential overhead.
• Simulations on QAOA circuits under four distinct error models (S, H, H+S, H-2Q) show that MCFE accurately estimates circuit fidelity within 1–2% of the true value across all models.
• The method remains robust under various noise types, including stochastic Pauli errors, over-rotation Hamiltonian errors, and readout depolarizing noise.
• MCFE successfully estimates fidelity for circuits with up to 100 physical qubits, demonstrating feasibility for near-term quantum hardware.
• The protocol enables verification of quantum advantage claims by providing a practical, efficient, and scalable method to quantify execution accuracy.