20 Qubit Mapping: Simpler Quantum Technique

Researchers at Korea University have developed a new direct quantum state tomography scheme to address the escalating challenge of characterising quantum states, a fundamental requirement for validating quantum devices. Conventional quantum state tomography methods suffer from a prohibitive increase in complexity as the number of qubits in a system grows, rendering them impractical for larger-scale devices. Jaekwon Chang and colleagues utilise a novel fan-out coupling architecture to achieve a constant circuit depth, independent of system size, offering a potential pathway to scalable quantum state reconstruction and verification, and representing a significant advance in quantum information science.

Direct tomography characterises GHZ-state fidelity in systems of up to twenty qubits

GHZ-state fidelity estimation has now been successfully extended to 20 qubits, a substantial improvement over previous methods which were limited by the exponential scaling of measurement overhead. Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits, quickly becoming intractable for systems beyond a few qubits. This new scheme circumvents this limitation by employing a fan-out coupling architecture, which enables a constant circuit depth irrespective of qubit count. This constant depth is crucial as it limits the accumulation of errors during the quantum computation. The researchers also implemented an involutory fan-out coupling, a specific design choice that simplifies the application of quantum error mitigation techniques, leading to more reliable results even when utilising noisy intermediate-scale quantum (NISQ) processors. The fan-out coupling allows for parallel access to multiple qubits, reducing the overall circuit length and minimising the impact of decoherence and gate errors.

A four-qubit state reconstruction experiment served to validate the new direct quantum state tomography scheme on a superconducting processor accessed via the IBM Quantum Platform. This initial validation confirmed the scheme’s ability to accurately reconstruct a known quantum state. Following this, fidelity of GHZ-states, a specific type of multi-qubit entangled state, was estimated for up to 20 qubits, leveraging quantum error mitigation techniques to enhance reliability and explore the limits of this approach. The GHZ-state, or Greenberger-Horne-Zeilinger state, is a crucial resource for quantum communication and computation, and accurately assessing its fidelity is vital for building practical quantum technologies. The results demonstrate that the scheme is scalable. Future research will concentrate on optimising the error mitigation strategies employed and thoroughly assessing the impact of noise on larger quantum systems. The involutory nature of the coupling simplifies the error mitigation process by allowing for easier cancellation of systematic errors, and the constant circuit depth afforded by the architecture streamlines the process and reduces the computational demands on classical post-processing.

Scalable quantum state verification via direct tomography and error mitigation

Verifying the correct operation of quantum systems is paramount to realising the transformative potential of quantum computation. However, accurately ‘reading out’ a quantum state, a process known as quantum state tomography, remains a formidable challenge. Conventional methods require an exponentially increasing number of measurements to achieve accurate reconstruction, quickly becoming impractical for systems with more than a few qubits. This new scheme offers a compelling alternative, effectively sidestepping the exponential growth in complexity as qubit numbers rise. The approach focuses on directly measuring specific elements of the quantum state’s density matrix, rather than attempting to reconstruct the entire state at once. This is particularly advantageous for sparse target states, where only a few density matrix elements are non-zero, and for certain verification tasks where only specific properties of the state need to be confirmed. The authors acknowledge that the demonstrated error mitigation techniques haven’t been rigorously tested in isolation, meaning the extent to which they contribute to the observed performance, versus inherent improvements from the scheme itself, requires further investigation, leaving open the question of its ultimate scalability.

This direct tomography method represents a significant step forward in quantum verification, offering a potentially scalable alternative to conventional techniques. By employing a fan-out coupling architecture, the process maintains a consistent level of complexity regardless of system size, allowing for efficient access to specific quantum state elements. This selective access is achieved by strategically connecting qubits in a way that allows for parallel measurements of different parts of the quantum state. Validated on IBM Quantum Platform hardware, the scheme successfully reconstructed four-qubit states and estimated the fidelity of larger, entangled GHZ-states up to twenty qubits. The ability to accurately characterise the fidelity of GHZ-states is particularly important as these states are fundamental building blocks for many quantum algorithms and protocols, including quantum teleportation and superdense coding. The research highlights the importance of developing innovative techniques for quantum state characterisation to overcome the limitations of existing methods and pave the way for the development of practical, large-scale quantum computers. Further development could involve exploring different fan-out coupling designs and integrating more sophisticated error mitigation strategies to improve the accuracy and reliability of the scheme.

The researchers successfully demonstrated a new direct quantum state tomography scheme on a superconducting quantum processor. This method efficiently reconstructs quantum states by selectively accessing individual elements of the density matrix, offering an advantage over conventional techniques as system size increases. Validated with four qubits and extended to estimate fidelity in GHZ-states up to twenty qubits, the scheme maintains constant circuit depth and incorporates error mitigation. The authors note that further investigation is needed to fully understand the contribution of the error mitigation techniques used in the experiment.