By Dr Chris Mansell, Senior Scientific Writer at Terra Quantum
Shown below are summaries of a few interesting research papers in quantum computing and communications that we have seen over the past month.
Title: Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm
Organizations: University of California, Berkeley; Lawrence Berkeley National Laboratory; Rigetti Computing
An increasingly popular method for classically simulating quantum circuits is that of tensor networks. This paper focuses on a type of tensor network called a matrix product state (MPS). As the state of a quantum circuit evolves, it becomes more entangled and more classical resources are required for the MPS to simulate it with a high fidelity. The quantum circuits in question are those of the quantum approximate optimisation algorithm that can be employed to solve Max-Cut problems. The main result is that the classical hardness of simulating such circuits is an increasing function of the entanglement per qubit. This is important for the ongoing comparison between classical simulators and NISQ processors.
Title: Graphical quantum Clifford-encoder compilers from the ZX calculus
Organizations: Massachusetts Institute of Technology; Harvard University
When dealing with a complex system, such as a quantum computer, it is important to work at the right level of abstraction. While traditional compilers map high-level programming languages into Boolean gates, the concept of compilation – as Peter Shor and coauthors point out in their recent preprint – is more general. They consider Clifford operations and compile them into ZX calculus diagrams. Compared to conventional circuit diagrams, these visualisations highlight both the information propagation from input to output as well as the entanglement structure of the output.
Title: The Basis of Design Tools for Quantum Computing: Arrays, Decision Diagrams, Tensor Networks, and ZX-Calculus
Organizations: Technical University of Munich; Software Competence Center Hagenberg; Johannes Kepler University
As quantum hardware develops, the width and depth of circuits will grow and functionalities like “mid-circuit measurement and reuse” will become more common. Various tools to insightfully design efficient, effective and useful algorithms are being developed. In this preprint, three of these tools are discussed: decision diagrams, tensor networks and ZX-calculus. Clear examples are provided in order to give the reader intuition about how and where they can best be used.
Title: Quantum machine learning of large datasets using randomized measurements
Organizations: Imperial College
Some machine learning methods may be more natural to implement on quantum processors than others. Kernel methods work well on classical computers but while they do not produce state-of-the-art results, they do have some clear connections to quantum mechanics. Their main downside is that they scale quadratically with the size of the dataset, making them impractical for big data applications. This paper shows that randomised quantum measurements allow quantum kernels to be calculated in a time that scales linearly with the dataset size. Classification of images of handwritten digits is performed on IBM quantum computers and an error mitigation technique is implemented. Distributing the quantum computation over two devices is also demonstrated. Even though the technique requires classical post-processing that scales quadratically with the amount of data, this is not an issue because of the comparatively high speed and low cost of classical computing. Hence, this approach seems to allow quantum kernel methods to be explored in a more practical way than before.
Title: Limitations of Variational Quantum Algorithms: A Quantum Optimal Transport Approach
Organizations: University of Bologna; University of New Mexico; Technische Universität München; University of Copenhagen; ENS Lyon
In the near term, it is likely that quantum processors will continue to be very noisy. Consequently, they can only be run reliably as long as there aren’t too many layers of gates. In this research, it is shown that for certain optimisation problems, noisy quantum circuits with just a few layers won’t give quantum advantages. Is it possible that a noisy quantum device performing a long sequence of gates could, by chance, give even a single output that is more helpful than a classical optimisation algorithm? To this, the research also gives a negative answer.
Title: Predicting Gibbs-State Expectation Values with Pure Thermal Shadows
The preparation and measurement of quantum states known as Gibbs states is a hard but important task in the study of quantum materials and for optimisation and machine learning.In this paper, the authors showed how the imaginary time evolution technique, that is usually used to find low energy eigenstates, could be implemented using quantum signal processing methods. They found that measuring the resulting state in randomly chosen bases means that very few measurements are required to accurately estimate the expectation values. They performed a classical simulation to show how this would work for so-called quantum Boltzmann machines. Overall, their approach could help with the training of larger machine learning models.
Title: On-demand electrical control of spin qubits
Organizations: The University of New South Wales; Diraq; Keio University; Leibniz-Institut für Kristallzüchtung; VITCON Projectconsult GmbH; Simon Fraser University
An important aspect of silicon qubits is that they can make use of the CMOS technology that has been developed by the semiconductor industry over the last several decades. In order to realise this promise of scalability, the authors of this paper have devised a simple, fast, high-fidelity, all-electrical method of controlling silicon spins. They sped up the Rabi frequency by a factor of 650 and hence achieved a single-qubit gate duration of 3 ns. Furthermore, the ability to switch the electrical interactions on and off – if it can be done more reliably – could allow the spins to be addressed with less noise.
Title: Entangling microwaves with optical light
Organizations: Institute of Science and Technology Austria; Vienna Center for Quantum Science and Technology
The coherent conversion of single photons between the optical and microwave regimes would enable superconducting quantum processors to be networked together over optical fibers. Just as the conversion between different frequencies of light is important for today’s internet, a quantum transducer could be a key component in a future quantum internet. To this end, the authors of this paper developed an optically pulsed, ultra-low noise, superconducting, cavity electro-optical modulator. They experimentally demonstrated deterministic quantum entanglement between propagating optical and microwave photons in a millikelvin environment and violated a separability criterion by more than five standard deviations.
Title: Manipulation and Certification of High-Dimensional Entanglement through a Scattering Medium
Organizations: Sorbonne Université; University of Glasgow
High-dimensional entangled states could bring enhancements to secure quantum communication protocols and high-performance microscopes. Unfortunately, quantum states are fragile when travelling through disordered and inhomogeneous media. In the atmosphere, there is turbulence while in multimode fibers, there is random mode mixing. In this work, a classical beam of light is used to infer the details of the scattering medium and then a spatial light modulator is used to prepare a pair of spatially entangled photons. By compensating for the perturbations they will experience, the researchers manage to restore their entanglement at the output of the medium. They certify 17-dimensional entanglement by measuring the photons in position and momentum bases, obtaining results that violate an Einstein-Podolski-Rosen criterion by 998 standard deviations. Experimentally compensating for the disturbances caused by thicker materials is expected to be very challenging but the demonstrated approach is a good starting point for making entangled states more robust in the real world.
Title: Provably-secure quantum randomness expansion with uncharacterised homodyne detection
Organizations: National University of Singapore; JPMorgan Chase & Co
Random number generators are an important component of many modern computing platforms. Because measuring a quantum system is a probabilistic process, the development of quantum random number generators (QRNGs) is deemed to hold great promise. The goal is to produce sequences of bits that are perfectly uniform and unpredictable. Often, a model of the QRNG equipment is needed in its security analysis but this can lead to overestimations of the amount of generated randomness, which is disastrous for security applications. If researchers can guarantee security with fewer modelling assumptions, the QRNG is described as being semi-device-independent. In this paper, a simple system based on balanced homodyne detection is constructed. Theoretically, the authors treated it as a black box that doesn’t necessarily produce independent and identically distributed outputs. They took finite-size effects into account and proved that the uncharacterised homodyne detector provides security against side-channel attacks.
Title: Approaching optimal entangling collective measurements on quantum computing platforms
Organizations: Australian National University; Friedrich-Schiller University of Jena; University of Cambridge; Institute for Experimental Physics, Innsbruck; Fraunhofer Institute for Applied Optics and Precision Engineering IOF; Max Planck School of Photonics; Macquarie University; Amazon Web Services; Institute for Quantum Optics and Quantum Information, Innsbruck; Alpine Quantum Technologies; Nanyang Technological University; Agency for Science Technology and Research (A*STAR)
Quantum states are typically thought of as being very delicate and fragile. However, this sensitivity to interactions with their surroundings means they can be used as excellent probes of environmental fields. By allowing two quantum states to undergo small Bloch sphere rotations and then performing a collective measurement on them, it is possible to estimate these rotation angles to a precision better than what can be achieved classically with the same resources. The authors of this paper managed to achieve this on several quantum computing platforms. The experiments were performed with superconducting, trapped-ion and photonic qubits. Error mitigation was investigated and insightful observations were made regarding uncertainty relations. Overall, this work paves the way to a future where quantum sensors connected to quantum processors could implement enhanced imaging and sensing protocols.
January 31, 2023