Theory: Turning noisy intermediate scale quantum information processing into practical quantum computing

An outline of our interests in these areas is provided in the figure. Results are being applied to various platforms in quantum computing with cold atoms, ions and solid-state quantum dots, and dopant-based quantum computing and simulations. Our work on understanding noise and developing fault tolerance also impacts our efforts to develop a deployable quantum current standard.

The theory of tomography, learning, and verification describes how to extract information from quantum states or processes, as well as validate the operation of quantum information processors. Full tomography provides complete information about a quantum state or process; however, the exponential scaling of quantum many-body systems implies it is only possible on systems with a small number of quantum degrees of freedom (e.g., a few qubits or oscillators). A central challenge in the field is, therefore, to develop scalable methods to probe quantum systems while maintaining as much generality or flexibility as possible. These efficient characterization efforts are crucially needed for scalable quantum computation. More generally, these efforts help inform how to “learn” from general quantum systems [1-3]. An important frontier in these problems that connects is the challenge of learning correlated or non-Markovian noise, which is particularly prevalent in solid-state quantum computing platforms [4]. Finally, this research ties into basic questions about sensing and metrology of quantum systems [5].

Another focus in our research centers around the theory of quantum error correction (QEC). To make scalable quantum computation a reality, one needs a strategy to deal with noise and imperfections in physical devices. The primary application of QEC is to fault-tolerant quantum computation, which seeks to design quantum circuits that are robust to noise in every individual component of the circuit. A foundational result in QIS is the threshold theorem that proves that reliable quantum computation is possible in the asymptotic limit, provided the noise rate is below a certain threshold value. Reliable solutions to the so-called “decoding problem” are a central need of QEC. Decoding solves the inverse problem of determining errors on an encoded quantum system using quantum measurement results. Decoding is intimately tied to problems in tomography and learning theory as it is always based on prior assumption for the type of noise affecting the quantum system. A defining goal in QEC is a general solution to the class of optimization problems that minimize the resources needed in terms of qubit overhead, noise rates, and circuit depth to achieve a given quantum algorithm or information-theoretic task. This optimization task is incredibly rich because of the interplay with the decoder and the vast family of quantum codes that have been discovered in the last several decades. We search for novel and systematic approaches to solve these outstanding problems in QEC [6-10]. A common theme in our work is to adapt methods from quantum many-body physics and statistical mechanics to analyze QEC theory, codes and protocols.

The third thrust in our research centers around the study of quantum many-body physics and quantum algorithms. One of our primary goals in this context is the development of reliable approaches to quantum simulation. Foundational remarks by Richard Feynman introduced quantum simulation as a key application of quantum computers. The amount of progress in quantum simulation in the last few decades has been remarkable as a host of platforms are now at the point where they regularly achieve quantum simulation that is near, or arguably beyond, the limit of classical computation. The long-term goal in our research is to push these results to the domain of useful quantum simulation, where the problems being studied are of industrial or broad scientific interest. In recent years we have taken steps in this direction by analyzing applications of near-term fault-tolerant systems [11-12]. A second important thread in our research is utilizing native fermionic degrees of freedoms in solid-state or cold atom devices to speed up quantum simulation of quantum chemistry and lattice gauge theory [13-14]. Finally, we are studying the dynamics of monitored quantum systems as a general way of understanding quantum error correction systems [15-20]. Looking beyond simulation, we have a strong interest in analyzing quantum many-body systems using tools in computational complexity theory. Our work in this area has focused on the complexity of quantum random sampling problems [1,12,20-24]. Another important theme in our research is developing statistical mechanics methods to describe quantum many-body dynamics. In the case of systems in thermal equilibrium, well-established methods allow one to map imaginary time evolution to a classical statistical mechanics problem. For quantum dynamics, no such general mapping is possible, but recent years have found a variety of rich correspondences between quantum and classical problems that we explore and utilize in our research [24-26].

References:
[1] D. Hangleiter and M. J. Gullans, Bell sampling from quantum circuits, Phys. Rev. Lett. 133, 020601 (2024).
[2] S. Gandhari, V. V. Albert, T. Gerrits, J. M. Taylor, and M. J. Gullans, Precision bounds on continuous-variable state tomography using classical shadows, PRX Quantum 5, 010346 (2024).
[3] J. T. Iosue, K. Sharma, M. J. Gullans, and V. V. Albert, Continuous-variable quantum state designs: theory and applications, Phys. Rev. X 14, 011013 (2024). 
[4] M. J. Gullans, M. Caranti, A. R. Mills, and J. R. Petta, Compressed gate characterization for quantum devices with time-correlated noise, PRX Quantum 5, 010306 (2024).
[5] P. Niroula, J. Dolde, X. Zheng, J. Bringewatt, A. Ehrenberg, K. C. Cox, J. Thompson, M. J. Gullans, S. Kolkowitz, and A. V. Gorshkov, Quantum sensing with erasure qubits, Phys. Rev. Lett. 133, 080801 (2024).
[6] M. J. Gullans, S. Krastanov, D. A. Huse, L. Jiang, and S. T. Flammia, Quantum coding with low-depth random circuits, Phys. Rev. X 11, 031066 (2021). 
[7] J. Nelson, G. Bentsen, S. T. Flammia, and M. J. Gullans, Fault-tolerant quantum memory using low-depth random circuit codes, (2023) arXiv:2311.17985.
[8] A. Dua, A. Kubica, L. Jiang, S. T. Flammia, and M. J. Gullans, Clifford-deformed surface codes, PRX Quantum 5, 010347 (2024).
[9] A. Fahimniya, H. Dehghani, K. Bharti, S. Mathew, A. J. Kollár, A. V. Gorshkov, and M. J. Gullans, Fault-tolerant hyperbolic Floquet quantum error correcting codes, (2023) arXiv:2309.10033.
[10] C. Cao, M. J. Gullans, B. Lackey, and Z. Wang, Quantum Lego expansions pack: Enumerators from tensor networks, PRX Quantum 5, 030313 (2024).
[11] D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. Pablo Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. S. Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletić, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature 626, 7997 (2024).
[12] D. Hangleiter, M. Kalinowski, D. Bluvstein, M. Cain, N. Maskara, X. Gao, A. Kubica, M. D. Lukin, and M. J. Gullans, Fault-tolerant compiling of classically hard IQP circuits on hypercubes, (2024) arXiv:2404.19005.
[13] A. Rad, A. Schuckert, E. Crane, G. Nambiar, F. Fei, J. Wyrick, R. M. Silver, M. Hafezi, Z. Davoudi, and M. J. Gullans, Analog quantum simulator of a quantum field theory with Fermion-spin systems in silicon, (2024) arXiv:2406.03419.
[14] A. Schuckert, E. Crane, M. Hafezi, A. V. Gorshkov, and M. J. Gullans, Fermion-qubit fault-tolerant quantum computing, (2024), arXiv:2411.08955.
[15] M. J. Gullans and D. A. Huse, Dynamical purification phase transition induced by quantum measurements, Phys. Rev. X 10, 041020 (2020).
[16] M. J. Gullans and D. A. Huse, Scalable probes of measurement-induced criticality, Phys. Rev. Lett. 125, 070606 (2020).
[17] M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, Entanglement phase transitions in measurement-only dynamics, Phys. Rev. X 11, 011030 (2021).
[18] C. Noel, P. Niroula, D. Zhu, A. Risinger, L. Egan, D. Biswas, M. Cetina, A. V. Gorshkov, M. J. Gullans, D. A. Huse, and C. Monroe, Observation of measurement-induced quantum phases in a trapped-ion quantum computer, Nature Phys. 18, 760 (2022).
[19] H. Dehgani, A. Lavasani, M. Hafezi, and M. J. Gullans, Neural-network decoders for measurement induced phase transitions, Nat. Commun. 14, 2918 (2023).
[20] P. Niroula, C. D. White, Q. Wang, C. Monroe, C. Noel and M. J. Gullans, Phase transition in magic with random quantum circuits, Nature Phys. 20, 1786 (2024). 
[21] A. Deshpande, P. Niroula, O. Shtanko, A. V. Gorshkov, B. Fefferman, and M. J. Gullans, Tight bounds on the convergence of noisy random circuits to the uniform distribution, PRX Quantum 3, 040329 (2022). 
[22] P. Niroula, S. Gopalakrishnan, and M. J. Gullans, Error mitigation thresholds in noisy random quantum circuits, (2023) arXiv:2302.04278.
[23] B. Fefferman, S. Ghosh, M. J. Gullans, K Kuroiwa, and K. Sharma, Effect of non-unital noise on random circuit sampling, PRX Quantum 5, 030317 (2024).
[24] B. Ware, A. Deshpande, D. Hangleiter, P. Niroula, B. Fefferman, A. V. Gorshkov, and M. J. Gullans, A sharp phase transition in linear cross-entropy benchmarking, (2023) arXiv:2305.04954. 
[25] G. Sommers, D. A. Huse, and M. J. Gullans, Crystalline quantum circuits, PRX Quantum 4, 030313 (2023).
[26] A. Zabalo, M. J. Gullans, J. H. Wilson, R. Vasseur, A. W. W. Ludwig, S. Gopalakrishnan, D. A. Huse, and J. H. Pixley, Operator scaling dimensions and multifractality at measurement-induced transitions, Phys. Rev. Lett. 128, 050602 (2022).