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Jacob Biamonte portrait

Photo: Vincent Lemelin

Jacob Biamonte

Professor

Chairholder, MEIE Principal Research Chair in Quantum Computing

What Minimal Structure Enables Quantum Computation?

I study computational models between efficient classical simulation and universal quantum computation. I examine how interactions, rules of composition, and the statistical structure of problem-instance families determine what these models can compute.

Selected concepts and frameworks. Concepts and frameworks reported in my single- and coauthored publications include ground-state spin logic (1, 2); categorical tensor-network states, including a construction for representing arbitrary n-qubit states using specified tensor building blocks and a demonstration that AND, COPY, and |−⟩ tensors can realize a computationally universal gate set (3); continuous-time chiral quantum walks obtained by breaking time-reversal symmetry (4); spectral-entropy measures for comparing complex networks (5); reachability deficits in QAOA (6); and training saturation in layerwise QAOA (7).

Selected results. The cited publications establish QMA-completeness for two restricted families of 2-local Hamiltonians containing one-local X/Z terms and two-local XX/ZZ or ZX/XZ couplings (8); perturbative-gadget constructions used to establish restricted XX/ZZ and ZX/XZ models and to simulate effective YY couplings using XX/ZZ-type interactions (8, 9); gate-complexity and resource analyses for quantum simulation of electronic-structure Hamiltonians (10); tensor-network representations of polynomial local-unitary invariants, with matrix-product states as a principal example (11); polynomial-time contraction for counting problems whose tensor-network expressions contain O(log n) COPY tensors with polynomially bounded fan-out (12); a graphical calculus relating the Liouville, Choi, process-matrix, Kraus, and system–environment representations of completely positive maps (13); precise universality conditions for a class of one-dimensional QAOA constructions, with extensions to specified graph and hypergraph cost Hamiltonians (14); and two objective-function constructions establishing the computational universality of variational quantum computation (15).

I also coauthored experimental studies of photonic quantum chemistry in 2010 (16), chiral quantum walks in 2016 (17), and quantum adversarial learning with superconducting qubits in 2022 (21). My publications also include work on quantum complex networks (5, 20) and quantum machine learning (18, 21).

The Research Program Introduction gives readers new to the topic a guided visual introduction and presents technical results and references organized across Physical Models → Programming Languages → Emergent Properties.

Annotated References

Some of this work is reviewed in Quantum Machine Learning (18), Tensor Networks in a Nutshell (19), and Complex Networks from Classical to Quantum (20).

  1. Nonperturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spinsJ. BiamontePhysical Review A 77, 052331 (2008).Related Boolean-to-Ising reduction methods were later used in invertible probabilistic logic, including a stochastic-MTJ p-bit demonstration of integer factorization.
  2. Ground-state spin logicJ. Whitfield, M. Faccin, and J. BiamonteEurophysics Letters 99, 57004 (2012).Provided a symmetry-group analysis of the logical gadgets introduced as part of the framework in (1).
  3. Categorical tensor network statesJ. Biamonte, S. Clark, and D. JakschAIP Advances 1, 042172 (2011).This paper transferred the ground-space-span representation of Boolean logic developed in (1) into tensor networks and established two distinct forms of universality. AND, COPY, and parameterized rank-one tensors are expressively complete: every tensor—or, equivalently after reshaping, every vector—in the target space can be represented by a tensor network constructed from them. AND, COPY, and |−⟩ tensors are computationally universal: they can realize the Hadamard and Toffoli gates and therefore simulate any quantum circuit. The framework also connects these constructions to graphical structures used in categorical quantum mechanics, including spiders.
  4. Quantum transport enhancement by time-reversal symmetry breakingZ. Zimborás, M. Faccin, Z. Kádár, J. Whitfield, B. P. Lanyon, and J. BiamonteScientific Reports 3, 2361 (2013).This work introduced the term chiral quantum walk for time-reversal-symmetry-breaking quantum-walk dynamics. The effect was subsequently implemented experimentally in (17) and later developed for chiral quantum routing.
  5. Spectral entropies as information-theoretic tools for complex network comparisonM. De Domenico and J. BiamontePhysical Review X 6, 041062 (2016).
  6. Reachability deficits in quantum approximate optimizationV. Akshay, H. Philathong, M. Morales, and J. BiamontePhysical Review Letters 124, 090504 (2020).A later study, motivated by Google’s QAOA experiment, reproduced the reported problem setting in an ideal noiseless simulation and found that the studied regime approached a density-dependent fall-off in approximation quality.
  7. Training saturation in layerwise quantum approximate optimisationE. Campos, D. Rabinovich, V. Akshay, and J. BiamontePhysical Review A 104, L030401 (2021). Letter.The work showed that single-layer training can halt at critical values and, under the studied conditions, can be revived by certain types of noise.
  8. Realizable Hamiltonians for universal adiabatic quantum computersJ. Biamonte and P. LovePhysical Review A 78, 012352 (2008).Co-inventor of US 11,816,536 B2, “Physical realizations of a universal adiabatic quantum computer,” assigned to D-Wave Systems.
  9. Hamiltonian gadgets with reduced resource requirementsY. Cao, R. Babbush, J. Biamonte, and S. KaisPhysical Review A 91, 012315 (2015).The fourth-order YY gadget, together with the Bravyi–Kitaev transformation, provides an in-principle effective low-energy encoding route from electronic-structure Hamiltonians to the restricted interaction families in (8), with ancillary-qubit and perturbative overhead.
  10. Simulation of electronic structure Hamiltonians using quantum computersJ. Whitfield, J. Biamonte, and A. Aspuru-GuzikMolecular Physics 109, 735–750 (2011).A Molecular Physics Young Author Prize was awarded to James D. Whitfield for this paper in the 2011 prize cycle; the award was announced in 2012.
  11. Tensor network methods for invariant theoryJ. Biamonte, V. Bergholm, and M. LanzagortaJournal of Physics A: Mathematical and Theoretical 46, 475301 (2013).
  12. Tensor network contractions for #SATJ. Biamonte, J. Morton, and J. TurnerJournal of Statistical Physics 160, 1389–1404 (2015).
  13. Tensor networks and graphical calculus for open quantum systemsC. J. Wood, J. D. Biamonte, and D. G. CoryQuantum Information & Computation 15, 759–811 (2015).A derivation using the identity typically called the snake equation later appeared on a blackboard in Rick and Morty, “Rattlestar Ricklactica” (Season 4, Episode 5). Context and earlier references.
  14. On the universality of the quantum approximate optimization algorithmM. E. S. Morales, J. D. Biamonte, and Z. ZimborásQuantum Information Processing 19, 291 (2020).
  15. Universal variational quantum computationJ. BiamontePhysical Review A 103, L030401 (2021).APS Editors’ Suggestion; Letter.
  16. Towards quantum chemistry on a quantum computerB. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. WhiteNature Chemistry 2, 106–111 (2010).
  17. Chiral quantum walksD. Lu, J. Biamonte, J. Li, H. Li, T. H. Johnson, V. Bergholm, M. Faccin, Z. Zimborás, R. Laflamme, J. Baugh, and S. LloydPhysical Review A 93, 042302 (2016).Experimental follow-on to (4).
  18. Quantum machine learningJ. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. LloydNature 549, 195–202 (2017).
  19. Tensor Networks in a NutshellJ. Biamonte and V. BergholmarXiv:1708.00006 (2017).
  20. Complex networks from classical to quantumJ. Biamonte, M. Faccin, and M. De DomenicoCommunications Physics 2, 53 (2019).
  21. Experimental quantum adversarial learning with programmable superconducting qubitsW. Ren, W. Li, S. Xu, K. Wang, W. Jiang, F. Jin, X. Zhu, J. Chen, Z. Song, P. Zhang, H. Dong, X. Zhang, J. Deng, Y. Gao, C. Zhang, Y. Wu, B. Zhang, Q. Guo, H. Li, Z. Wang, J. Biamonte, C. Song, D.-L. Deng, and H. WangNature Computational Science 2, 711–717 (2022).