Jacob Biamonte portrait

Photo: Vincent Lemelin

Jacob Biamonte

Professor and MEIE Chairholder in Quantum Computing

ÉTS, Université du Québec

What Minimal Structure Enables Quantum Computation?

I build and analyze models of computation that lie between efficient classical simulation and universal quantum computation. Selected Results:

Minimal interactions can still support universal ground-state quantum computation. With Peter Love, we discovered that systems with local X and Z terms and two-qubit ZX/XZ interactions can embed universal ground-state quantum computation. The associated ground-state problem is QMA-complete—meaning it remains as difficult as the general quantum ground-state problem. (1)

Quantum states can be expressed using a small algebraic vocabulary. With Stephen Clark and Dieter Jaksch, we developed a systematic way to represent arbitrary multiqubit states using tensor building blocks with defined algebraic rules. This provides a normal-form language connecting tensor networks, logic, and computation. (2)

The structure of a tensor network can make a hard counting problem tractable. With collaborators, we identified a class of counting problems whose tensor networks can be contracted efficiently, despite counting being difficult in general. (3)

Calculating expected values is universal in principle. I constructed expected-value objective functions whose solutions reproduce the outputs of arbitrary quantum circuits, establishing feed-forward variational quantum computation as a universal model—not merely a heuristic family of algorithms. (4)

Other concepts and results: My single-authored and collaborative publications also include:

For an accessible introduction, read Terra Incognita. Technical results and references can be explored through the Research Program page, organized across Models of Computation → Programming Languages → Emergent Properties.

Annotated References

Some of this work is synthesized in the Nature Perspective Quantum Machine Learning (11), and in the reviews Tensor Networks in a Nutshell (15) and Complex Networks from Classical to Quantum (14).

  1. 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.
  2. 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 (5) into tensor networks and gave a constructive normal form. AND, COPY, and parameterized rank-one tensors are expressively complete: every tensor—or, equivalently after reshaping, every vector—in the target space can be built directly from them. The proof works within the tensor-network language instead of establishing universality indirectly through a quantum gate set. The framework also connects these constructions to graphical structures used in categorical quantum mechanics, including spiders.
  3. Tensor network contractions for #SATJ. Biamonte, J. Morton, and J. TurnerJournal of Statistical Physics 160, 1389–1404 (2015).
  4. Universal variational quantum computationJ. BiamontePhysical Review A 103, L030401 (2021).APS Editors’ Suggestion; Letter.
  5. 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.
  6. 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 (5).
  7. 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 (8) and later developed for chiral quantum routing.
  8. 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 (7).
  9. 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.
  10. 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.
  11. Quantum machine learningJ. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. LloydNature 549, 195–202 (2017).
  12. 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).
  13. Spectral entropies as information-theoretic tools for complex network comparisonM. De Domenico and J. BiamontePhysical Review X 6, 041062 (2016).
  14. Complex networks from classical to quantumJ. Biamonte, M. Faccin, and M. De DomenicoCommunications Physics 2, 53 (2019).
  15. Tensor Networks in a NutshellJ. Biamonte and V. BergholmarXiv:1708.00006 (2017).
  16. 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 (1), with ancillary-qubit and perturbative overhead.
  17. 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.
  18. Tensor network methods for invariant theoryJ. Biamonte, V. Bergholm, and M. LanzagortaJournal of Physics A: Mathematical and Theoretical 46, 475301 (2013).
  19. 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.
  20. On the universality of the quantum approximate optimization algorithmM. E. S. Morales, J. D. Biamonte, and Z. ZimborásQuantum Information Processing 19, 291 (2020).
  21. 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).