About

Bojko Bakalov is a professor and the Director of Graduate Programs in the Department of Mathematics at NC State University. He holds a PhD in Mathematics from the Massachusetts Institute of Technology, obtained in 2000. His areas of expertise include mathematical physics, quantum computing, representation theory, and integrable systems. Bakalov has made significant contributions to the understanding of the connection between classical and quantum descriptions of spin waves using quantum circuits, as well as advancements in geometric quantum machine learning with horizontal quantum gates. His research also encompasses the study of Poisson pseudoalgebras, logarithmic vertex algebras, and the classification of dynamical Lie algebras of spin systems, among other topics. Recognized for his scholarly work, he received the Hermann Weyl Prize in 2006.

Research topics

• Computer Science
• Mathematics
• Pure mathematics
• Mathematical analysis
• Physics
• Quantum mechanics
• Discrete mathematics
• Algorithm
• Statistical physics

Selected publications

• Connection between classical and quantum descriptions of spin waves using quantum circuits

  Physica Scripta · 2026-02-19

  articleOpen access

  Abstract A quantum computing circuit is presented that approximates a single spin wave quantum on a linear chain of spin 1/2 particles described by a Heisenberg Hamiltonian. The circuit is a product state where each qubit represents a spin. The spin wave motion is represented by opening the cone angle using Y rotations and then adding progressive Z rotations along the chain to represent wave propagation. We show analytically that this product state yields the correct dispersion relation in the limit of an unbounded chain. This observation is confirmed using both a simulator and various quantum processors. The use of the quantum computing paradigm in this case does not lead to a computational advantage, but rather leads to a novel conceptual connection between classical and quantum descriptions of spin waves, and may also be useful for characterizing the error in quantum processors.

  PublisherDOI

• Efficient Qubit Simulation of Hybrid Oscillator-Qubit Quantum Computation

  arXiv (Cornell University) · 2026-03-10

  preprintOpen access

  We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method efficiently simulates all Gaussian and conditional Gaussian operations -- encompassing the phase-space instruction set (beam splitter, single-qubit rotation, conditional displacement) and extending to squeezing, conditional squeezing, conditional rotation, and conditional beam splitter -- using $O\!\left(\log^2\!\left(Γ+ \log(1/ε)\right)\right)$ qubit gates per hybrid gate, where $Γ$ is the Fock-level bound and $ε$ is the target precision. This polylogarithmic per-gate complexity represents an exponential improvement over Fock basis encoding approaches, which require exponential quantum or classical resources in the number of qubits per mode. We provide rigorous numerical characterization of quantum Fourier transform errors for Fock-bounded states, enabling precise resource estimation for practical implementations. This work establishes that hybrid oscillator-qubit algorithms can be implemented on qubit processors with polynomial overhead, providing new insights into the computational power trade-offs between discrete-variable and hybrid continuous-discrete-variable quantum computing.

  PublisherDOI

• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors

  ArXiv.org · 2026-02-25

  articleOpen access1st authorCorresponding

  The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$ in the Hamiltonian formulation. We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large $N_f$ and $L$. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$ using the adaptive-variational quantum imaginary time algorithm. In addition, we also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class. Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models relevant for chiral symmetry breaking, understanding dimensional transmutation, and exploring the conformal window of field theories on near-term and early fault-tolerant quantum computers.

  PublisherOA PDF

• Efficient Qubit Simulation of Hybrid Oscillator-Qubit Quantum Computation

  ArXiv.org · 2026-03-10

  articleOpen access

  We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method efficiently simulates all Gaussian and conditional Gaussian operations -- encompassing the phase-space instruction set (beam splitter, single-qubit rotation, conditional displacement) and extending to squeezing, conditional squeezing, conditional rotation, and conditional beam splitter -- using $O\!\left(\log^2\!\left(Γ+ \log(1/ε)\right)\right)$ qubit gates per hybrid gate, where $Γ$ is the Fock-level bound and $ε$ is the target precision. This polylogarithmic per-gate complexity represents an exponential improvement over Fock basis encoding approaches, which require exponential quantum or classical resources in the number of qubits per mode. We provide rigorous numerical characterization of quantum Fourier transform errors for Fock-bounded states, enabling precise resource estimation for practical implementations. This work establishes that hybrid oscillator-qubit algorithms can be implemented on qubit processors with polynomial overhead, providing new insights into the computational power trade-offs between discrete-variable and hybrid continuous-discrete-variable quantum computing.

  PublisherOA PDF

• Classification of dynamical Lie algebras generated by spin interactions on undirected graphs

  Journal of Mathematical Physics · 2026-05-01 · 3 citations

  preprintOpen accessSenior author

  Dynamical Lie algebras (DLAs) are a versatile tool for various topics that span from the expressibility-trainability of variational quantum algorithms (VQAs), to simulation of many body Hamiltonians. Quantum gates and most of the Hamiltonians of interest consist of local interactions; therefore, the analysis of all possible DLAs generated by 1- and 2-local operators is crucial for quantum simulation and VQAs on current hardware. Previously in [R. Wiersema et al., npj Quantum Inf. 10, 110 (2024)], we analyzed the DLAs on linear, circular and all-to-all topologies, and obtained results about their dimensions and algebraic structure. In this work, we extend our analysis into any possible hardware topology and provide a classification of all DLAs generated by Pauli strings on any undirected interaction graph. Our results indicate that the DLAs depend solely on whether the connectivity or interaction graph is bipartite or not. In addition, we find that the non-trivial polynomially scaling DLAs appear only on 1D line or circle topologies, and all other DLAs have dimensions scaling exponentially with the system size. Together with the current VQA literature, our results imply that either the majority of VQAs are non-trainable, or we are yet to understand the role of DLAs on the trainability of VQAs.

  PublisherOA PDFDOI

• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors

  Open MIND · 2026-02-25

  preprint1st authorCorresponding

  The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$ in the Hamiltonian formulation. We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large $N_f$ and $L$. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$ using the adaptive-variational quantum imaginary time algorithm. In addition, we also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class. Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models relevant for chiral symmetry breaking, understanding dimensional transmutation, and exploring the conformal window of field theories on near-term and early fault-tolerant quantum computers.

  DOI

• Implementing Finite Impulse Response Filters on Quantum Computers

  ArXiv.org · 2025-01-17

  preprintOpen access

  While signal processing is a mature area, its connections with quantum computing have received less attention. In this work, we propose approaches that perform classical discrete-time signal processing using quantum systems. Our approaches encode the classical discrete-time input signal into quantum states, and design unitaries to realize classical concepts of finite impulse response (FIR) filters. We also develop strategies to cascade lower-order filters to realize higher-order filters through designing appropriate unitary operators. Finally, a few directions for processing quantum states on classical systems after converting them to classical signals are suggested for future work.

  PublisherOA PDFDOI

• Approximate Message Passing for Quantum State Tomography

  ArXiv.org · 2025-11-17

  preprintOpen access

  Quantum state tomography (QST) is an indispensable tool for characterizing many-body quantum systems. However, due to the exponential scaling of the cost of the protocol with system size, many approaches have been developed for quantum states with specific structure, such as low-rank states. In this paper, we show how approximate message passing (AMP), an algorithmic framework for sparse signal recovery, can be used to perform low-rank QST. AMP provides asymptotically optimal performance guarantees for large sparse recovery problems, which suggests its utility for QST. We discuss the design challenges that come with applying AMP to QST, and show that by properly designing the AMP algorithm, we can reduce the reconstruction error by over an order of magnitude compared to existing approaches to low-rank QST. We also performed tomographic experiments on IBM Kingston and considered the effect of device noise on the reliability of the predicted fidelity of state preparation. Our work advances the state of low-rank QST and may be applicable to other quantum tomography protocols.

  PublisherOA PDFDOI

• Implementing Finite Impulse Response Filters on Quantum Computers

  2025-03-12 · 1 citations

  article

  While signal processing is a mature area, its connections with quantum computing have received less attention. In this work, we propose approaches that perform classical discrete-time signal processing using quantum systems. Our approaches encode the classical discrete-time input signal into quantum states, and design unitaries to realize classical concepts of finite impulse response (FIR) filters. We also develop strategies to cascade lower-order filters to realize higher-order filters through designing appropriate unitary operators. Finally, a few directions for processing quantum states on classical systems after converting them to classical signals are suggested for future work.

  PublisherDOI

• Provable avoidance of barren plateaus for the Quantum Approximate Optimization Algorithm with Grover mixers

  arXiv (Cornell University) · 2025-09-12

  preprintOpen accessSenior author

  We analyze the dynamical Lie algebras (DLAs) associated with the Grover-mixer variant of the Quantum Approximate Optimization Algorithm (GM-QAOA). When the initial state is the uniform superposition of computational basis states, we show that the corresponding DLA is isomorphic to $\mathfrak{su}(d) \oplus \mathfrak{u}(1)\oplus \mathfrak{u}(1)$, where $d$ denotes the number of distinct values of the objective function. We also establish an analogous result for other choices of initial states and Grover-type mixers. Furthermore, we prove that the DLA of GM-QAOA has the largest possible commutant among all QAOA variants initialized with the same state, corresponding physically to the maximal set of conserved quantities. We derive an explicit formula for the variance of the GM-QAOA loss function in terms of the objective function values, and we show that for a broad class of optimization problems, GM-QAOA with sufficiently many layers avoids barren plateaus.

  PublisherOA PDFDOI

Recent grants

• Algebraic Structures Related to Quantum Field Theory

  NSF · $110k · 2007–2011

Frequent coauthors

• Victor G. Kač

  41 shared

• Alberto De Sole

  30 shared

• Reimundo Heluani

  23 shared

• Nikolay Nikolov

  University of Oxford

  21 shared

• Emil Horozov

  20 shared

• Milen Yakimov

  Northeastern University

  20 shared

• Иван Тодоров

  Delft University of Technology

  7 shared

• McKay Sullivan

  Utah Tech University

  6 shared

Labs

• P. L. Combettes - NCSU Department of MathematicsPI

  The lab webpage does not provide a specific research focus.

Education

• Ph.D., Mathematics

  University of ...

  2005

• M.S., Mathematics

  University of ...

  2001

• B.S., Mathematics

  University of ...

  1998

Awards & honors

• Hermann Weyl Prize (2006)