Quantum computation · Physics · Mathematics
I study quantum algorithms using geometry, Lie theory, and mathematical physics. My recent work concerns trainable observables, circuit expressivity, and transfer learning. I also work on learning-assisted quantum characterization and control.
Research Scientist, Brookhaven National Laboratory
Gauge-field strength as the curvature of a connection.
01 About
I am a Research Scientist at Brookhaven National Laboratory. My research focuses on quantum algorithms, particularly the geometry of circuits and observables, transfer learning, and learning-assisted quantum characterization and control.
I received a B.S. in mathematics and a Ph.D. in physics from National Tsing Hua University. My dissertation, Gravitational Theories with Torsion (2015), studied Poincaré gauge gravity, scalar-torsion cosmology, and higher-dimensional teleparallel gravity.
My earlier work includes reinforcement learning for adaptive radiotherapy at the University of Michigan, and theoretical machine learning at Academia Sinica: Layer Variational Analysis, optimal transport for domain adaptation, and generalized stochastic neighbor embedding. These studies use variational, geometric, and algebraic methods to analyze computational problems.
Selected stages of my academic training and research.
02 Research interests
My main interests are mathematical methods for quantum algorithms, quantum inference and control, and the theory of learning.
Stabilizer subspaces, cellular maps, relative homology, and logical operators.
Identifiable Hamiltonian models, adaptive probes, and molecular state preparation.
Device noise, phonon-induced quasiparticles, materials, and learning-assisted characterization.
Conditional forward models, Monte Carlo simulation, and reconstructed physics observables.
Observable equivalence, Lie-group actions, spectral structure, and circuit and measurement resources.
Variational response, domain adaptation, distribution geometry, and information constraints.
Principal bundles, connections, curvature, torsion, and variational principles in gravitational theory.
I also have an exploratory interest in quantum methods for learning and inference, with explicit comparison of quantum and classical resource costs.
Cellular maps · stabilizer subspaces · homological decoding
I study error-correcting subspaces through algebra and topology. For a surface code, boundary and coboundary maps generate commuting Pauli checks. Their common invariant subspace is the code; homology describes the logical transformations that the checks cannot distinguish.
Let \(K\) be a cellulated surface, \(A\) its rough boundary subcomplex, and \(C_n=C_n(K,A;\mathbb F_2)\). Qubits occupy the remaining edges. The cellular maps organize both local checks and global logical classes:
A recovery \(\widehat z\) can match the syndrome yet leave a logical error:
The note builds the topology first, then works through the boundary matrices and error paths of a planar surface code.
Read moreFor the relative chain groups above, let \(C^i=\operatorname{Hom}_{\mathbb F_2}(C_i,\mathbb F_2)\) and \(\delta^i\phi=\phi\circ\partial_{i+1}\). Assign \(n=\dim C_1\) edge qubits with Hilbert space \(\mathcal H=(\mathbb C^2)^{\otimes n}\).
The support maps \(Z:C_1\to\mathrm U(\mathcal H)\) and \(X:C^1\to\mathrm U(\mathcal H)\) label products of edge Pauli operators. They turn the cellular maps into checks:
\(v^\vee\in C^0\) is a vertex basis functional and \(f\in C_2\) a face. The Pauli commutation phase is the evaluation of an edge cochain on an edge chain.
The checks generate a finite abelian stabilizer group \(S\subset\mathrm U(\mathcal H)\), with \(-I\notin S\). Group averaging projects onto its invariant subspace, the trivial-character sector:
\(\mathcal H^S=\{\psi\in\mathcal H:g\psi=\psi\text{ for every }g\in S\}\). The second equation is the Knill–Laflamme condition for a specified error set \(\{E_a\}\), with \(c_{ab}\in\mathbb C\). An invariant or isotypic subspace must satisfy this additional condition to correct those errors.
The full note connects these projectors to representation theory, then works through a planar code with explicit boundary matrices, syndromes, and logical operators.
03 Research
Conceptual illustrations use AI-generated artwork. Figures from the papers are identified in their captions.
Measurement and feedback for trapped molecular ions
Quantum-logic spectroscopy couples a molecular ion to a controllable atomic logic ion through shared motion. Raman pulses correlate molecular transitions with motional excitation; logic-ion readout then conditions the next control. I study such pulse-and-measurement sequences for molecular state preparation.
\(H_a\) acts on molecular internal states and shared motion. \(H_{\mathrm{mol}}\) is the internal Hamiltonian; \(I\) denotes the identity on each indicated space. The motional mode has angular frequency \(\omega_m\) and annihilation operator \(b\). Pulse \(a\) has duration \(\tau_a\); \(\mathcal T\) orders time evolution. The effective instrument \(\mathcal I_{a,y}\) includes evolution, readout \(y\), and reset. The conditional update requires \(p(y\mid a,\rho)>0\). \(\rho\) is the molecular state and \(|\psi_\star\rangle\) its target.
The control objective is to increase target-state fidelity under uncertain outcomes and an experimental time budget. This builds on established molecular QLS and learning-assisted control; the equations describe the general physical setting.
Phonon-induced quasiparticles · material sensitivity · error-correcting subspaces
Material sensitivity of superconducting quantum processors · ongoing
Energy deposited in a substrate produces phonons that can reach multiple superconducting electrodes. Above the pair-breaking threshold, they generate quasiparticles; tunneling across a junction increases relaxation and reduces coherence. I use Geant4/G4CMP-based modeling to study how materials and device geometry affect this process.
\(E_{\mathrm{ph}}\) is phonon energy and \(\Delta\) the superconducting gap. \(n_{\mathrm{qp}}\) is quasiparticle density; \(g_{\mathrm{qp}},r,s\) describe generation, recombination, and removal. \(x_{\mathrm{qp}}=n_{\mathrm{qp}}/n_{\mathrm{cp}}\) is normalized to the Cooper-pair density; \(\omega_{01}\) is angular transition frequency. \(\Delta\Gamma_1\) is the quasiparticle-induced excess relaxation rate; \(\Gamma_{1,b},\Gamma_\phi\) are baseline relaxation and total pure-dephasing rates. \(T_1,T_2\) are relaxation and coherence times. The rate expression is a standard-transmon, quasi-equilibrium model.
Geant4 models particle interactions and energy deposition; G4CMP supplies low-temperature charge and phonon transport. Quasiparticle kinetics and qubit-response models connect these simulations to decoherence. The concern is quasiparticle poisoning and loss of quantum information, rather than necessarily permanent electrode damage.
Bayesian Active Learning for Sample-Efficient and Symmetry-Aware Qubit Layout Optimization · QCE 2026
In collaborative work, we study active learning for radiation-sensitive qubit layouts. The aim is to choose informative simulations while accounting for layout symmetries.
Two related interests are learned decoding from error syndromes and estimation of a reduced density matrix \(\rho_A=\operatorname{Tr}_{\bar A}\rho\) from partial measurements. A state estimate must be positive and have unit trace; incomplete measurements need not identify a unique state.
Forward foundation model · ongoing collaboration with UConn
QuantumMC Forward Foundation Model · UConn collaboration · ongoing
A particle-physics generator predicts truth-level final states; a detector records signals from which particle trajectories and identities must be inferred. Given a generated event, which outcomes would the detector and reconstruction produce? A forward model describes this conditional distribution, including its fluctuations.
GEMC/Geant4 follows particle transport and energy deposition. Digitization turns simulated hits into readout, and COATJAVA reconstructs particle candidates. With UConn collaborators, I am developing learned approximations to selected parts of this combined response, retaining the upstream physics generator.
Let \(X\in\mathcal X\) be a truth event, \(Y\in\mathcal Y\) a reconstructed outcome, and \(c\in\mathcal C_{\mathrm{det}}\) the detector conditions. Outcomes include missing or failed reconstructions. The end-to-end response is a probability kernel \(K\); \(\mathcal P(\mathcal Y)\) denotes probability measures on the outcome space:
\(h\) denotes simulated hits and \(d\) digitized readout. \(P_{\mathrm{gen}}\) is the truth-event probability law, with physics-model parameters \(\alpha\). Integrating the transport and digitization kernels propagates the truth event to reconstructed outcomes. A learned response approximates this detector factor while retaining \(P_{\mathrm{gen}}\).
The current study models kinematic residuals and reconstructed particle identity for selected, successfully matched forward-detector reconstructions. A conditional distribution is needed because detector smearing, response tails, and particle misidentification cannot be represented by a single corrected momentum.
The broader aim is a reusable forward response across particle species and detector conditions, with acceptance, reconstruction efficiency, and event correlations treated explicitly as the scope expands. These determine which generated particles appear in a reconstructed sample and how their measured distributions change.
Validation compares reconstructed spectra, response tails, particle-identification patterns, and analysis observables against full simulation. Detector control data provide a further check on the simulation used as the learning target. Agreement at both stages is needed for a fast surrogate to support physics inference.
Observable Geometry · ANO and DANO · quasi-polar analysis · transfer learning
Observable Geometry for Effective Quantum Circuits · QCE 2026
Different circuits can produce the same transformed observable. For an \(n\)-qubit system, let \(N=2^n\), \(O\in\mathrm{Herm}(N)\), and \(U\in U(N)\). The measurement-operator map has an exact redundancy:
\(\mathrm{Herm}(N)\) is the space of Hermitian operators; \(m_j\) are the multiplicities of the distinct eigenvalues of \(O\). The stabilizer acts on the left.
Principal-bundle projection
\[ \pi(p\cdot g)=\pi(p),\qquad g\in G. \]Observable redundancy
\[ F_O(SU)=F_O(U),\qquad S\in S_O. \]Both maps are constant along their fibers. Here the gauge-like redundancy is relative to a chosen observable, rather than a local spacetime gauge symmetry. We use its stabilizer to identify effective circuit directions.
Adaptive Non-local Observable on Quantum Neural Networks · QCE 2025
Unitary conjugation changes an observable's basis but preserves its spectrum. ANO also learns the observable, allowing the model to move between spectral classes.
\(\rho_x\) is the encoded input state. The trainable Hermitian block \(H_\eta\) acts on \(k\) measured qubits; \(I\) acts on the remaining qubits. A general block has \(4^k\) real coefficients.
Diagonal Adaptive Non-local Observables on Quantum Neural Networks · ICCCN 2026
DANO separates spectral weights from basis rotations. For a \(k\)-qubit block, the spectral theorem gives
The real spectral weights \(\lambda_j\) replace \(4^k\) observable coefficients with \(2^k\) diagonal coefficients. Basis rotations still require circuit resources; a fixed shallow ansatz need not represent every basis.
Quasi-polar Decomposition of Quantum Neural Networks via Adaptive Non-local Observables · 2026 preprint
Quasi-polar analysis follows the spectral and unitary coordinates of a learned observable. Along a smooth choice of basis, their contributions to its change separate:
\(t\) indexes training, not physical time. The first term changes the spectrum; the commutator changes the basis. Eigenbases and unitary logarithms are nonunique. This is a spectral-coordinate description, rather than the matrix polar decomposition.
Transfer Learning Analysis of Variational Quantum Circuits · ICASSP Workshops 2025
For nearby, aligned domains, Lie-algebraic response describes how input changes affect a pretrained circuit and how parameter changes can compensate. For Hermitian \(A\), with \(iA\in\mathfrak u(N)\), the local adjoint response is
\(J_x\) and \(J_\theta\) are the input and parameter Jacobians, stacked over aligned samples; \(J_\theta^+\) is the Moore–Penrose pseudoinverse. The update solves the linearized least-squares problem, under the local-response approximation.
Layer Variational Analysis · optimal transport · generalized SNE
Interpretations of Domain Adaptations via Layer Variational Analysis · ICLR 2023
Layer Variational Analysis studies the response of network layers to changes in data and model parameters. The analysis gives conditional error estimates and an analytical adaptation procedure. A local-response picture is
For \(f:\mathbb R^d\times\mathbb R^p\to\mathbb R^m\), the Jacobians map input and parameter perturbations to output changes. This first-order expression illustrates the response; the paper states the assumptions of its layer-wise analysis.
Discriminator-constrained optimal transport · NeurIPS 2021
We combine distribution coupling with an adversarial constraint for unsupervised speech adaptation. The underlying discrete transport problem is
\(\mu\) and \(\nu\) are probability-weight vectors, \(C\) is a pairwise cost matrix, and \(\gamma\) is a coupling. The paper adds a discriminator constraint to the adaptation objective.
Generalized stochastic neighbor embedding with alpha-divergence · IEEE Access 2024
The similarity metric, distribution kernel, and divergence determine the attraction and repulsion between embedded points. We derive these forces for generalized SNE:
\(y_i\) are latent points, \(\eta,\beta>0\), and \(Z\) normalizes the pairwise similarities. \(P\) and \(Q\) are source and embedding similarities. The expression shown uses Euclidean latent distance; the framework also studies more general metrics.
Related work on INSURE studies information-based feature disentanglement and purification for domain generalization.
FoundationPh.D. dissertation (2015) and papers in JCAP, Phys. Rev. D, Class. Quantum Grav., and Phys. Lett. B — with C.-Q. Geng, C.-C. Lee, L.-W. Luo, and C. Lai.
My doctoral work studied gravity through gauge geometry. Connections, curvature, torsion, and variational principles gave me a way to move between geometric structure and physical dynamics — and they remain the language in which I think about the problems above. The dissertation builds Poincaré gauge theory from its fibre-bundle formulation to the resulting Riemann–Cartan spacetime, then studies theories descended from it.
In Poincaré gauge theory the coframe \(e^a\) and the Lorentz connection \(\omega^a{}_b\) are independent fields. Their field strengths are the curvature and torsion two-forms, given by Cartan’s structure equations; the action \(S[e, \omega, \psi] = \int_M L\) is varied with respect to each separately.
Frame indices \(a = 0,\dots,3\), \(\eta_{ab} = \mathrm{diag}(-1,1,1,1)\), and \(\omega_{ab} = -\omega_{ba}\) for a metric-compatible connection. The gauge group is the Poincaré group \(ISO(1,3) = \mathbb R^{1,3} \rtimes SO(1,3)\). Standard background, which the dissertation develops in full.
I studied the cosmological dynamics of the scalar-torsion \(0^+\) mode in a quadratic Poincaré gauge model. In the positive-kinetic-energy case, the high-redshift analysis gives radiation-like asymptotic behavior for the effective torsion component:
High-redshift limit: \(a\ll1\), \(z\gg0\).
\(a\) is the scale factor, \(\rho_T\) and \(p_T\) the effective torsion density and pressure. A property of the studied theoretical model, not an observational claim about dark energy.
Using differential forms, I studied five-dimensional teleparallel gravity and its dimensional reduction. The work compares braneworld and Kaluza–Klein constructions and identifies scalar–torsion couplings generated in the reduced theory.
The opening displays standard identities and field equations from David Bleecker’s Gauge Theory and Variational Principles: curvature, the Bianchi identity, matter-field variation, Yang–Mills and Einstein equations, and the bundle metric.
Curvature of a connection \(\omega\) on a principal bundle — the field strength.
The homogeneous field equation, true for every connection.
Stationary particle fields \(\psi\) for a fixed connection; \(\delta^\omega\) is the formal adjoint of \(D^\omega\).
Stationarity of the self-action \(\mathcal S(g,\omega) = -\tfrac12 (gk)(\Omega^\omega, \Omega^\omega)\) in \(\omega\).
Stationarity of \(\int_U [\underline R(g) + \mathcal S(g,\omega) + c]\,\mu_g\) in the metric \(g\); \(k\) is an \(\mathrm{Ad}\)-invariant inner product on the Lie algebra.
The scalar curvature of the total-space metric decomposes into base curvature, gauge self-action, and fiber curvature. Here \(R_G\) is constant for the group metric used in this construction.
D. Bleecker, Gauge Theory and Variational Principles (Addison-Wesley, 1981; Dover reprint 2005). Equations newly typeset in the book’s notation; \(\underline R\) denotes the curvature functions of \(g\).
Selected collaborative work in quantum algorithms and applications.
Energy systems
Hybrid quantum soft actor-critic agents for transmission switching and Volt-VAR control, with SMU.
Stochastic analysis
Variational-circuit approximations for high-dimensional parabolic PDEs, formulated through backward stochastic differential equations and tested in simulation.
Quantum networks
Fidelity bounds from CHSH violations, sample-complexity analysis, and verification protocols for hop-by-hop quantum networks.
Photonics
Photonic quantum circuits as teachers that distill knowledge into classical models.
04 Connections
Both settings distinguish a mathematical representation from the information it represents.
A principal G-bundle over spacetime
The unitary group over the orbit of an observable
The shared structure is a projection that is constant along symmetry fibers. In observable geometry, the stabilizer of the chosen operator determines the quotient and its dimension. This is an operator-level redundancy: equality of a single state’s expectation value can introduce further, state-dependent degeneracies.
| Method | Gravity foundation | Learning theory | Quantum program |
|---|---|---|---|
| Geometry | Bundles, coframes, curvature, torsion | Distribution geometry and embeddings | Observable orbits and effective circuit directions |
| Symmetry & algebra | Gauge groups and local frame changes | Structural constraints on representations | Stabilizers, commutators, spectral freedom, code projectors |
| Variation | Independent coframe and connection variation | Layer response and adaptation | Gate response, observable optimization, control |
| Information | Fields and observables of a specified model | Divergences, useful features, domain shift | Identifiability and measurement design |
| Realization | Model assumptions and cosmological predictions | Data assumptions and numerical validation | Hardware constraints, physical noise, error protection |
05 Publications
A selection across quantum computing, learning, and gravitation. The full bibliography is on Google Scholar.
Medical-physics work from the University of Michigan (2016–2019) and further speech and signal-processing papers are listed on Google Scholar.
06 Experience
