arXiv subjects

Bojko N. Bakalov

Publications and source records attributed to Bojko N. Bakalov.

At least 19 recordsLinked to original sources

arXiv2026

Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks

We study non-stabilizerness (magic) in the ground state of $(2+1)$-dimensional $\mathrm{SU}(2)$ Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) $M_2$, its non-local component $M_2^{\rm NL}$, and a lower bound in terms of the anti-flatness $F$ of the entanglement spectrum. We also prove a stronger form of the sandwich relation: $-\log_2(1-4F)\le M_2^{\rm NL}\le M_2$; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, thus resolving the open problem of finding the maximal lower bound. We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, both the non-local magic and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling on lattices up to $6\times 6$ with bond dimension up to $128$, we find that the non-local magic furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself.

quant-ph↗

arXiv2026

Depth analysis of the Quantum Approximate Optimization Algorithm with a Grover mixer

We study the Quantum Approximate Optimization Algorithm with a Grover mixer and independently sampled cost and mixing angles. Under a lattice condition on the cost values carried by the initial state, we prove a depth-independent lower bound for the variance of the loss at every depth, together with the same bound for the derivative with respect to the final mixing angle. The estimate is instance-dependent and, for fixed locality, is inverse polynomial in the number of qubits for integer-valued local objective functions with uniformly bounded local terms, in particular for MaxCut. We also establish Grover-type reachability bounds showing that the depth required to approximate a prescribed carried eigenspace is bounded below by a constant multiple of the inverse square root of its initial probability.

quant-ph↗

arXiv2026

Spin models with critical ground space degeneracy from Lie algebra relations

We introduce an $\mathrm{SO}(3)$-symmetric spin model derived from the algebraic structure of $\mathfrak{so}(3)$: It is obtained as the nearest-neighbor parent Hamiltonian of a Matrix Product State (MPS) built from the generators of the Lie algebra $\mathfrak{so}(3)$ and the identity matrix, and therefore encodes the quadratic relations of the Lie algebra. We characterize the ground space structure of the resulting model and show that for open boundary conditions (OBC), it exhibits a quadratic ground space degeneracy, given by one irreducible representation (irrep) of each odd dimension (integer spin). For periodic boundary conditions (PBC), it has a linear ground space degeneracy, consisting of a singlet --- namely, the MPS underlying the model --- and a ferromagnet (the irrep with maximal spin), and thus exhibits gapless excitations. We also generalize the construction and the analysis of the OBC ground space to $\mathrm{SO}(d)$ and other compact simple Lie groups. The MPS on which the model is based is an injective MPS, and therefore, its 3-site parent Hamiltonian has a unique ground space and is gapped. The observed critical behavior thus has its origin in the small parent Hamiltonian considered. The model's algebraic ground space scaling thus provides an example distinct from that reported in (Schuch et al., 2025, arXiv:2503.10767), where it was shown that small parent Hamiltonians of injective MPS generically have unique ground states, and examples with an exponential ground space degeneracy were given.

quant-ph↗

arXiv2026

Hybrid Qubit-Rotor Quantum Systems: Clifford Structure, Universal Control, and Applications

A $U(1)$ quantum rotor pairs a periodic angle with an integer-valued conjugate momentum, and occurs in molecular rotation, superconducting phase-charge circuits, and compact gauge fields. Coupling such a rotor coherently to qubits gives a hybrid register whose control structure is not inherited from either the oscillator-qubit or the qudit case. We develop a Clifford theory, together with a universal-control result, for registers of $n$ qubits and $r$ rotors. We classify all automorphisms of the hybrid phase space $\mathbb{F}_2^{2n}\times\mathbb{Z}^r\times\mathbb{T}^r$ that preserve the Weyl commutation relations, and give an explicit finite Clifford circuit for each one. The classification is directional: rotor momentum parity may control qubit Pauli operations within the Clifford group, while every nonzero qubit-controlled rotor momentum shift is non-Clifford. It also yields normal forms for the mixed qubit-rotor couplings and the exact minimum number of elementary mixed gates needed to synthesize them. Adding a rotor cosine potential and one fixed qubit-rotor conditional phase to the local Clifford operations gives universal control on the full Hilbert space in the strong operator topology. We then apply this structure in three settings: an exact controlled-shift realization of gauge-covariant matter hopping, which is necessarily non-Clifford; rotor phase estimation with direct angle readout and probe optimization under momentum-support and energy constraints; and finite Fourier transforms on rotor momentum codes, where the one-rotor transform for $d=2^s$ compiles into $O(s)$ momentum-selective and controlled-shift instructions and each cross-register Fourier factor is implemented by one quadratic rotor Clifford gate.

quant-ph↗

arXiv2026

Symmetry Constraints Regularize Neural Quantum State Learning

Neural quantum states (NQS) offer highly expressive variational wavefunctions, but their optimization is frequently bottlenecked by redundant parameters and poorly conditioned landscapes. We demonstrate that embedding Hamiltonian symmetries directly into the variational parameterization geometrically regularizes this learning problem. For Boltzmann-family NQS, we enforce symmetries by tying local Pauli-$Z$ generators along physical geometric orbits, analytically collapsing the trainable coefficient space prior to optimization. To quantify the resulting optimization geometry, we introduce a geometric metric built on the Jacobian and Hessian of the optimization landscape. This framework evaluates the fraction of the physically accessible state space that corresponds to high-quality, low-energy solutions. Evaluating our approach on transverse-field Ising (TFIM) and XXZ spin chains shows that symmetry compilation excises the vast majority of parameters while maintaining ground-state accuracy within the resolution of the reported benchmarks. In large TFIM systems, strong spatial constraints compress thousands of parameters down to tens, delivering substantial runtime accelerations. Our geometric diagnostics indicate that symmetry produces a more favorable target-aware geometry by concentrating the reachable state space around low-energy solutions while retaining broad target basins. Together, our results indicate that symmetry compilation concentrates the expressive power of NQS on states relevant to the target problem, thereby reducing model size and training cost without sacrificing accuracy.

quant-ph↗

arXiv2026

Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory

Entanglement and non-stabilizerness (magic) quantify two distinct departures of quantum systems from classical description: the former measures non-local correlations, while the latter measures the deviation from stabilizer states that can be efficiently simulated classically. Understanding magic in physically relevant quantum field theories is essential for identifying where quantum advantage may be realized in the early fault-tolerant quantum computing era. We calculate the gauge-invariant entanglement entropy and stabilizer Rényi entropy of the ground state of the (1+1)-dimensional SU(2) lattice gauge theory formulated in a dressed-site basis that enforces Gauss's law exactly. Using tensor networks, we obtain results for system sizes up to $L=100$ (300 qubits). We find a crossover denoted by $g_{\star}$ where the ground state passes from a more magic-rich regime into a regime with less magic; this is also tracked by the sharpest change of both the entanglement entropy and lattice particle density. Our large-scale study of non-stabilizerness and entanglement entropy in a non-Abelian lattice gauge theory with matter provides new insight into the interplay of magic and entanglement in gauge theories, both of which are relevant for classical and early fault-tolerant quantum simulations.

quant-ph↗

arXiv2026

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

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.

quant-ph↗

arXiv2026

Efficient Qubit Simulation of Hybrid Oscillator-Qubit Quantum Computation

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.

quant-ph↗

arXiv2026

Approximate Message Passing for Quantum State Tomography

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.

quant-ph↗

arXiv2025

RedCarD: A Quantum Assisted Algorithm for Fixed-Depth Unitary Synthesis via Cartan Decomposition

A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to several algorithms for synthesis based on a Cartan decomposition of the dynamical Lie algebra. For unitaries of the form $e^{-itH}$, such as time-independent Hamiltonian simulation, the resulting circuits have depth that does not depend on simulation time $t$. However, finding such circuits has a large classical overhead in the cost function evaluation and the high dimensional optimization problem. In this work, by further partitioning the dynamical Lie algebra, we break down the optimization problem into smaller independent subproblems. Moreover, the resulting algebraic structure allows us to easily shift the evaluation of the cost function to the quantum computer, further cutting the classical overhead of the algorithm. As an application of the new hybrid algorithm, we synthesize the time evolution unitary for the 4-site transverse field Ising model on several IBM devices and Quantinuum's H1-1 quantum computer.

quant-ph↗

arXiv2025

Hybrid continuous-discrete-variable quantum computing: a guide to utility

Quantum computing has traditionally centered around the discrete variable paradigm. A new direction is the inclusion of continuous variable modes and the consideration of a hybrid continuous-discrete approach to quantum computing. In this paper, we discuss some of the advantages of this modality, and lay out a number of potential applications that can make use of it; these include applications from physics, chemistry, and computer science. We also briefly overview some of the algorithmic and software considerations for this new paradigm.

quant-ph↗

arXiv2025

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

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.

quant-ph↗

arXiv2025

Connection Between Classical and Quantum Descriptions of Spin Waves Using Quantum Circuits

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 surprising observation is confirmed using both a simulator and various quantum processors. The quantum circuit calculation leads to insight into the connection between classical and quantum descriptions of spin waves, and may also be useful for characterizing the error in quantum processors.

quant-ph↗

arXiv2025

Implementing Finite Impulse Response Filters on Quantum Computers

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.

eess.SP↗

arXiv2025

Quantum Coherent State Transform on Continuous-Variable Systems

While continuous-variable (CV) quantum systems are believed to be more efficient for quantum sensing and metrology than their discrete-variable (DV) counterparts due to the infinite spectrum of their native operators, our toolkit of manipulating CV systems is still limited. We introduce the quantum coherent state transform~(QCST) and a framework for implementing it in CV quantum systems with two ancilla CV states and six two-mode SUM gates. Measurement of the resulting quantum state under the momentum eigenbasis is equivalent to a positive operator-valued measure (POVM) with elements $\left\{\frac{1}π \left|α\right\rangle \left\langleα\right| \right\}_{α\in \mathbb{C}}$ , which provides an efficient way to learn the original CV state. Our protocol makes it possible to estimate the coherent state parameter within minimum-uncertainty precision using a single copy of the state, which finds applications in single-shot gate calibration of beam splitter and rotation gates to arbitrary precision. With repeated runs of our protocol, one can also estimate the parameters of any Gaussian state, which helps to calibrate other Gaussian gates, such as squeezing. For non-Gaussian states, our protocols can be used to perform Husimi Q-function tomography efficiently. With DV systems as ancilla instead, we can realize QCST approximately, which can be used to transfer CV states to DV states and back. The simplicity and broad applicability of the quantum coherent state transform make it an essential tool in continuous-variable quantum information science and engineering.

quant-ph↗

arXiv2024

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

We provide a classification of all dynamical Lie algebras generated by 2-local spin interactions on undirected graphs. Building on our previous work where we provided such a classification for spin chains, here we consider the more general case of undirected graphs. As it turns out, the one-dimensional case is special; for any other graph, the dynamical Lie algebra solely depends on whether the graph is bipartite or not. An important consequence of this result is that the cases where the dynamical Lie algebra is polynomial in size are special and restricted to one dimension.

quant-ph↗

arXiv2024

A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits

Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit's generators.

quant-ph↗

arXiv2024

Geometric Quantum Machine Learning with Horizontal Quantum Gates

In the current framework of Geometric Quantum Machine Learning, the canonical method for constructing a variational ansatz that respects the symmetry of some group action is by forcing the circuit to be equivariant, i.e., to commute with the action of the group. This can, however, be an overzealous constraint that greatly limits the expressivity of the circuit, especially in the case of continuous symmetries. We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits, based on homogeneous spaces, relaxing the overly stringent requirement of equivariance. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions orthogonal to those of the symmetry. We show that horizontal quantum gates are much more expressive than equivariant gates, and thus can solve problems that equivariant circuits cannot. For instance, a circuit comprised of horizontal gates can find the ground state of an $\mathrm{SU}(2)$-symmetric model where the ground state spin sector is unknown--a task where equivariant circuits fall short. Moreover, for a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem. Finally, we highlight a particular class of horizontal quantum gates that behave similarly to general $\mathrm{SU}(4)$ gates, while achieving a quadratic reduction in the number of parameters for a generic problem.

quant-ph↗