Yuan Liu

We translate the one-mode unitary-dilation framework for nonunitary linear dynamics into a gate-level hybrid oscillator-qubit architecture. An ancillary oscillator encodes the integral kernel through state preparation and postselection. A qubit register represents and simulates the discretized system operator. The construction applies to time-independent dynamics u ˙ = − ( L + i H ) u , including discretized partial differential equations, and removes the O ( log ⁡ M a ) ancilla-qubit overhead of a discrete-variable (DV) M a -term quadrature register. We bound the squeezed-Fock coefficient-projection error of the ideal kernel state. It decays superalgebraically with cutoff N for Schwartz-class kernels and at a stretched-exponential rate under stronger joint decay and smoothness assumptions. The finite squeezed-Fock kernel state generically has stellar rank N − 1 , making N a discrete measure of the oracle’s non-Gaussian resource. For hybrid oscillator-qubit evolution, a p th-order product formula requires O ( t 1 + 1 / p N Fock ( p + 1 ) / ( 2 p ) ϵ t − 1 / p ) Trotter steps in the worst case, up to generator-dependent commutator factors, to reach error ϵ t , where N Fock is the oscillator dimension. A perturbation bound separates the total scaled-map error from the physical postselection probability. We benchmark Law–Eberly synthesis and assess a variational SNAP+ D route at the state-preparation level on discretized heat-equation instances. For full circuit-level maps of one-dimensional heat and non-normal advection–diffusion instances up to D = 32 , the fixed-scale map error is at most 1.48 % and the conditional infidelity at most 4.68 × 10 − 4 over all computational-basis inputs. At kernel parameters selected on the one-dimensional family, a 4 × 4 two-dimensional stress case reaches 7.40 % fixed-scale error under a reference norm shrunk by the stronger two-dimensional damping, with worst-input conditional infidelity 6.20 × 10 − 3 . At the prescribed DV sizing, the hybrid CV–DV route has smaller fixed-scale error in all ten instances. The DV route accepts with fewer repetitions in every instance. These results provide a block-by-block finite-size resource account of when a single continuous qumode can replace a discretized ancilla register.

We present COMPOSER, a compile‐once modular parametric oracle for similarity‐encoded effective reduction of electronic‐structure operators (e.g., Schrieffer–Wolff‐type constructions). Low‐rank factorizations compress Hamiltonians into empirically near‐linear ladder pools at fixed factorization thresholds, and represent anti‐Hermitian generators through threshold‐controlled bilinear, decomposable‐pair, or generic elementary‐excitation branch libraries; each declared primitive branch admits a number‐conserving Fock‐space block encoding, with coefficient‐space dyads understood through their number‐conserving second‐quantized lifts. A fixed PREP‐SELECT‐PREP template multiplexes these branches, and a standard block‐Hamiltonian simulation/QSP primitive exponentiates the Hermitian generator with degree or query complexity set by operator norms and the chosen error tolerance. For a fixed orbital pool, qubit register, branch‐primitive library, selector address map, ancilla layout, routing plan, maximum branch set, and global normalization, the two‐qubit fabric is compiled once; geometry, active‐space (mask) updates, and truncations are absorbed by updated numerical weights, rotation angles, and classical masks. We introduce a mask‐aware similarity‐sandwich effective‐Hamiltonian construction and benchmark stability under low‐rank and second‐order‐perturbation‐guided screening. COMPOSER is an execution architecture: algorithmic errors (block‐encoding and QSP approximation) are tunable for any supplied parameters, while physical accuracy depends on how those parameters are obtained if not refined.

A cross-sector panel on quantum computing suggests that the field’s next milestone will not be another headline about qubit counts but the quieter and more consequential moment when quantum methods begin to fit credibly into real computational workflows.

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.

Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many prominent quantum algorithms. We propose a framework of quantum signal processing and quantum singular value transformation on U ( N ) , which realizes multiple polynomials simultaneously from a block-encoded input, as a generalization of those on U ( 2 ) in the original frameworks. We provide a comprehensive characterization of achievable polynomial matrices and give recursive algorithms to construct the quantum circuits that realize desired polynomial transformations. As three example applications, we propose a framework to realize bi-variate polynomial functions, demonstrate N -interval decision achieving O ( d ) query complexity with a log 2 ⁡ N improvement over iterative U ( 2 ) -QSP requiring O ( d log 2 ⁡ N ) queries, and present a quantum amplitude estimation algorithm achieving the Heisenberg limit without adaptive measurements.

We develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

One of the main applications for which quantum computers are hoped to find utility is in simulating ground state energies and other observables of molecular chemical systems. The recently proposed sample-based diagonalization method is a readily implementable method for this task on current-day hardware using short circuit depths and has been demonstrated on as many as 85 qubits in recent works. In this work, we combine the recently proposed quantum bootstrap embedding (QBE) method with sampled-based diagonalization (QBE-SQD) and present the first benchmarking study of the QBE method on real quantum hardware, ibm_pittsburgh, a heron r3 processor with 156 qubits. Our test system is a hydrogen ring with 8 hydrogen atoms in the cc-pVDZ basis. We show that for this system, QBE-SQD using an active space of (8e, 19o) per fragment with a 43 qubit footprint produces a ground state energy accuracy which exceeds that of an SQD calculation with a (8e, 30o) active space with a 67 qubit footprint when using a comparable number of Slater determinants. This demonstrates that the use of quantum bootstrap embedding techniques are a promising path towards extending the capabilities of state-of-the-art quantum eigensolvers on near-term devices.

Significant developments made in quantum hardware and error correction recently have been driving quantum computing toward practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. Recent advancements on these topics are presented, including the construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. The scalability of QSP methods on parallel and distributed quantum architectures is also highlighted. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this perspective serves as a gentle introduction to state-of-the-art quantum algorithms for the computational science community and inspires future development of scalable quantum computational science methodologies that bridge theory and practice.