QUANTUM

When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum systems, this has been achieved using first and second-order Trotter-Suzuki product formulas or probabilistic algorithms. In this work, we introduce novel non-probabilistic algorithms for simulating Markovian open quantum systems using randomisation. Our methods, including first and second-order randomised Trotter-Suzuki formulas and the QDRIFT channel, not only maintain the physicality of the system's evolution but also enhance the scalability and precision of quantum simulations. We derive error bounds and step count limits for these techniques, bypassing the need for the mixing lemma typically employed in Hamiltonian simulation proofs. Furthermore, we implement these randomised algorithms using Classical Sampling (CS), demonstrating their gate complexity advantages over deterministic TS product formulas. This work systematically extends powerful randomisation techniques from Hamiltonian simulation to the general setting of Markovian open quantum systems, highlighting their potential to enable faster and more accurate simulations.

In this work, we study the complexity of graph-state preparation in a general model of quantum algorithms that allows measurements in the computational basis, single-qubit Clifford operations, and two-qubit Clifford operations. We define the CZ-complexity of a graph state $|G\rangle$ as the minimum number of two-qubit Clifford operations required to generate $|G\rangle$ from $|0\rangle^{\otimes (n+s)}$ for some $s\ge 0$. Equivalently, every optimal algorithm can be taken to use only controlled-Z (CZ) gates as its two-qubit Clifford operations. We then give a combinatorial characterization of graph-state transformations. Specifically, $|G\rangle$ can be generated from another graph state $|H\rangle$ by an algorithm of CZ-complexity at most $t$ if and only if $G$ can be obtained from $H$ by vertex deletions, local complementations and at most $t$ elementary edge-complementations. Here, an elementary edge-complementation toggles either a single edge, all edges between one vertex and the neighborhood of another, or all edges between the neighborhoods of two non-adjacent vertices. Using this characterization, we relate CZ-complexity to rank-width. For any graph $G$ with $n$ vertices and rank-width $r$, the CZ-complexity is $O(rn)$, and if $G$ is connected then it is at least $n+r-2$. We also show that these bounds are close to optimal. Finally, for interval graphs and circle graphs, whose rank-width is unbounded, we present preparation algorithms with CZ-complexity $O(n)$ and $O(n\log n)$, respectively.

Building upon Wan, Zhong (2025) \cite{wan2025cuttingstabiliserdecompositionsmagic} we present a few methods on how to simulate the non-Clifford d = 5 magic state cultivation circuits\cite{gidney2024magicstatecultivationgrowing} with a sum of ≈ 8 Clifford ZX-diagrams on average, at 0.1 % noise. Compared to a magic cat state stabiliser decomposition of all 53 non-Clifford spiders ( 6,377,292 terms required), this is more than 7 × 10 5 times reduction in the number of terms. Our stabiliser decomposition has the advantage of representing the final non-Clifford state (in light of circuit errors) as a sum of Clifford ZX-diagrams. This will be useful in simulating the escape stage of magic state cultivation, where one needs to port the resultant state of cultivation into a larger Clifford circuit with many more qubits. Still, it's necessary to only track ≈ 8 Clifford terms. Our result sheds light on the simulability of operationally relevant, high T -count quantum circuits with some internal structure.Finally, we provide numerical results for full non-Clifford stabiliser rank simulation based on t s i m along with optimisations using our cutting decompositions. Nearly 4 × 10 6 shots per second can be obtained on a laptop for the smaller d = 3 circuits at uniform circuit level noise p = 0.0005 , making it only ∼ 1.1 times slower than its (circuit-unspecific and un-optimised) fully Clifford proxy simulation via s t i m using S gates.

We analyze the task of estimating a multi-parameter unitary belonging to the $SU(2)$ or $SU(1,1)$ groups, in a two-bosonic-mode scenario and investigate the scaling of the precision in terms of the total particle number. For the $SU(2)$ case, the total particle number is conserved by the evolution and we discuss optimal states in fixed-$n$ subspaces, identifying eigenstates of $J_z^2$ as useful resources, even allowing simultaneous Heisenberg precision scaling for all three parameters. In the $SU(1,1)$ case instead, the conserved quantity is the particle number difference between the two modes, and we identify useful probe states in the sector with an equal number of particles in the two modes. These states are analogous to the $SU(2)$ case and would also allow simultaneous Heisenberg precision scaling for all three parameters. We then consider the more pragmatic scenario of an estimation via expectation values of time-evolved observables, which we restrict to be the first two moments of the generators. We analyze the maximal precision achievable in this setting and we find that the twin-Fock state emerges in both the $SU(2)$ and the $SU(1,1)$ cases as the only one potentially allowing Heisenberg scaling for the estimation of two out of the three parameters. As a complement, we also consider other probe states with fluctuating number of particles, with measurements restricted to quadratic expressions in the mode operators. In this scenario, simultaneous Heisenberg scaling in multiple parameters seems mostly forbidden, with the only exception being an input two-mode squeezed state for the estimation of a two-parameter $SU(2)$. This extends to the multiparameter scenario the well-established intuition that the performance of a $SU(2)$ interferometer can be enhanced by a prior $SU(1,1)$ operation.

Approximating the k-th spectral gap triangle(k) = |lambda(k)-lambda(k+1)| and the corresponding midpoint & micro;k = lambda(k)-lambda(k+1) /2 of an N & times; N Hermitian matrix with eigenvalues lambda(1 )>= lambda(2) >=...>=lambda(N), is an important special case of the eigenproblem with numerous applications in science and engineering. In this work, we present a quantum algorithm which approximates these values up to additive error & varepsilon; triangle(k) using a logarithmic number of qubits. Notably, in the QRAM model, its total complexity (queries and gates) is bounded by O (N-2 /& varepsilon;(2)triangle(2)(k )polylog (N, 1/triangle(k), 1/& varepsilon;,1/delta ))where & varepsilon;, delta E (0,1) are the accuracy and the failure probability, respectively. For large gaps triangle(k), this provides a speed-up against the best-known complexities of (()) classical algorithms, namely, O (N(omega)polylog N, 1 /triangle k, 1/& varepsilon;)), where omega less than or similar to 2.371 is & varepsilon; the matrix multiplication exponent. A key technical step in the analysis is the preparation of a suitable random initial state, which ultimately allows us to efficiently count the number of eigenvalues that are smaller than a threshold, while maintaining a quadratic complexity in N. In the black-box access model, we also report an ohm(N-2) query lower bound for deciding the existence of a spectral gap in a binary (albeit non-symmetric) matrix.

We present an efficient spin-photon inpling. Using a dipole model, we show that our design achieves a far-field collection efficiency of 96% at the numerical aperture of 0.7 with a 95% overlap to a Gaussian mode. Our approach is based on a dual perturbation layer design. The first perturbation layer extracts and redirects the resonant mode of a diamond micro disk resonator around the optical axis. The second and concentrates most of the light intensity near the center. This dual-layer design enhances control over the farfield pattern and also reduces alignment sensitivfaster than full-wave FDTD simulations. for quantum information applications.

The quantum linear system problem provides one of the most enticing sources of exponential quantum speedups, and its resolution underlies other interesting quantum algorithms for differential equations and eigenvalue processing. The goal is to produce a state proportional to the solution A-1|b > of a linear system, by querying an oracle OA that block encodes the coefficient matrix and an oracle Ob that prepares the initial state. We present a quantum linear system algorithm with query complexity Theta (1/root p) to Ob that is optimal, and query complexity O (kappa log (1/p) (log log (1/p) + log (1/& varepsilon;))) to OA that is nearly optimal in all parameters including the condition number kappa = parallel to A parallel to parallel to A-1 parallel to, success amplitude root p = parallel to A-1|b >parallel to/parallel to A-1 parallel to, and accuracy & varepsilon;. In various applications to solving differential equations, preparing ground states of operators with real spectra, estimating and transforming eigenvalues of non-normal matrices, we can further improve the dependence on p to nearly match or outperform best previous results based on other methods. As kappa can be arbitrarily larger than 1/root p, our algorithm contrasts with recent results that have O (kappa log (1/& varepsilon;)) complexity to both oracles, which, while optimal in OA, is highly suboptimal in Ob. We achieve this using a new Variable Time Amplitude Amplification algorithm with Tunable thresholds (Tunable VTAA), which fully characterizes generic nested amplitude amplifications, eliminates redundant nestings, and is of independent interest. With an optimized schedule of thresholds, we prove that the complexity of Tunable VTAA scales with & ell;2 3 the input cost, improving over the & ell;1-norm result of Ambainis and the more common & ell;2-norm scaling. Specialized to the quantum linear system problem, we construct a discretized inverse state, for which a deterministic amplification schedule exists. This leads to a substantially simplified VTAA with an optimal initial state preparation cost, even when the value of p is not known a priori. We also introduce a block preconditioning scheme that can artificially boost root p in generic situations, in contrast to previous negative preconditioning results focusing on reducing kappa. This further reduces the cost of initial state preparation in linear-system-based differential equation solvers, ground state preparators and eigenvalue processors. Additionally, block preconditioning 1 furnishes a particularly simple quantum linear system algorithm with optimal O kappa log & varepsilon; queries to OA using |b > itself as the preconditioner. It also realizes a block-encoded eigenvalue transformer with O(n) scaling in degree of the target polynomial, compared to the best existing result of O (n1.5).-quasinorm of

As quantum computing moves toward fault-tolerant architectures, quantum error correction (QEC) decoder performance is increasingly critical for scalability. Understanding the impact of transitioning from floating-point software to finite-precision hardware is essential, as hardware decoder performance affects code distance, qubit requirements, and connectivity between quantum and classical control units. This paper introduces a hardware emulator to evaluate QEC decoders using real hardware instead of software models. The emulator can explore $10^{13}$ different error patterns in 20 days with a single FPGA device running at 150 MHz, guaranteeing the decoder's performance at logical rates of $10^{-12}$, the requirement for most quantum algorithms. In contrast, an optimized C++ software on an Intel Core i9 with 128 GB RAM would take over a year to achieve similar results. The emulator also enables the storage of uncorrectable error patterns that generate logical errors, allowing for offline analysis and the design of new decoders. Using results from the emulator, we propose a method that combines several belief propagation (BP) decoders with different quantization levels, which we define as a diversity-based decoder. Individually, these decoders may show subpar error correction, but together they outperform the floating-point version of BP for quantum low-density parity-check (QLDPC) codes like hypergraph or lifted product. Preliminary results with circuit-level noise and bivariate bicycle codes suggest that hardware insights can also improve software. Our diversity-based proposal achieves a similar logical error rate as the well-known approach, BP with ordered statistics (BP+OSD) decoding, with average speed improvements ranging from 30% to 80%, and 10% to 120% in worst-case scenarios, while reducing post-processing algorithm activation from 47% to 96.93%, maintaining the same accuracy.

Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed by the Lindblad master equation, has received attention recently with the current state-of-the-art algorithms having an input model query complexity of O ( T p o l y l o g ( T / ϵ ) ) , where T and ϵ are the desired time and precision of the simulation respectively. For the Hamiltonian simulation problem it has been show that the optimal Hamiltonian query complexity is O ( T + log ⁡ ( 1 / ϵ ) ) , which is additive in the two parameters, but for Lindbladian simulation this question remains open. In this work we show that the additive query complexity to a Lindbladian's jump operators is reachable for the simulation of a large class of Lindbladians by constructing a novel quantum algorithm based on quantum trajectories.

We propose a class of metrological resource states whose quantum Fisher information scales optimally in both system size and noise rate. In these states, qubits are partitioned into sensing groups with relatively large correlations within a group but small correlations between groups. The states are obtainable from local Hamiltonian evolution, and we design a metrologically optimal and efficient measurement protocol utilizing time-reversed dynamics and single-qubit on-site measurements. Using quantum domino dynamics, we also present a protocol free of the time-reversal step that has an estimation error roughly twice the best possible value. Finally, we show that spin squeezed states are also optimal for noisy metrology under general conditions.

Current proposals to probe the quantum nature of gravity in the low-energy regime predominantly focus on the Newtonian interaction term. In this work, we present a theoretical exploration of gravitationally mediated entanglement arising from a genuinely general relativistic effect: frame dragging. This interaction gives rise to an effective dipolar coupling between the angular momenta of two rotating, spherically symmetric masses, allowing entanglement generation between angular momentum degrees of freedom. We represent the quantum states by angular momentum eigenstates and show that, while the maximal entangling rate is achieved for highly delocalized initial states, non-negligible quantum correlations can still emerge even when the initial states are not prepared in superposition. We then analyze the robustness of the resulting entanglement in the presence of common noise sources, explicitly acknowledging the challenges associated with a potential implementation. We also note that, for spherically symmetric masses, angular momentum degrees of freedom are intrinsically insensitive to Casimir and Coulomb interactions, thereby mitigating key decoherence channels present in existing proposals. Finally, we discuss possible state preparation and detection strategies while framing our results within the broader landscape of gravitationally mediated entanglement schemes, emphasizing the role of this framework as a conceptual avenue for exploring genuinely relativistic quantum gravitational effects.

In this work, a novel quantum neural network is introduced as a means to approximate any unitary evolution through the Standard Recursive Block Basis (SRBB) and is subsequently redesigned with the number of CNOTs asymptotically reduced by an exponential contribution. This algebraic approach to the problem of unitary synthesis exploits Lie algebras and their topological features to obtain scalable parameterizations of unitary operators. First, the original SRBB-based scalability scheme, already known in the literature only from a theoretical point of view, is reformulated for efficient algorithm implementation and complexity management. Remarkably, 2-qubit operators emerge as a special case of the original scaling scheme. Furthermore, an algorithm is proposed to reduce the number of CNOT gates in the scalable variational quantum circuit, thus deriving a new implementable scaling scheme that requires only one layer of approximation. The single layer CNOT-reduced quantum neural network is implemented, and its performance is assessed with a variety of different unitary matrices, both sparse and dense, up to 6 qubits via the PennyLane library. The effectiveness of the approximation is measured with different metrics in relation to two optimizers: a gradient-based method and the Nelder-Mead method. The approximate CNOT-reduced SRBB-based synthesis algorithm is also tested on real hardware and compared with other valid approximation and decomposition methods available in the literature.

The heralded exact one-way distillable secret key is equal to the largest expected rate at which perfect secret key bits can be probabilistically distilled from a bipartite state by means of local operations and one-way classical communication. Here we define the set of super two-extendible states and prove that an arbitrary state in this set cannot be used for heralded exact one-way secret-key distillation. This broad class of states includes both erased states and all full-rank states. Comparing the heralded exact one-way distillable secret key with the more commonly studied approximate one-way distillable secret key, our results demonstrate an extreme gap between them for many states of interest, with the approximate one-way distillable secret key being much larger. Our findings naturally extend to heralded exact one-way entanglement distillation, with similar conclusions.

We introduce the stellar decomposition, a novel method for characterizing non-Gaussian states produced by photon-counting measurements on Gaussian states. Given an (m + n)-mode Gaussian state G, we express it as an (m + n)-mode "Gaussian core state" Gcore followed by an m-mode Gaussian transformation T that only acts on the first m modes. The defining property of the Gaussian core state Gcore is that measuring the last n of its modes in the photon-number basis leaves the first m modes on a finite Fock support, i.e. a core state. Since T is measurement-independent and Gcore has an exact and finite Fock representation, this decomposition exactly describes all non-Gaussian states obtainable by projecting n modes of G onto the Fock basis. For pure states we prove that a physical pair (Gcore, T) always exists with Gcore pure and T unitary. For mixed states, we establish necessary and sufficient conditions for (Gcore, T) to be a Gaussian mixed state and a Gaussian channel. We also develop a semidefinite program to extract the 'largest' possible Gaussian channel when these conditions fail. Finally, we present a formal stellar decomposition for generic operators, which is useful in simulations where the only requirement is that the two parts contract back to the original operator. The stellar decomposition leads to practical bounds on achievable state quality in photonic circuits and for GKP state generation in particular. Our results are based on a new characterization of Gaussian completely positive maps in the Bargmann picture, which may be of independent interest.

In this paper, we provide a complete mathematical theory for the entanglement of mixtures of Dicke states. These quantum states form an important subclass of bosonic states arising in the study of indistinguishable particles. We introduce a tensor-based parametrization where the diagonal entries of these states are encoded as a symmetric tensor, enabling a direct translation between entanglement properties and well-studied convex cones of tensors. Our results bridge multipartite entanglement theory with semialgebraic geometry and the theory of completely positive and copositive tensors. This dictionary maps separability to completely positive tensors, the PPT property to moment tensors, entanglement witnesses to copositive tensors, and decomposable witnesses to sum of squares tensors. Using this framework, we construct explicit PPT entangled states in three or more qutrits, disproving a recent conjecture. We establish that PPT entanglement exists for all multipartite systems with local dimension d >= 3 and n >= 3 parties. We also show that, for mixtures of Dicke states, the PPT condition with respect to the most balanced bipartition implies all other PPT conditions. We further connect bosonic extendibility of mixtures of Dicke states to the duals of known hierarchies for non-negative polynomials, such as the ones by Reznick and Polya. We thus provide semidefinite programming relaxations for separability and entanglement testing in the Dicke subspace.

We develop a theoretical framework for fast, robust and high-fidelity topological quantum state transfer in one-dimensional systems with long-range couplings, motivated by chains of Rydberg atoms with dipole-dipole interactions. Such long-range interactions naturally give rise to extended Su-Schrieffer-Heeger and Rice-Mele models supporting topologically protected edge states. We show that these edge states enable high-fidelity edge-to-edge excitation transfer using both time-independent protocols, based on coherent edge state dynamics, and time-dependent protocols, based on adiabatic modulation of system parameters. Long-range couplings play a central role by enhancing the relevant energy gaps, leading to a substantial improvement in transfer efficiency compared to nearest neighbour models. The resulting transfer is robust against positional disorder, reflecting its topological origin and highlighting the potential of long-range interacting platforms for reliable quantum state transfer.

Photonic systems offer a promising platform for interconnecting quantum processors and enabling scalable, networked architectures. Designing and verifying such architectures requires a unified formalism that integrates linear algebraic reasoning with probabilistic and control-flow structures. In this work, we introduce a graphical framework for distributed quantum computing that brings together linear optics, the ZX-calculus, and dataflow programming. Our language supports the formal analysis and optimization of distributed protocols involving both qubits and photonic modes, with explicit interfaces for classical control and feedforward, all expressed within a synchronous dataflow model with discrete-time dynamics. Within this setting, we classify entangling photonic fusion measurements, show how their induced Pauli errors can be corrected via a novel flow structure for fusion networks, and establish correctness proofs for new repeat-until-success protocols enabling arbitrary fusions. Layer by layer, we construct qubit architectures incorporating practical optical components such as beam splitters, switches, and photon sources, with graphical proofs that they are deterministic and support universal quantum computation. Together, these results establish a foundation for verifiable compilation and automated optimization in networked quantum computing.