Sampling from a probability distribution is a core task in many quantum and classical algorithms. Variational quantum circuits provide a natural approach to generating such distributions, as measurement outcomes directly define the probability values. However, designing circuits that train reliably while utilizing limited quantum resources remains largely a heuristic approach. In particular, the roles of expressibility, entanglement capability, and quantum resources in training performance and scalability are not well understood. In this work we present a systematic study of variational quantum circuits where we compare different ansatze family across multiple cost functions and classical optimization methods. We use expressibility and entanglement capability as circuit descriptors to explain convergence behaviors, optimizer sensitivity and robustness to noise. Our results provide a practical guidelines for designing resource aware, efficient and trainable quantum circuits, moving beyond heuristic methods for near term applications.

A well-balanced decoder has been central to the development of modern fault-tolerant quantum computing. However, the inherent topologies of quantum error correcting codes can limit the performance of many well-studied decoding algorithms. In this work, we introduce Noise Assisted Ensemble Decoding (NAED), a highly accurate decoding framework with a significant advantage in real-time speed. NAED constructs an ensemble of Tanner forests, obtained as acyclic subgraphs of the original Tanner graph, and performs exact inference on each Tanner forest using a lightweight dynamic programming algorithm. The forest construction is guided by synthetic soft information derived jointly from the measured syndrome and channel statistics, with controlled noise perturbations generating diverse yet informative decoding matrix column orderings for the Tanner forest construction across the ensemble. Our benchmark results show that the proposed synthetic soft information-driven construction and inference on the Tanner forests can achieve improved or comparable decoding performances to the state-of-the-art decoding solutions, such as BP+OSD$0$, while also providing orders-of-magnitude improvements in per-round decoding speed under circuit-level noise.

Variational quantum algorithms (VQAs) have emerged as a leading paradigm that extracts practical computation from near-term intermediate-scale quantum devices, enabling advances in quantum chemistry simulations, combinatorial optimization, and quantum machine learning. However, the performance of VQAs is highly sensitive to the design of the ansatzes. To be effective, ansatzes must be expressive enough to capture target states but shallow enough to be trainable. We propose a genetic algorithm-inspired framework for designing ansatzes that achieve high expressibility while maintaining shallow depth and low parameter count. Our approach evolves ansatzes through mutation and selection based on an expressibility metric. The circuit generated by our framework consistently demonstrates high expressibility at any target depth and performs comparably to traditional ansatz design approaches. In this work, we present a problem-agnostic, scalable solution for ansatz design, producing expressive, low-depth circuits that need to be designed only once and can serve a wide range of applications.

We construct a hybrid quantum-classical Viterbi decoder for the classical error-correcting codes. Viterbi decoding is a trellis-based procedure for maximum likelihood decoding of classical error-correcting codes. In this article, we demonstrate that the quantum approximate optimization algorithm can find any path on the trellis with the minimum Hamming distance relative to the received erroneous vector. We construct a generalized method to map the Viterbi decoding problem into optimization of a parameterized quantum circuit for any classical linear block code. Also, we propose a uniform parameter optimization strategy to optimize the parameterized quantum circuit using a classical optimizer. We observe that the proposed method efficiently generates low-depth trainable parameterized quantum circuits. Our approach makes the hybrid decoder more efficient than previous attempts at making quantum Viterbi algorithm. We show that using uniform parameter optimization, we obtain parameters more efficiently for the parameterized quantum circuit than previously used methods such as random sampling and fixing the parameters.

As large-scale quantum computers become a reality, they will likely exist as centralized cloud resources accessible to a broad user base. Securely delegating private quantum computations to untrusted servers is therefore a foundational challenge. This requires rigorous guarantees of privacy (blindness), correctness (completeness), and integrity against malicious actions (verifiability). This paper presents an integrated architectural framework for noise-aware distributed quantum computation. The framework combines three technical components into a unified system: (1) a distributed stabilizer code backbone to encode and store quantum states across multiple server nodes, with security analyzed under non-communication and bounded collusion assumptions; (2) a two-level error management structure, where each server node can locally handle errors based on its specific noise model; and (3) a trap-based verification protocol to detect malicious deviations with probability controlled by a security parameter. We provide a security analysis showing that, under the stated assumptions, the framework achieves completeness, blindness, and verifiability with respect to the permitted leakage. Our work provides an architectural blueprint for trustworthy distributed quantum computation under explicitly stated assumptions, paving the way for further development of secure quantum cloud services.

Fault tolerance of quantum protocols require on-par contributions from error-correcting codes and its suitable decoders. One of the most explored error-correcting codes is the family of Quantum Low-Density Parity Check (QLDPC) codes. Although faster than many of the reported decoders for QLDPC codes, iterative decoders fails to produce suitable success rates due to the colossal degeneracy and short cycles intrinsic to these codes. We present a strategy to improve the performance of the iterative decoders based on a collaborative way to use the message passing of the iterative decoders and stabilizer check node removal from the quantum code's Tanner graph. We particularly introduce a notion of qubit separation, which gives us a metric to analyze and improve the min-sum Belief Propagation (BP) based iterative decoder's performance towards harmful configurations of QLDPC codes. We further show that an integration of information measurements (IM) for qubits and it's adjacent stabilizer checks, can be exploited to extract far better performing results from the collaborative decoding architecture compared to its classical predecessor. We analyze the performance of the proposed collaborative decoding architecture, in the context of Generalized Hypergraph Product (GHP) codes. We discuss that the collaborative decoding architecture overcomes iterative decoding failures regarding the harmful trapping set configurations by increasing the separation of trapped qubits without incurring any significant overhead.

Quantum simulation in its current state faces experimental overhead in terms of physical space and cooling. We propose boson sampling as an alternative compact synthetic platform performing at room temperature. Identifying the capability of estimating matrix permanents, we explore the applicability of boson sampling for tackling the dynamics of quantum systems without having access to information about the full state vector. By mapping the time-evolution unitary of a Hamiltonian onto an interferometer via continuous-variable gate decompositions, we present proof-of-principle results of localization characteristics of a single particle. We study the dynamics of one-dimensional tight-binding systems in the clean and quasiperiodic-disordered limits to observe Bloch oscillations and dynamical localization, and the delocalization-to-localization phase transition in the Aubry- Andre-Harper model respectively. Our computational results obtained using boson sampling are in complete agreement with the dynamical and static results of non-interacting tight-binding systems obtained using conventional numerical calculations. Additionally, our study highlights the role of number of sampling measurements or shots for simulation accuracy.

The reliability of quantum computation critically depends on the performance of quantum error-correcting codes (QECCs), which can be severely degraded by hook errors that reduce the effective code distance. In this work, we construct a family of [[n,1,3]] non-CSS QECCs to achieve fault-tolerant (FT) syndrome measurement, where 6 ≤ n ≤ 10. We employ the bare-ancilla method of Muyuan Li et al. to demonstrate fault tolerance in the presence of hook errors during syndrome extraction. We present a systematic protocol for generating these QECCs using graph codes. Using a custom lookup-table decoder, we simulate the code's performance under both anisotropic and circuit-level depolarizing noise. Our results reveal a trade-off in performance with respect to the code rate and identify optimized codes under these noise models. We benchmark our results against the infamous flag-qubit method of Chao et al.. Notably, we introduce a code with improved code rate while maintaining the same distance as the work of Muyuan Li et al. Our approach facilitates the identification and construction of a family of distance three FT non-CSS QECCs.

We present an approach for encoding an Z_$[[n,\ k]]$_Z stabilizer code within the measurement-based quantum computing (MBQC) framework. Our proposed method leverages projective measurements of stabilizer generators, inspired by a stabilizer encoding methodology within gate-based quantum computation [1]. To achieve the encoding of a general stabilizer code, we introduce a suite of gadgets tailored for stabilizer projective measurements utilizing a three-dimensional regular cluster state. The sequential nature of the proposed method offers a new perspective and ensures simplicity, flexibility, and intuitive visualization for stabilizer code encoding using MBQC.

Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is a challenging one. Given the practical difficulty in building a monolithic architecture for quantum computers based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected quantum processors. In such a setting, all syndrome measurements and logical operations must be performed using high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond DQC since entanglement purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder for distilling $3$-qubit GHZ states using a rate $0.118$ family of lifted product QLDPC codes and obtain an input threshold of $\approx 0.7974$ under i.i.d. single-qubit depolarizing noise. This represents the best threshold for a yield of $0.118$ for any GHZ purification protocol. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of $3$-qubit GHZ states to construct a scalable GHZ purification protocol.

Suppose Alice has access to $n$ remote quantum computing nodes capable of universal quantum computation, connected to her by a quantum channel. She wants to use these remote nodes jointly to make computations and store her quantum states such that the actual computation is hidden from these remote nodes. We describe a protocol to help Alice carry out her computation using these remote nodes and store her computation results. We also make sure these nodes can handle noise themselves in case of any error on these nodes. More precisely, we develop an architecture for distributed quantum computation and storage, addressing key challenges in quantum processing across remote nodes. Additionally, we enhance the robustness of each node against noise by developing quantum error-correcting methods suitable for each node.

We develop algorithms for optimizing purity and fidelity from a noisy mixed quantum state through a two-step process: (a) By iteratively optimizing the cost function for purity under regularity conditions using a set of anticommutating Pauli operators, we obtain an optimal set of parameters for the unitary transformation with a significant reduction in complexity. (b) Once the desired level of purity is reached, we align the pure state to the original reference pure state via a unitary transformation. We provide an analysis into the working of the procedure along with simulation results towards validation.

We present a fault-tolerant [[8, 1, 3]] non-CSS quantum error correcting code and study its logical error rates. We modify Gottesman's encoding procedure for stabilizer codes to suit a class of non-CSS quantum codes. We adopt the bare ancilla method presented by Brown et al. to reorder the measurement sequence in the syndrome extraction step and upgrade it to obtain higher pseudo-thresholds and lower leading order terms of logical error rates under the standard depolarizing and anisotropic noise models.

We show the fault-tolerance of the not-so-well known [[8,1,4]] non-CSS code and study the logical error rates of the code. To do so, we adopt the procedure of the bare ancilla method presented by Brown \emph{et al.} We choose the encoding procedure for stabilizer codes given by Gottesman and modify it to suit the setting of a class of non-CSS codes. We consider two types of noise models for this study, namely the depolarizing noise and anisotropic noise to depict the logical error rates obtained in decoding.

Classical network coding uses encoding of information over networks to achieve secure and high throughput communication with low latency. Its quantum analog, namely Quantum Network Coding (QNC) is a promising protocol to achieve quantum communication over quantum networks. In this paper, we propose a method for establishing QNC in Measurement-Based Quantum Computing (MBQC), which is a universal quantum computational model. We demonstrate that the problem of multiple unicast or multiple multicast of distinct computational basis states over a quantum network can be solved by simulating existing classical networks, with the CNOT implementation in MBQC as a basis for transmitting and encoding of states. We also show how it can be further extended to simultaneously distribute the Bell pairs and Greenberger–Horne–Zeilinger (GHZ) states required for quantum communication between distant transmitter and corresponding receiver nodes of a network.

We use a variational method for generating probability distributions, specifically, the Uniform, the Normal, the Binomial distribution, and the Poisson distribution. To do the same, we use many different architectures for the two, three and four-qubit cases using the Jensen-Shannon divergence as our objective function. We use gradient descent with momentum as our optimization scheme instead of conventionally used gradient descent. To calculate the gradient, we use the parameter shift rule, whose formulation we modify to take the probability values as outputs instead of the conventionally taken expectation values. We see that this method can approximate probability distributions, and there exists a specific architecture which outperforms other architectures, and this architecture depends on the number of qubits. The four, three and two-qubit cases consist of a parameterized layer followed by an entangling layer; a parameterized layer followed by an entangling layer, which is followed by a parameterized layer and only parameterized layers, respectively.

Quantum systems are a natural choice for generating probability distributions due to the phenomena of quantum measurements. The data that we observe in nature from various physical phenomena can be modelled using quantum circuits. To load this data, which is mostly in the form of a probability distribution, we present a hybrid classical-quantum approach. The classical pre-processing step is based on the concept of deconvolution of discrete signals. We use the Jensen-Shannon distance as the cost function to quantify the closeness of the outcome from the classical step and the target distribution. The chosen cost function is symmetric and allows us to perform the deconvolution step using any appropriate optimization algorithm. The output from the deconvolution step is used to construct the quantum circuit required to load the given probability distribution, leading to an overall reduction in circuit depth. The deconvolution step splits a bell-shaped probability mass function into smaller probability mass functions, and this paves the way for parallel data processing in quantum hardware, which consists of a quantum adder circuit as the penultimate step before measurement. We tested the algorithm on IBM Quantum simulators and on the IBMQ Kolkata quantum computer, having a 27-qubit quantum processor. We validated the hybrid Classical-Quantum algorithm by loading two different distributions of bell shape. Specifically, we loaded 7 and 15-element PMF for (i) Standard Normal distribution and (ii) Laplace distribution.

Entanglement distribution is a critical task in quantum networks. Since the distributed entanglement can suffer from noise in the channel, it is necessary to develop methods that distill higher quality entanglement from the shared noisy entangled states. In this work, we propose a protocol to distill multi-qubit Greenberger-Horne-Zeilinger (GHZ) states among the nodes of a network using quantum error correcting codes. The method builds upon a Bell state distillation protocol by Wilde et at. (2007) that we recently generalized to 3-qubit GHZ states. The key technical result that enables our protocol shows how measuring a Pauli operator, or in general a set of code stabilizers, on one subsystem of a multipartite GHZ state affects the other subsystems. The design and analysis of the protocol is driven by the stabilizer formalism for measurements, and we provide discussions to elucidate the steps of the protocol. A similar approach can be applied to distill other multipartite entangled states as long as they are stabilizer states.

Surface codes are one of the most important topological stabilizer codes in the theory of quantum error correction. In this paper, we provide an efficient way to obtain surface codes through Measurement-based quantum computation (MBQC) using cluster state as the resource state. Simple twodimensional surface codes are studied and analyzed using stabilizer formalism. We also present an algorithm to computationally obtain the stabilizer of the surface codes, through which we later determine the distance of the codes. We note the difference in the stabilizers of the surface codes obtained by Fowler et al. wherein they used CNOT entangling operation to create the resource state as opposed to the cluster state which is formed using CZ entangling operation. We provide a theoretical calculation to understand this difference. The obtained surface codes can be used practically as an encoder circuit to encode one logical qubit.

Quantum information processing is now a well-evolved field of study with roots to quantum physics that has significantly evolved from pioneering works over almost more than a century. Today, we are at a stage where elementary forms of quantum computers and communication systems are being built and deployed. In this paper, we begin with a historical background into quantum information theory and coding theory for both entanglement-unassisted and assisted quantum communication systems, motivating the need for quantum error correction in such systems. We then begin with the necessary mathematical preliminaries towards understanding the theory behind quantum error correction, central to the discussions within this article, starting from the binary case towards the non-binary generalization, using the rich framework of finite fields. We will introduce the stabilizer framework, build upon the Calderbank-Shor-Steane framework for binary quantum codes and generalize this to the non-binary case, yielding generalized CSS codes that are linear and additive. We will survey important families of quantum codes derived from well-known classical counterparts. Next, we provide an overview of the theory behind entanglement-assisted quantum ECCs along with encoding and syndrome computing architectures. We present a case study on how to construct efficient quantum Reed-Solomon codes that saturate the Singleton bound for the non-degenerate case. We will also show how positive coding rates can be realized using tensor product codes from two zero-rate entanglement-assisted CSS codes, an effect termed as the coding analog of superadditivity, useful for entanglement-assisted quantum communications. We discuss how quantum coded networks can be realized using cluster states and modified graph state codes. Last, we will motivate fault-tolerant quantum computation from the perspective of coding theory. We end the article with our perspectives on interesting open directions in this exciting field.