Abstract Quantum computers may offer multiple advantages, consisting of quantum speed-up when performing hard computation tasks, better compression and expressivity, reduced power consumption, and the capability of simulating natively elementary processes by representing their constituents by qubit. Therefore, chemical, nuclear and elementary particle reactions or Hamiltonian dynamics have been simulated consistently with the number of available qubits. The compact use of resources is of paramount importance for both simulating larger problems or, in prospect, introduce more robust quantum error correction routines to extend the depth of the circuits. Measurement-based quantum computing (MBQC) consists of a virtualization of gate model quantum computing over a limited subset of gate operation involving intermediate measurement processes as well, particularly suitable for photonic hardware. Here, we review the method recently introduced for direct compiling gate model circuit based on unitary processes over the measurement-based scheme. Surprisingly, in addition to better performances with respect to previously known methods, we find a gauge freedom which makes possible to even improve the efficiency. Such gauge invariance provides graphical rules, as happens with Feynman rules in perturbative quantum mechanics. Compared to Measurement Calculus, the ancillary qubits are reduced by 50% on QFT and 75% on QAOA algorithms.
Abstract Quantum computers may offer multiple advantages, consisting of quantum speed-up when performing hard computation tasks, better compression and expressivity, reduced power consumption, and the capability of simulating natively elementary processes by representing their constituents by qubit. Therefore, chemical, nuclear and elementary particle reactions or Hamiltonian dynamics have been simulated consistently with the number of available qubits. The compact use of resources is of paramount importance for both simulating larger problems or, in prospect, introduce more robust quantum error correction routines to extend the depth of the circuits. Measurement-based quantum computing (MBQC) consists of a virtualization of gate model quantum computing over a limited subset of gate operation involving intermediate measurement processes as well, particularly suitable for photonic hardware. Here, we review the method recently introduced for direct compiling gate model circuit based on unitary processes over the measurement-based scheme. Surprisingly, in addition to better performances with respect to previously known methods, we find a gauge freedom which makes possible to even improve the efficiency. Such gauge invariance provides graphical rules, as happens with Feynman rules in perturbative quantum mechanics. Compared to Measurement Calculus, the ancillary qubits are reduced by 50% on QFT and 75% on QAOA algorithms.
The measurement-based architecture is a paradigm of quantum computing, relying on the entanglement of a cluster of qubits and the measurements of a subset of it, conditioning the state of the unmeasured output qubits. While methods to map the gate model circuits into the measurement-based are already available via intermediate steps, we introduce a paradigm for quantum compiling directly converting any quantum circuit to a class of graph states, independently from its size. This method relies on the stabilizer formalism to describe the register of the input qubits. An equivalence class between graph states able to implement the same circuit is defined, giving rise to a gauge freedom when compiling in the MBQC frame. The graph state can be rebuilt from the circuit and the input by employing a set of graphical rules. A system of equations describes the overall process. Compared with measurement calculus, the ancillary qubits are reduced by 50% on the quantum Fourier transform and 75% on the Quantum Approximate Optimization Algorithm, still preserving similar scaling laws for the number of entangling gates.
Despite progress in quantum computing technology, the optimization of quantum circuit compilation for real-world quantum processing units (QPUs) [1] continues to pose a significant challenge. Current compilers use static gate-based models, which cannot adjust to changes in hardware limitations and noise fluctuations. In this study, we introduce Qukkos, a novel measurement-based quantum compilation system that optimizes resource utilization, improves circuit dependability, and achieves higher execution efficiency. To increase its adaptability for real-world quantum devices, Qukkos uses measurement-based quantum computing (MBQC) [2], [3], [4], [5], [6] to conduct dynamic circuit change. This system combines a quantum compiler with a quantum resource virtualization manager and standardized API interfaces to achieve seamless cross-platform execution alongside efficient task scheduling. Our experimental results across various QPU architectures show that Qukkos improves circuit depth reduction while increasing fidelity and speeding up compilation times relative to conventional methods. The modular design of Qukkos enables interoperability between superconducting qubits and trapped-ion systems as well as photonic quantum platforms and establishes it as a scalable solution for future quantum computing applications.
Abstract Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations only requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate its effectiveness, efficiency, and advantages with the two-dimensional Heisenberg model and the Fermi–Hubbard chain. Numerical experiments show that MBHVA can have similar performance as circuit-based ansatz, and is expected to reduce operation counts during execution compared to quantum circuits, bringing the advantage of running time. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in the noisy intermediate-scale quantum era, especially in the presence of large multi-qubit rotation operations.
Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared to the unitary model, scaling as N×D, where N is the number of logical qubits (width) and D is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be learned by the corresponding unitary model.
Circuit-based quantum computing (CBQC), also known as the gate model, is currently regarded as the leading paradigm for performing quantum computation and has garnered widespread interest due to its relatively better-established implementation and close intuitive resemblance to classical computation. However, an alternative model that solely utilizes single-qubit measurements on entangled states to perform computation, namely the measurement-based quantum computing (MBQC), has started to attract further research interest as it is deemed more naturally suited for certain quantum hardware architectures, though its actual implementation remains largely underexplored. Recently, there have been preliminary efforts to characterize the specific regimes in which MBQC may potentially be more advantageous compared to CBQC. Nevertheless, a more systematic assessment is necessary to assess the suitability of each model across a broader range of more practical cases. In this work, we present a detailed comparative analysis of CBQC and MBQC, beginning with reviewing the theoretical foundations of each model before highlighting its distinguishing features that set the two paradigms apart. Furthermore, building on previous work, we propose a generalized regime analysis that more accurately captures the conditions under which a given quantum algorithm is more favorably executed in MBQC or CBQC. Subsequently, we identify critical parameters that likely determine whether a quantum algorithm is better suited to CBQC or MBQC, categorizing detailed key factors and performance metrics into layers of quantum computation. Next, we propose a decision flow that, given specific hardware constraints and algorithm requirements, guides the selection to the most appropriate model, discussing suitability in two representative worked examples of quantum algorithm applications: Quantum Fourier Transform (QFT) and Variational Quantum Algorithm (VQE). Last, we discuss the potential to combine both models as a hybrid approach to leverage the best of both worlds and explore its benefits for practical quantum computing applications.
Quantum computers hold the promise of solving certain computational problems significantly faster than classical computers. Unlocking the full potential of quantum hardware depends on our ability to efficiently translate high-level quantum algorithms into executable sequences of quantum operations tailored to the specific constraints of a given device, a task known as quantum compilation. Among the most promising applications is the simulation of quantum systems, such as in quantum chemistry, where scalable, error resilient, and experimentally feasible Hamiltonian simulation techniques are essential. In the first part of this thesis, we present recent advances in the field of quantum compilation, emphasizing on efficient gate decomposition and circuit optimization. In particular, we analyze compilation techniques for Clifford circuits and general single-qubit rotations. Clifford operations play a central role in quantum error correction, the characterization of quantum devices and quantum cryptography. We explore asymptotically optimal decomposition methods, including constructions using either two-qubit gates or global entangling operations, the latter being especially well-suited for platforms like trapped ions. For single-qubit unitaries, we discuss approximation schemes that achieve the theoretically optimal scaling of gate count with respect to the desired precision. Beyond gate synthesis, we examine various hardware-aware optimization strategies aimed at reducing circuit depth and gate overhead. These include techniques for qubit routing in systems with limited connectivity, as well as methods for removing redundant operations. The second and primary, scientific contribution of this thesis focuses on implementation of effective many-body interactions on quantum hardware by combining the system’s native dynamics with control operations, which we call Hamiltonian engineering. Motivated by the central role of Hamiltonian simulation in quantum science, we introduce a general and efficient framework for synthesizing arbitrary target Hamiltonians under mild locality constraints. We propose a novel linear programming (LP) approach that computes pulse sequences consisting of single-qubit π or π/2 rotations applied at certain times during free evolution under the system’s native Hamiltonian. Our LP-based framework offers multiple advantages. First, its classical runtime depends only on the number and locality of the interactions in the system Hamiltonian, not directly on the overall system size. Second, we extend the method to include robustness against common error sources such as finite pulse time effects and systematic control errors, leveraging tools from average Hamiltonian theory and robust composite pulses. Our approach enables the efficient realization of high-fidelity Hamiltonian dynamics with minimal experimental overhead. The scalability of the approach are demonstrated through simulations, including the engineering of a random two-body Hamiltonian on a 225 qubit lattice in under a minute of classical preprocessing. In conclusion, this thesis contributes both theoretical insights and practical tools that bridge the gap between algorithm design and experimental implementation in quantum computing. The techniques developed here are directly applicable to a variety of platforms, including trapped ions, neutral atoms, and superconducting circuits. By advancing the frontiers of Hamiltonian engineering, this work enables more efficient, robust, and scalable quantum simulations on nearterm devices. Finally, it brings us closer to realizing quantum technologies, which are possibly capable of solving meaningful problems.