Abstract The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directly implemented through quantum gates prior to final measurements. In this work, we incorporate concepts from MBQC into the circuit model to create a hybrid simulation technique, permitting us to split any quantum circuit into a classically efficiently simulatable Clifford-part and a second part consisting of a stabilizer state and local (adaptive) measurement instructions—a so-called standard form—which is executed on a quantum computer. We further process the stabilizer state with the graph state formalism, thus, enabling a significant decrease in circuit depth for certain applications. We show that groups of mutually-commuting operators can be implemented using fully-parallel, i.e. non-adaptive, measurements within our protocol. In addition, we discuss how groups of mutually commuting observables can be simulatenously measured by adjusting the resource state, rather than performing a costly basis transformation prior to the measurement as it is done in the circuit model. Finally, we demonstrate the utility of our technique on two examples of high practical relevance—the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver (VQE) for the ground-state energy estimation of the water molecule. For the VQE, we find a reduction of the depth by a factor of 4 to 5 using measurement patterns vs. the standard circuit model. At the same time, since we incorporate the simultaneous measurements, our patterns allow us to save shots by a factor of at least 3.5 compared to measuring Pauli strings individually in the circuit model.
Abstract The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directly implemented through quantum gates prior to final measurements. In this work, we incorporate concepts from MBQC into the circuit model to create a hybrid simulation technique, permitting us to split any quantum circuit into a classically efficiently simulatable Clifford-part and a second part consisting of a stabilizer state and local (adaptive) measurement instructions—a so-called standard form—which is executed on a quantum computer. We further process the stabilizer state with the graph state formalism, thus, enabling a significant decrease in circuit depth for certain applications. We show that groups of mutually-commuting operators can be implemented using fully-parallel, i.e. non-adaptive, measurements within our protocol. In addition, we discuss how groups of mutually commuting observables can be simulatenously measured by adjusting the resource state, rather than performing a costly basis transformation prior to the measurement as it is done in the circuit model. Finally, we demonstrate the utility of our technique on two examples of high practical relevance—the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver (VQE) for the ground-state energy estimation of the water molecule. For the VQE, we find a reduction of the depth by a factor of 4 to 5 using measurement patterns vs. the standard circuit model. At the same time, since we incorporate the simultaneous measurements, our patterns allow us to save shots by a factor of at least 3.5 compared to measuring Pauli strings individually in the circuit model.
The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directly implemented through quantum gates prior to final measurements. In this work, we incorporate concepts from MBQC into the circuit model to create a hybrid simulation technique, permitting us to split any quantum circuit into a classically efficiently simulatable Clifford-part and a second part consisting of a stabilizer state and local (adaptive) measurement instructions—a so-called standard for —which is executed on a quantum computer. We further process the stabilizer state with the graph state formalism, thus, enabling a significant decrease in circuit depth for certain applications. We show that groups of mutually-commuting operators can be implemented using fully-parallel, i.e. non-adaptive, measurements within our protocol. In addition, we discuss how groups of mutually commuting observables can be simulatenously measured by adjusting the resource state, rather than performing a costly basis transformation prior to the measurement as it is done in the circuit model. Finally, we demonstrate the utility of our technique on two examples of high practical relevance—the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver (VQE) for the ground-state energy estimation of the water molecule. For the VQE, we find a reduction of the depth by a factor of 4 to 5 using measurement patterns vs. the standard circuit model. At the same time, since we incorporate the simultaneous measurements, our patterns allow us to save shots by a factor of at least 3.5 compared to measuring Pauli strings individually in the circuit model.
The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to the more common quantum circuit model, in which unitary operations are directly implemented through quantum gates prior to final measurements. In this work, we incorporate concepts from MBQC into the circuit model to create a hybrid simulation technique, permitting us to split any quantum circuit into a classically efficiently simulatable Clifford-part and a second part consisting of a stabilizer state and local (adaptive) measurement instructions, a so-called standard form, which is executed on a quantum computer. We further process the stabilizer state with the graph state formalism, thus enabling a significant decrease in circuit depth for certain applications. We show that groups of fully commuting operators can be implemented using fully-parallel, i.e., non-adaptive, measurements within our protocol. In addition, we discuss how such circuits can be implemented in constant quantum depths by employing quantum teleportation. Finally, we demonstrate the utility of our technique on two examples of high practical relevance: the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE).
We introduce an open-source software library Graphix, which optimizes and simulates measurement-based quantum computation (MBQC). By combining the measurement calculus with an efficient graph state simulator, Graphix allows the classical preprocessing of Pauli measurements in the measurement patterns, significantly reducing the number of operations required to perform the quantum computation while maintaining determinism. For a measurement pattern translated from a quantum circuit, this corresponds to the preprocessing of all Clifford gates, and this improvement in the one-way model is important for efficient operations in quantum hardware with limited qubit numbers. In addition to the direct translation from gate networks, we provide a pattern generation method based on flow-finding algorithms, which automatically generates byproduct correction sequences to ensure determinism. We further implement optimization strategies for measurement patterns beyond the standardization procedure and provide tensor-network backend for classically simulating the MBQC.
Abstract Measurement-based quantum computing (MBQC) is a promising approach to reducing circuit depth in noisy intermediate-scale quantum algorithms such as the variational quantum eigensolver (VQE). Unlike gate-based computing, MBQC employs local measurements on a preprepared resource state, offering a trade-off between circuit depth and qubit count. Ensuring determinism is crucial to MBQC, particularly in the VQE context, as a lack of flow in measurement patterns leads to evaluating the cost function at irrelevant locations. This study introduces MBVQE-ansätze that respect determinism and resemble the widely used problem-agnostic hardware-efficient VQE ansatz. We evaluate our approach using ideal simulations on the Schwinger Hamiltonian and XY-model and perform experiments on IBM hardware with an adaptive measurement capability. In our use case, we find that ensuring determinism works better via postselection than by adaptive measurements at the expense of increased sampling cost. Additionally, we propose an efficient MBQC-inspired method to prepare the resource state, specifically the cluster state, on hardware with heavy-hex connectivity, requiring a single measurement round, and implement this scheme on quantum computers with 27 and 127 qubits. We observe notable improvements for larger cluster states, although direct gate-based implementation achieves higher fidelity for smaller instances.
Measurement-based quantum computing (MBQC) is a promising approach to reducing circuit depth in noisy intermediate-scale quantum algorithms such as the Variational Quantum Eigensolver (VQE). Unlike gate-based computing, MBQC employs local measurements on a preprepared resource state, offering a trade-off between circuit depth and qubit count. Ensuring determinism is crucial to MBQC, particularly in the VQE context, as a lack of flow in measurement patterns leads to evaluating the cost function at irrelevant locations. This study introduces MBVQE-ansätze that respect determinism and resemble the widely used problem-agnostic hardware-efficient VQE ansatz. We evaluate our approach using ideal simulations on the Schwinger Hamiltonian and XY-model and perform experiments on IBM hardware with an adaptive measurement capability. In our use case, we find that ensuring determinism works better via postselection than by adaptive measurements at the expense of increased sampling cost. Additionally, we propose an efficient MBQC-inspired method to prepare the resource state, specifically the cluster state, on hardware with heavy-hex connectivity, requiring a single measurement round, and implement this scheme on quantum computers with 27 and 127 qubits. We observe notable improvements for larger cluster states, although direct gate-based implementation achieves higher fidelity for smaller instances.
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.