Variational Quantum Configuration Interaction Achieves Exact Ground States with Subspace Selection

Determining the ground-state energy of a quantum system represents a significant challenge in computational chemistry and physics. Koray Aydoğan, Anna R. Spak, Kade Head-Marsden, and Anthony W. Schlimgen, from the University of Minnesota and University of Rochester, present a novel variational quantum eigensolver (VQE) approach to finding ground state configuration interaction (CI) wavefunctions. Their research maps CI for fermions onto a quantum circuit utilising a subspace superposition and diagonal Walsh operators to encode the wavefunction, offering a pathway to both exact and near-exact solutions for electronic ground states. This method circumvents computationally expensive classical matrix diagonalisations, potentially enabling accurate calculations for larger, more complex systems. Demonstrations using both simulators and quantum hardware highlight the potential of this new technique for advancing quantum simulations of molecular systems.

Fermionic CI Wavefunctions via Quantum Subspace Superposition

Estimating the ground-state energy of a quantum system represents a significant challenge, yet holds immense promise for the application of quantum algorithms. Scientists have now demonstrated a novel variational quantum eigensolver (VQE) approach, specifically designed to determine ground state configuration interaction (CI) wavefunctions with unprecedented efficiency. The research team mapped fermionic CI calculations to a quantum circuit utilizing a subspace superposition technique, subsequently employing diagonal Walsh operators to precisely encode the wavefunction. This innovative algorithm successfully solves both full and selected CI wavefunctions, yielding exact and near-exact solutions for electronic ground states, and is applicable to any Hamiltonian expressible in a qubit basis.

The core of this breakthrough lies in the algorithm’s ability to bypass computationally expensive classical matrix diagonalizations, a critical advantage for large-scale quantum simulations. Researchers achieved this by constructing a diagonal Ansatz for VQE, effectively controlling overparameterization and avoiding the problematic barren plateaus often encountered in quantum optimization. The method comprises two key stages: the preparation of a superposition over physically relevant bit strings, and the application of a diagonal Ansatz that encodes wavefunction coefficients directly into these bit strings. This approach requires only one ancilla qubit and yields a probabilistic algorithm with a consistent 50% success rate, streamlining the computational process.

Experiments conducted using both quantum simulators and actual hardware, specifically IBMQ’s Torino processor, validate the efficacy of this new method. The study reveals that the number of one- and two-qubit gates required scales linearly with the number of Slater determinants, representing a substantial reduction in quantum resource demands. By preparing a uniform superposition over selected determinants, and then applying a diagonal operator to encode the wavefunction coefficients, the team established a pathway towards systematically improvable and non-overparameterized Ansätze for complex many-body Hamiltonians. This work establishes a new standard for quantum state preparation of multireference CI wavefunctions, crucial for accurately modelling strongly correlated systems.

The algorithm’s efficiency stems from its ability to leverage both number-conserving and unstructured subspaces, preparing superpositions with optimized gate scaling. By utilizing a dilated diagonal unitary implemented with Walsh operators, the researchers have created a physically motivated quantum circuit that minimizes computational overhead while maximizing accuracy in ground-state energy estimation. The findings open new avenues for tackling complex molecular simulations and accelerating the development of quantum chemistry applications.

Fermionic CI to Quantum Circuit Mapping

Scientists developed a novel variational quantum eigensolver (VQE) approach for determining ground state configuration interaction (CI) wavefunctions, offering a pathway to solve both full and selected CI problems with exact or near-exact solutions for electronic ground states. The research bypasses computationally expensive classical matrix diagonalizations, a significant advantage for large-scale quantum applications. This method maps fermionic CI to a quantum circuit utilising a subspace superposition, subsequently applying diagonal Walsh operators to encode the desired wavefunction. The technique is applicable to any Hamiltonian expressible in a qubit basis, broadening its potential impact across diverse quantum systems.

The study pioneers a two-step algorithm: superposition preparation and Ansatz application, beginning with a system of r qubits. Researchers meticulously prepare a uniform superposition over selected determinants, encompassing either a full FCI expansion or an unstructured subspace, leveraging number-conserving Dicke spaces with CNOT-gate scaling of O(rN) or quantum walk algorithms scaling at O(rD). Crucially, the team engineered a diagonal operator of CI coefficients, implemented via an ancillary qubit and a dilated diagonal unitary, to prepare the wavefunction. This innovative approach circumvents the limitations of standard unitary transformations when dealing with non-unitary operators inherent in CI calculations.

To achieve the desired superposition, the team harnessed Hadamard gates and a specifically constructed unitary matrix, U, defined by the CI coefficients. Application of U, acting over r+1 qubits, followed by another Hadamard gate on the ancilla, allows for wavefunction preparation conditioned on the ancilla’s measurement outcome. The algorithm inherently yields a 50% success probability, with each outcome producing a unit-norm wavefunction. Experiments were conducted using both simulators and IBMQ’s Torino processor to compute ground-state energies for a range of molecules. This work establishes a foundation for systematically improvable, non-overparameterized Ansätze for many-body Hamiltonians, enabled by relatively simple and physically motivated quantum circuits.

Diagonal Ansatz Maps CI to Quantum Circuits

Scientists have achieved a breakthrough in quantum computation by developing a novel variational quantum eigensolver (VQE) approach for determining ground-state configurations in complex systems. The research introduces a diagonal Ansatz that efficiently prepares multireference configuration interaction (CI) wavefunctions, bypassing computationally expensive classical matrix diagonalizations. This new method demonstrates a path towards systematically improvable and non-overparameterized Ansätze for many-body Hamiltonians, utilising relatively simple quantum circuits. Experiments reveal the algorithm successfully maps CI for fermions to a quantum circuit using a subspace superposition, followed by the application of diagonal Walsh operators to encode the wavefunction.

The team measured performance across a range of molecules, utilising both quantum simulators and hardware, specifically IBMQ’s Torino processor. Results demonstrate the capability to solve both full CI and selected CI wavefunctions, yielding exact and near-exact solutions for electronic ground states, with the number of one- and two-qubit gates scaling linearly with the number of Slater determinants. The core of this work lies in a two-step process: superposition preparation and Ansatz application, beginning with the creation of a superposition over selected, physically-relevant bitstrings. Scientists prepared number-conserving SDs, utilising a quantum circuit with CNOT-gate scaling of O(rN), where ‘r’ represents the number of qubits and ‘N’ the number of electrons.

Furthermore, the team successfully prepared states preserving both number and spin, alongside unstructured states, employing a quantum walk algorithm exhibiting CNOT-gate scaling of O(rD), where ‘D’ denotes the number of SDs. Measurements confirm the superposition preparation, denoted as |S⟩ = US|0⟩⊗r, where |S⟩ is the superposed subspace and |0⟩⊗r represents the r-fold tensor product of the ground state. The algorithm’s probabilistic nature, with a success probability of 50%, is balanced by its efficiency and scalability. This breakthrough delivers a significant advancement in quantum algorithms for eigenvalue estimation, offering a promising route for tackling strongly correlated systems where classical calculations are often limited by parameter space growth and many-body entanglement.

Fermion CI Mapped to Quantum Circuits

This work details a novel variational quantum eigensolver (VQE) approach for determining ground state configurations in quantum systems. This technique successfully yields exact and near-exact solutions for electronic ground states, and is applicable to any Hamiltonian expressible in a qubit basis, circumventing computationally expensive classical matrix diagonalisations. Demonstrated on several molecules using both simulators and quantum hardware, the algorithm achieves increasingly accurate results as the selected CI space expands.

The presented wavefunction Ansatz requires O(DlogD) CNOT gates, with a classical cost of O(D2log2D), and avoids characteristics that lead to barren plateaus, a common challenge in quantum machine learning. Authors acknowledge limitations related to the classical cost of maintaining surjectivity, which scales similarly to existing QSCI methods, and the sensitivity of VQE algorithms to optimisation details. Future research could focus on further reducing the classical overhead by relaxing surjectivity requirements and oversampling the Hilbert space, offering a scalable strategy for both weakly and strongly correlated ground states. The flexible subspace preparation step also allows for the incorporation of symmetries, potentially enhancing the efficiency of quantum algorithms for condensed matter models and other complex systems. This work represents a significant step towards utilising quantum computation for accurate and efficient molecular simulations.