Quantum-Enhanced Simulation-Based Optimization

In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is approximated via simulation. Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up over classical Monte Carlo simulation. Hence, in many cases, it can achieve a speed-up for simulation-based optimization as well. Combining QAE with ideas from quantum optimization, we show how this can be used not only for continuous but also for discrete optimization problems. Furthermore, the algorithm is demonstrated on illustrative problems such as portfolio optimization with a Value at Risk constraint and inventory management.Comment: 9 pages, 9 figure

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with $d$ parameters, however, is computationally expensive and generally requires $\mathcal{O}(d^2)$ function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines

Variational Quantum Time Evolution without the Quantum Geometric Tensor

The real- and imaginary-time evolution of quantum states are powerful tools in physics and chemistry to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. They also find applications in wider fields such as quantum machine learning or optimization. On near-term devices, variational quantum time evolution is a promising candidate for these tasks, as the required circuit model can be tailored to trade off available device capabilities and approximation accuracy. However, even if the circuits can be reliably executed, variational quantum time evolution algorithms quickly become infeasible for relevant system sizes. They require the calculation of the Quantum Geometric Tensor and its complexity scales quadratically with the number of parameters in the circuit. In this work, we propose a solution to this scaling problem by leveraging a dual formulation that circumvents the explicit evaluation of the Quantum Geometric Tensor. We demonstrate our algorithm for the time evolution of the Heisenberg Hamiltonian and show that it accurately reproduces the system dynamics at a fraction of the cost of standard variational quantum time evolution algorithms. As an application, we calculate thermodynamic observables with the QMETTS algorithm

Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection

We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum algorithms for optimization where a classical objective function is provided as a given Quadratic Unconstrained Binary Optimization problem and mapped to a sum of Pauli operators. Furthermore, we provide theoretical justification for our method based on convergence guarantees of quantum imaginary time evolution. To investigate the performance of our algorithm and its potential advantages, we tackle a challenging real-world optimization problem: $\textit{feature selection}$. This refers to the problem of selecting a subset of relevant features to use for constructing a predictive model such as fraud detection. Optimal feature selection---when formulated in terms of a generic loss function---offers little structure on which to build classical heuristics, thus resulting primarily in ‘greedy methods’. This leaves room for (near-term) quantum algorithms to be competitive to classical state-of-the-art approaches. We apply our quantum-optimization-based feature selection algorithm, termed VarQFS, to build a predictive model for a credit risk data set with $20$ and $59$ input features (qubits) and train the model using quantum hardware and tensor-network-based numerical simulations, respectively. We show that the quantum method produces competitive and in certain aspects even better performance compared to traditional feature selection techniques used in today's industry

Iterative quantum amplitude estimation

We introduce a variant of Quantum Amplitude Estimation (QAE), called Iterative QAE (IQAE), which does not rely on Quantum Phase Estimation (QPE) but is only based on Grover’s Algorithm, which reduces the required number of qubits and gates. We provide a rigorous analysis of IQAE and prove that it achieves a quadratic speedup up to a double-logarithmic factor compared to classical Monte Carlo simulation with provably small constant overhead. Furthermore, we show with an empirical study that our algorithm outperforms other known QAE variants without QPE, some even by orders of magnitude, i.e., our algorithm requires significantly fewer samples to achieve the same estimation accuracy and confidence level

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with d parameters, however, is computation-ally expensive and generally requires O(d(2)) function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines.ISSN:2521-327

Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection

We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum algorithms for optimization where a classical objective function is provided as a given Quadratic Unconstrained Binary Optimization problem and mapped to a sum of Pauli operators. Furthermore, we provide theoretical justification for our method based on convergence guarantees of quantum imaginary time evolution. To investigate the performance of our algorithm and its potential advantages, we tackle a challenging real-world optimization problem: feature selection. This refers to the problem of selecting a subset of relevant features to use for constructing a predictive model such as fraud detection. Optimal feature selection -- when formulated in terms of a generic loss function -- offers little structure on which to build classical heuristics, thus resulting primarily in 'greedy methods'. This leaves room for (near-term) quantum algorithms to be competitive to classical state-of-the-art approaches. We apply our quantum-optimization-based feature selection algorithm, termed VarQFS, to build a predictive model for a credit risk data set with 20 and 59 input features (qubits) and train the model using quantum hardware and tensor-network-based numerical simulations, respectively. We show that the quantum method produces competitive and in certain aspects even better performance compared to traditional feature selection techniques used in today's industry

Qiskit/qiskit: Qiskit 0.25.3

<h1>Changelog</h1> <h2>Fixed</h2> <ul> <li>Fix input normalisation of <code>transpile(initial_layout=...)</code> (backport #11031) (#11058)</li> <li>Fix calling backend.name() for backendV2 (#11065) (#11076) (#11092)</li> <li>Fix build filter coupling map with mix ideal/physical targets (#11009) (#11049)</li> <li>Emit a descriptive error when the QPY version is too new (#11094)</li> <li>BackendEstimator support BackendV2 without coupling_map (#10956) (#11006)</li> <li>Support dynamic circuit in BackendEstimator (#9700) (#10984)</li> <li>Avoid useless deepcopy of target with custom pulse gates in transpile (#10973) (#10978)</li> <li>Fix bug in qs_decomposition (#10850) (#10957)</li> </ul&gt