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Grover's algorithm searches through an unstructured database, offering a quadratic speedup over classical search algorithms. We implement it, as well as two deterministic variants, on IBM (Kingston) and IQM (Garnet) hardware. Additionally, we test dynamical decoupling as an error mitigation technique. We compare our results to a classical, brute force approach to evaluate current hardware capabilities.
We pursue scientific research at the interface of High Energy Physics and Quantum Information Science. This includes studies of thermal radiation and quantum entanglement in high-energy collisions at the Large Hadron Collider (LHC), with special emphasis on entanglement entropy and the Higgs boson. This project has also been extended to include quantum entanglement and charged current weak interactions using Fermilab results. And most recently, we have begun tests of the temporal entanglement using LHC data. Collider experiments such as proton-proton collisions at the LHC yield hadrons that exhibit an exponential behavior at low transverse momenta. This surprising behavior is seen in data from both the ATLAS and CMS collaborations. We attribute this phenomenon to quantum entanglement between the regions in the nucleon wave function. The exponential component to the transverse momentum distribution is a result of thermal radiation that is akin to Hawking or Unruh radiation that should exist at the event horizon of astrophysical black holes and neutron stars. The Principal Investigator, in collaboration with a theoretical physicist at Stony Brook University and Brookhaven National Laboratory, and with Yale University students, has shown evidence for this thermal radiation in several production and decay processes in the ATLAS and CMS data, and its connection to entanglement entropy (O.K. Baker and D.E Kharzeev, Phys. Rev. D 98, 054007 (2018)), including even the Higgs boson sector. Interestingly, this thermal behavior is also seen in momentum distributions of charged current weak interactions according to our studies. These findings suggest a deep connection between quantum entanglement (entanglement entropy) and thermalization in both hadron collisions at the energy frontier and neutrino scattering at the intensity frontier. We have confirmed the proposed relation between the effective temperature and the hard-scattering scale at lower energies using the most recent LHC data for the following systems: Higgs bosons, top quarks, and charged hadrons. Additionally, we have results for hadron production in neutrino scattering from nuclei using Fermilab weak interaction data. This study is carried out using data from the MINERvA collaboration. In those cases where entanglement is expected, there is an exponential component to the momentum distribution, while this component is absent in those processes where no entanglement is expected. This research thus tests the hypothesis about a link between quantum entanglement and thermalization in strong and weak interactions. See Phys Lett B 811, 135948 (2020). We also initiated research applying a quantum search algorithm (Grover's Algorithm) to LHC data. This quantum algorithm was used to show how rare events in LHC data can be searched for in large, unsorted databases, with quadratic speedup compared to classical search algorithms on classical computers. See "Application of a Quantum Search Algorithm to High- Energy Physics Data at the Large Hadron Collider", arXiv:2010.00649 [quant-ph].
Environmental screening of gamma radiation consists of detecting weak nuisance and anomaly signal in the presence of strong and highly varying background. In a typical scenario, a mobile detector-spectrometer continuously measures gamma radiation spectra in short, e.g., one-second, signal acquisition intervals. In principle, gamma radiation sources can be detected and identified by their unique spectral lines. However, detecting sources from data measured in a search scenario is difficult due to the highly varying background because of naturally occurring radioactive material (NORM), and low signal-to-noise ratio (S/N) of spectral signal measured during one-second acquisition intervals. In recent prior work, we have developed a Hopfield Neural Network (HNN) in conjunction with an image processing algorithm to detect a weak signal anomaly hidden among the highly fluctuating background spectra. The objective of this work is to explore quantum computing methods to increase the speed of HNN. The approach is based on the Grover’s search algorithm in conjunction with a 3-SAT problem formalism. The Grover’s algorithm is implemented on a quantum computing simulator using Qiskit software. Performance of HNN algorithm is benchmarked using search data from an environmental screening campaign, where the anomaly is a subset of measurements containing a 137 Cs source. Results indicate that using Grover’s algorithm on a quantum simulator reduces runtime of HNN by two orders of magnitude.
Abstract Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's algorithm was designed without considering the physical resources, such as depth, in the real implementations. Therefore, Grover's algorithm can be improved for NISQ devices. In this paper, we demonstrate how to implement quantum search algorithms better on NISQ devices. We present detailed benchmarks of the five-qubit quantum search algorithm on different quantum processors, including IBMQ, IonQ, and Honeywell quantum devices. We report the highest success probability of the five-qubit search algorithm compared to previous works. Our results show that designing the error-aware quantum search algorithms is possible, which can maximally harness the power of NISQ computers.
Performance of the Rigetti quantum computing platform was tested during the period of time from 12/16/2019 to 05/18/2020. The Grover's search (GS) algorithm was used as a testing tool, in particular, 3- and 4-level versions of the algorithm. As a result, a number of hardware issues were revealed, so the algorithm was split to smaller blocks and individual gates, and all of them were tested separately. The fidelity decay was found to be due to both decoherent processes and coherent errors of the native hardware gates. These errors were estimated from RX gate benchmarks and were in a form of extra rotation of the quantum state. As a consequence of that, performance of the algorithm was shown to be strongly dependent on the native gate decomposition of the program. Suggestions and possible improvements of the future Rigetti runs are made based on the obtained observations.
Quantum multi-programming is a method utilizing contemporary noisy intermediate-scale quantum computers by executing multiple quantum circuits concurrently. Despite early research on it, the research remains on quantum gates or small-size quantum algorithms without correlation. In this paper, we propose a quantum multi-programming (QMP algorithm for Grover's search. Our algorithm decomposes Grover's algorithm by the partial diffusion operator and executes the decomposed circuits in parallel by QMP. We proved that this new algorithm increases the rotation angle of the Grover operator which, as a result, increases the success probability. The new algorithm is implemented on IBM quantum computers and compared with the canonical Grover's algorithm and other variations of Grover's algorithms. So, the empirical tests validate that our new algorithm outperforms other variations of Grover's algorithms as well as the canonical Grover's algorithm.
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We designed a quantum search algorithm, giving the same quadratic speedup achieved by Grover's original algorithm; we replace Grover's diffusion operator (hard to implement) with a product diffusion operator generated by transverse fields (easy to implement). In our algorithm, the problem Hamiltonian (oracle) and the transverse fields are applied to the system alternatively. We construct such a sequence that the corresponding unitary generates a closed transition between the initial state (even superposition of all states) and a modified target state, which has a high degree of overlap with the original target state.
Protein design is a technique to engineer proteins by permuting amino acids in the sequence to obtain novel functionalities. However, exploring all possible combinations of amino acids is generally impossible due to the exponential growth of possibilities with the number of designable sites. The present work introduces circuits implementing a pure quantum approach, Grover’s algorithm, to solve protein design problems. Our algorithms can adjust to implement any custom pair-wise energy tables and protein structure models. Moreover, the algorithm’s oracle is designed to consist of only adder functions. Quantum computer simulators validate the practicality of our circuits, containing up to 234 qubits. However, a smaller circuit is implemented on real quantum devices. Our results show that using iterations, the circuits find the correct results among all N possibilities, providing the expected quadratic speed up of Grover’s algorithm over classical methods (i.e.,).
Grover's algorithm provides a quadratic speedup for searching unstructured databases and is traditionally implemented with qubits in Hilbert spaces whose dimensions are powers of two. With the advent of quantum platforms utilizing qudits---quantum systems with more than two levels---there is a need to generalize Grover search to these architectures, including heterogeneous systems with qudits of varying dimensions. Here, we present a unified framework for qudit-based Grover search, detailing the construction of oracles and diffusion operators with and without ancilla qubits and generalizing deterministic and fixed-point search variants that ensure exact or bounded success probabilities. We analyze phase-matching techniques and provide explicit circuit decompositions suitable for diverse hardware platforms. We also compare the corresponding trajectories on the Bloch sphere to provide an intuitive visualization of how the different phase choices amplify the target state. These results facilitate flexible, hardware-oriented protocols for implementing Grover search on qudit processors, potentially reducing circuit depth and enhancing success probabilities, thereby offering a practical toolkit for quantum computation and sensing applications leveraging multilevel quantum systems.
Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Here, examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover's algorithm based on the quantum alternating operator ansatz. In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward $\mathcal{O}\left({2}^{n/2}\right)$, the optimal oracle complexity of quantum unstructured search.
With the advent of the High-Luminosity Large Hadron Collider (HL-LHC) era, high energy physics (HEP) event selection will require new approaches to rapidly and accurately analyze vast databases. The current study addresses the enormity of HEP databases in an unprecedented manner—a quantum search using Grover’s Algorithm (GA) on an unsorted database, ATLAS Open Data, from the ATLAS detector. A novel method to identify rare events at 13 TeV in CERN’s LHC using quantum computing (QC) is presented. As indicated by the Higgs boson decay channel H→ZZ*→4l , the detection of four leptons in one event may be used to reconstruct the Higgs boson and, more importantly, evince Higgs boson decay to some new phenomena, such as H→ZZ d →4l . Searching the dataset for collisions resulting in detection of four leptons using a Jupyter Notebook, a classical simulation of GA, and several quantum computers with multiple qubits, the current application was found to make the proper selection in the unsorted dataset. Quantum search efficacy was analyzed for the incoming HL-LHC by implementing the QC method on multiple classical simulators and IBM’s quantum computers with the IBM Qiskit Open Source Software. The current QC application provides a novel, high-efficiency alternative to classical database searches, demonstrating its potential utility as a rapid and increasingly accurate search method in HEP.
Modern NISQ devices are subject to a variety of biases and sources of noise that degrade the solution quality of computations carried out on these devices. A natural question that arises in the NISQ era, is how fairly do these devices sample ground state solutions. To this end, we run five fair sampling problems (each with at least three ground state solutions) that are based both on quantum annealing and, on the Grover Mixer, -QAOA algorithm for gate-based NISQ hardware. In particular, we use seven IBM Q devices, the Aspen-9 Rigetti device, the IonQ device, and three D-Wave quantum annealers. For each of the fair sampling problems, we measure the ground state probability, the relative fairness of the frequency of each ground state solution with respect to the other ground state solutions, and the aggregate error as given by each hardware provider. Overall, our results show that NISQ devices do not achieve fair sampling yet. Furthermore, we also observe differences in the software stack with a particular focus on compilation techniques that illustrate what work will still need to be done to achieve a seamless integration of frontend (i.e., quantum circuit description) and backend compilation.
This research represents a continuation of our investigation of the Rigetti quantum platform as part of the Quantum Leap for Fusion Energy Sciences project. We evaluate the performance of the new Aspen-11, Aspen-M-2, Aspen-M-3 quantum processing units (QPU) through the application of the Grover’s search algorithm and the validation of single gate fidelities. The performance of the new QPUs is compared to the older Aspen-7 device, and it is shown that qubit pair selection plays a key role in the optimization process. Additionally, we delve into the examination of coherent and decoherent errors associated with native gates. To optimize our approach, we have developed several relatively inexpensive hardware protocols aimed at facilitating the selection of the most suitable qubit pairs. These protocols involve running various circuits on the hardware and assessing the overall performance of the tested qubit pairs. Through these protocols, we have demonstrated that the quality of qubit pairs on a single chip can exhibit significant variations.
This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-Boolean oracles. The action of a non-Boolean oracle $U_\varphi $ on an eigenstate $\mathinner {|{x}\rangle }$ is to apply a state-dependent phase-shift $\varphi (x)$. Unlike Boolean oracles, the eigenvalues $\exp (i\varphi (x))$ of a non-Boolean oracle are not restricted to be $\pm 1$. Two new oracular algorithms based on such non-Boolean oracles are introduced. The first is the non-Boolean amplitude amplification algorithm, which preferentially amplifies the amplitudes of the eigenstates based on the value of $\varphi (x)$. Starting from a given initial superposition state $\mathinner {|{\psi _0}\rangle }$, the basis states with lower values of $\cos (\varphi )$ are amplified at the expense of the basis states with higher values of $\cos (\varphi )$. The second algorithm is the quantum mean estimation algorithm, which uses quantum phase estimation to estimate the expectation $\mathinner {\langle {\psi _0|U_\varphi |\psi _0}\rangle }$, i.e., the expected value of $\exp (i\varphi (x))$ for a random x sampled by making a measurement on $\mathinner {|{\psi _0}\rangle }$. It is shown that the quantum mean estimation algorithm offers a quadratic speedup over the corresponding classical algorithm. Both algorithms are demonstrated using simulations for a toy example. Potential applications of the algorithms are briefly discussed.
Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.