Complete 3-Qubit Grover search on a programmable quantum computer

Effect of Pure Dephasing Quantum Noise in the Quantum Search Algorithm Using Atos Quantum Assembly

Quantum computing is tipped to lead the future of global technological progress. However, the obstacles related to quantum software development are an actual challenge to overcome. In this scenario, this work presents an implementation of the quantum search algorithm in Atos Quantum Assembly Language (AQASM) using the quantum software stack my Quantum Learning Machine (myQLM) and the programming development platform Quantum Learning Machine (QLM). We present the creation of a virtual quantum processor whose configurable architecture allows the analysis of induced quantum noise effects on the quantum algorithms. The codes are available throughout the manuscript so that readers can replicate them and apply the methods discussed in this article to solve their own quantum computing projects. The presented results are consistent with theoretical predictions and demonstrate that AQASM and QLM are powerful tools for building, implementing, and simulating quantum hardware.

A quantum-inspired probabilistic prime factorization based on virtually connected Boltzmann machine and probabilistic annealing

Probabilistic computing has been introduced to operate functional networks using a probabilistic bit (p-bit), broadening the computational abilities in non-deterministic polynomial searching operations. However, previous developments have focused on emulating the operation of quantum computers similarly, implementing every p-bit with large weight-sum matrix multiplication blocks and requiring tens of times more p-bits than semiprime bits. In addition, operations based on a conventional simulated annealing scheme required a large number of sampling operations, which deteriorated the performance of the Ising machines. Here we introduce a prime factorization machine with a virtually connected Boltzmann machine and probabilistic annealing method, which are designed to reduce the hardware complexity and number of sampling operations. From 10-bit to 64-bit prime factorizations were performed, and the machine offers up to 1.2 × 108 times improvement in the number of sampling operations compared with previous factorization machines, with a 22-fold smaller hardware resource.

Experimental demonstration of deterministic quantum search for multiple marked states without adjusting the oracle

Grover's search algorithm is a well-known quantum algorithm that has been extensively studied and improved to increase its success rate and enhance its flexibility. However, most improved search algorithms require an adjustment of the oracle, which may not be feasible in practical problem-solving scenarios. In this work, we report an experimental demonstration of a deterministic quantum search for multiple marked states without adjusting the oracle. A linear optical setup is designed to search for two marked states, one in a 16-state database with an initial equal-superposition state and the other in an 8-state database with different initial nonequal-superposition states. The evolution of the probability of finding each state in the database is also measured and displayed. Our experimental results agree well with the theoretical predictions, thereby proving the feasibility of the search protocol and the implementation scheme. This work is a pioneering experimental demonstration of deterministic quantum search for multiple marked states without adjusting the oracle.

N-Body Interactions between Trapped Ion Qubits via Spin-Dependent Squeezing

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows for the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.

Quantum-effective exact multiple patterns matching algorithms for biological sequences

This article presents efficient quantum solutions for exact multiple pattern matching to process the biological sequences. The classical solution takes Ο(mN) time for matching m patterns over N sized text database. The quantum search mechanism is a core for pattern matching, as this reduces time complexity and achieves computational speedup. Few quantum methods are available for multiple pattern matching, which executes search oracle for each pattern in successive iterations. Such solutions are likely acceptable because of classical equivalent quantum designs. However, these methods are constrained with the inclusion of multiplicative factor m in their complexities. An optimal quantum design is to execute multiple search oracle in parallel on the quantum processing unit with a single-core that completely removes the multiplicative factor m, however, this method is impractical to design. We have no effective quantum solutions to process multiple patterns at present. Therefore, we propose quantum algorithms using quantum processing unit with C quantum cores working on shared quantum memory. This quantum parallel design would be effective for searching all t exact occurrences of each pattern. To our knowledge, no attempts have been made to design multiple pattern matching algorithms on quantum multicore processor. Thus, some quantum remarkable exact single pattern matching algorithms are enhanced here with their equivalent versions, namely enhanced quantum memory processing based exact algorithm and enhanced quantum-based combined exact algorithm for multiple pattern matching. Our quantum solutions find all t exact occurrences of each pattern inside the biological sequence in O ( ( m / C ) N ) and O ( ( m / C ) t ) time complexities. This article shows the hybrid simulation of quantum algorithms to validate quantum solutions. Our theoretical-experimental results justify the significant improvements that these algorithms outperform over the existing classical solutions and are proven effective in quantum counterparts.

Multi-qubit entanglement and algorithms on a neutral-atom quantum computer

Gate-model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high-fidelity logic. Neutral-atom hyperfine qubits provide inherent scalability owing to their identical characteristics, long coherence times and ability to be trapped in dense, multidimensional arrays¹. Combined with the strong entangling interactions provided by Rydberg states^2-4, all the necessary characteristics for quantum computation are available. Here we demonstrate several quantum algorithms on a programmable gate-model neutral-atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits. Preparation of entangled Greenberger-Horne-Zeilinger (GHZ) states⁵ with up to six qubits, quantum phase estimation for a chemistry problem⁶ and the quantum approximate optimization algorithm (QAOA)⁷ for the maximum cut (MaxCut) graph problem are demonstrated. These results highlight the emergent capability of neutral-atom qubit arrays for universal, programmable quantum computation, as well as preparation of non-classical states of use for quantum-enhanced sensing.

Implementation of quantum compression on IBM quantum computers

Advances in development of quantum computing processors brought ample opportunities to test the performance of various quantum algorithms with practical implementations. In this paper we report on implementations of quantum compression algorithm that can efficiently compress unknown quantum information. We restricted ourselves to compression of three pure qubits into two qubits, as the complexity of even such a simple implementation is barely within the reach of today's quantum processors. We implemented the algorithm on IBM quantum processors with two different topological layouts-a fully connected triangle processor and a partially connected line processor. It turns out that the incomplete connectivity of the line processor affects the performance only minimally. On the other hand, it turns out that the transpilation, i.e. compilation of the circuit into gates physically available to the quantum processor, crucially influences the result. We also have seen that the compression followed by immediate decompression is, even for such a simple case, on the edge or even beyond the capabilities of currently available quantum processors.

Deterministic Search on Star Graphs via Quantum Walks

We propose a novel algorithm for quantum spatial search on a star graph using interleaved continuous-time quantum walks and marking oracle queries. Initializing the system in the star's central vertex, we determine the optimal quantum walk times to reach full overlap with the marked state using ⌈(π/4)sqrt[N]-(1/2)⌉ oracle queries, matching the well-known lower bound of Grover's search. We implement the deterministic search in a database of size seven on photonic quantum hardware, and demonstrate the effective scaling of the approach up to size 115. This is the first experimental demonstration of quantum walk-based search on the highly noise-resistant star graph, which provides new evidence for the applications of quantum walk in quantum algorithms and quantum information processing.

Using Molecular Design to Enhance the Coherence Time of Quintet Multiexcitons Generated by Singlet Fission in Single Crystals

Multiexciton quintet states, ⁵(TT), photogenerated in organic semiconductors using singlet fission (SF), consist of four quantum entangled spins, promising to enable new applications in quantum information science. However, the factors that determine the spin coherence of these states remain underexplored. Here, we engineer the packing of tetracene molecules within single crystals of 5,12-bis(tricyclohexylsilylethynyl)tetracene (TCHS-tetracene) to demonstrate a ⁵(TT) state that exhibits promising spin qubit properties, including a coherence time, T₂, = 3 μs at 10 K, a population lifetime, T_pop, = 130 μs at 5 K, and stability even at room temperature. The single-crystal platform also enables global alignment of the spins and, consequently, individual addressability of the spin-sublevel transitions. Decoherence mechanisms, including exciton diffusion, electronic dipolar coupling, and nuclear hyperfine interactions, are elucidated, providing design principles for increasing T₂ and the operational temperature of ⁵(TT). By dynamically decoupling ⁵(TT) from the surrounding spin bath, T₂ = 10 μs is achieved. These results demonstrate the viability of harnessing singlet fission to initiate multiple electron spins in a well-defined quantum state for next-generation molecular-based quantum technologies.

Photogenerated Spin-Correlated Radical Pairs: From Photosynthetic Energy Transduction to Quantum Information Science

More than a half century ago, the NMR spectra of diamagnetic products resulting from radical pair reactions were observed to have strongly enhanced absorptive and emissive resonances. At the same time, photogenerated radical pairs were discovered to exhibit unusual electron paramagnetic resonance spectra that also had such resonances. These non-Boltzmann, spin-polarized spectra were observed in both chemical systems as well as in photosynthetic reaction center proteins following photodriven charge separation. Subsequent studies of these phenomena led to a variety of chemical electron donor-acceptor model systems that provided a broad understanding of the spin dynamics responsible for these spectra. When the distance between the two radicals is restricted, these observations result from the formation of spin-correlated radical pairs (SCRPs) in which the spin-spin exchange and dipolar interactions between the two unpaired spins play an important role in the spin dynamics. Early on, it was recognized that SCRPs photogenerated by ultrafast electron transfer are entangled spin pairs created in a well-defined spin state. These SCRPs can serve as spin qubit pairs (SQPs), whose spin dynamics can be manipulated to study a wide variety of quantum phenomena intrinsic to the field of quantum information science. This Perspective highlights the role of SCRPs as SQPs, gives examples of possible quantum manipulations using SQPs, and provides some thoughts on future directions.

Electric-Circuit Realization of Fast Quantum Search

Quantum search algorithm, which can search an unsorted database quadratically faster than any known classical algorithms, has become one of the most impressive showcases of quantum computation. It has been implemented using various quantum schemes. Here, we demonstrate both theoretically and experimentally that such a fast search algorithm can also be realized using classical electric circuits. The classical circuit networks to perform such a fast search have been designed. It has been shown that the evolution of electric signals in the circuit networks is analogies of quantum particles randomly walking on graphs described by quantum theory. The searching efficiencies in our designed classical circuits are the same to the quantum schemes. Because classical circuit networks possess good scalability and stability, the present scheme is expected to avoid some problems faced by the quantum schemes. Thus, our findings are advantageous for information processing in the era of big data.

Quantum Speedup for Protein Structure Prediction

Protein structure prediction (PSP) predicts the native conformation for a given protein sequence. Classically, the problem has been shown to belong to the NP-complete complexity class. Its applications range from physics, through bioinformatics to medicine and quantum biology. It is possible however to speed it up with quantum computational methods, as we show in this paper. Here we develop a fast quantum algorithm for PSP in three-dimensional hydrophobic-hydrophilic model on body-centered cubic lattice with quadratic speedup over its classical counterparts. Given a protein sequence of n amino acids, our algorithm reduces the temporal and spatial complexities to, respectively, [Formula: see text] and O(n² logn) . With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed algorithm we successfully solve the problem on IBM quantum simulator involving 21 and 25 qubits. We confirm the experimentally obtained high probability of success in finding the desired conformation by calculating the theoretical probability estimations.

A multi-commodity network model for optimal quantum reversible circuit synthesis

Quantum computing is a newly emerging computing environment that has recently attracted intense research interest in improving the output fidelity, fully utilizing its high computing power from both hardware and software perspectives. In particular, several attempts have been made to reduce the errors in quantum computing algorithms through the efficient synthesis of quantum circuits. In this study, we present an application of an optimization model for synthesizing quantum circuits with minimum implementation costs to lower the error rates by forming a simpler circuit. Our model has a unique structure that combines the arc-subset selection problem with a conventional multi-commodity network flow model. The model targets the circuit synthesis with multiple control Toffoli gates to implement Boolean reversible functions that are often used as a key component in many quantum algorithms. Compared to previous studies, the proposed model has a unifying yet straightforward structure for exploiting the operational characteristics of quantum gates. Our computational experiment shows the potential of the proposed model, obtaining quantum circuits with significantly lower quantum costs compared to prior studies. The proposed model is also applicable to various other fields where reversible logic is utilized, such as low-power computing, fault-tolerant designs, and DNA computing. In addition, our model can be applied to network-based problems, such as logistics distribution and time-stage network problems.

Efficient Implementation of a Quantum Algorithm in a Single Nitrogen-Vacancy Center of Diamond

Quantum computers have the potential to speed up certain problems that are hard for classical computers. Hybrid systems, such as the nitrogen-vacancy (NV) center in diamond, are among the most promising systems to implement quantum computing, provided the control of the different types of qubits can be efficiently implemented. In the case of the NV center, the anisotropic hyperfine interaction allows one to control the nuclear spins indirectly, through gate operations targeting the electron spin, combined with free precession. Here, we demonstrate that this approach allows one to implement a full quantum algorithm, using the example of Grover's quantum search in a single NV center, whose electron is coupled to a carbon nuclear spin.

Implementation of three-qubit quantum computation with pendular states of polar molecules by optimal control

Ultracold polar molecules have been considered as the possible candidates for quantum information processing due to their long coherence time and strong dipole-dipole interaction. In this paper, we consider three coupled polar molecules arranged in a linear chain and trapped in an electric field with gradient. By employing the pendular states of polar molecules as qubits, we successfully realize three-qubit quantum gates and quantum algorithms via the multi-target optimal control theory. Explicitly speaking, through the designs of the optimal laser pulses with multiple iterations, the triqubit Toffoli gate, the triqubit quantum adders, and the triqubit quantum Fourier transform can be achieved in only one operational step with high fidelities and large transition probabilities. Moreover, by combining the optimized Hadamard, oracle, and diffusion gate pulses, we simulate the Grover algorithm in the three-dipole system and show that the algorithm can perform well for search problems. In addition, the behaviors of the fidelity and the average transition probability with respect to iteration numbers are compared and analyzed for each gate pulse. Our findings could pave the way toward scalability for molecular quantum computing based on the pendular states and could be extended to implement multi-particle gate operation in the molecular system.

Quantum Interference between Photons from an Atomic Ensemble and a Remote Atomic Ion

Many remote-entanglement protocols rely on the generation and interference of photons produced by nodes within a quantum network. Quantum networks based on heterogeneous nodes provide a versatile platform by utilizing the complementary strengths of the differing systems. Implementation of such networks is challenging, due to the disparate spectral and temporal characteristics of the photons generated by the different quantum systems. Here, we report on the observation of quantum interference between photons generated from a single ion and an atomic ensemble. The photons are produced on demand by each source located in separate buildings, in a manner suitable for quantum networking. Given these results, we analyze the feasibility of hybrid ion-ensemble remote entanglement generation.

Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms

We report the implementation of universal two- and three-qubit entangling gates on neutral-atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states and are implemented in parallel on several clusters of atoms in a one-dimensional array of optical tweezers. Specifically, we realize the controlled-phase gate, enacted by a novel, fast protocol involving only global coupling of two qubits to Rydberg states. We benchmark this operation by preparing Bell states with fidelity F≥95.0(2)%, and extract gate fidelity ≥97.4(3)%, averaged across five atom pairs. In addition, we report a proof-of-principle implementation of the three-qubit Toffoli gate, in which two control atoms simultaneously constrain the behavior of one target atom. These experiments demonstrate key ingredients for high-fidelity quantum information processing in a scalable neutral-atom platform.

Demonstration of slow light in rubidium vapor using single photons from a trapped ion

Practical implementation of quantum networks is likely to interface different types of quantum systems. Photonically linked hybrid systems, combining unique properties of each constituent system, have typically required sources with the same photon emission wavelength. Trapped ions and neutral atoms both have compelling properties as nodes and memories in a quantum network but have never been photonically linked because of vastly different operating wavelengths. Here, we demonstrate the first interaction between neutral atoms and photons emitted from a single trapped ion. We use slow light in ⁸⁷Rb vapor to delay photons originating from a trapped ¹³⁸Ba⁺ ion by up to 13.5 ± 0.5 ns, using quantum frequency conversion to overcome the frequency difference between the ion and neutral atoms. The delay is tunable and preserves the temporal profile of the photons. This result showcases a hybrid photonic interface usable as a synchronization tool-a critical component in any future large-scale quantum network.

Quantum Simulation Logic, Oracles, and the Quantum Advantage

Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. Our results clarify the assumptions made and the conditions needed when using quantum oracles. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, such as the Deutsch-Jozsa and Simon’s algorithms, there simply is no advantage in terms of query complexity. This does not detract from the fact that quantum query complexity provides examples of how a quantum computer can be expected to behave, which in turn has proved useful for finding new quantum algorithms outside of the oracle paradigm, where the most prominent example is Shor’s algorithm for integer factorization.

Direct Randomized Benchmarking for Multiqubit Devices

Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But, scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on one, two, and three qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the n-qubit Clifford gates at its core have to be compiled into large circuits over the one- and two-qubit gates native to a device. As n grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low n. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on two to five qubits using the publicly available ibmqx5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But, it can be extended to processors with more qubits-we present simulations on 10+ qubits-and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. We show how to use this flexibility to measure separate error rates for distinct sets of gates, and we use this method to estimate the average error rate of a set of cnot gates.

Privacy-preserving Quantum Sealed-bid Auction Based on Grover's Search Algorithm

Sealed-bid auction is an important tool in modern economic especially concerned with networks. However, the bidders still lack the privacy protection in previously proposed sealed-bid auction schemes. In this paper, we focus on how to further protect the privacy of the bidders, especially the non-winning bidders. We first give a new privacy-preserving model of sealed-bid auction and then present a quantum sealed-bid auction scheme with stronger privacy protection. Our proposed scheme takes a general state in N-dimensional Hilbert space as the message carrier, in which each bidder privately marks his bid in an anonymous way, and further utilizes Grover's search algorithm to find the current highest bid. By O(lnn) iterations, it can get the highest bid finally. Compared with any classical scheme in theory, our proposed quantum scheme gets the lower communication complexity.

Quantum-inspired microwave signal processing for implementing unitary transforms

Inspired by photonic one-way quantum computation, we describe a microwave signal processing method for implementing unitary transforms based on measuring the cebits encoded in the "classical microwave graph state (CMGS)." Here the terms "cebit" and "CMGS" defined in our system are classical analogies of a qubit and certain target quantum graph states in quantum physics respectively, which can exhibit some similar behaviors and resultants. The constructions of 4- and 16-cebit CMGSs as examples are discussed in detail and specific tomography methods are introduced to characterize their qualities. By performing operations on these CMGSs, we implement some basic 2 × 2, 4 × 4, and specific generalized unitary transforms, and obtain output results with high fidelities. Furthermore, we also demonstrate that a simulation of an efficient Grover's search algorithm, which has been executed in one-way quantum computing schemes, can be directly realized via a certain 4-cebit CMGS. Due to the excellent parallel efficiency and credible outcomes in the proposal, this quantum-inspired method may provide benefits for exploring new ways to microwave information processing, or in turn as an alternative tool for simulating particular quantum systems to some extent.

Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit

Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a paradigm, where quantum logic operations are realized through geometric phase manipulation that has some intrinsic noise-resilient advantages and may enable simplified implementation of multi-qubit gates compared to the dynamical approach. Here we report observation of a continuous-variable geometric phase and demonstrate a quantum gate protocol based on this phase in a superconducting circuit, where five qubits are controllably coupled to a resonator. Our geometric approach allows for one-step implementation of n-qubit controlled-phase gates, which represents a remarkable advantage compared to gate decomposition methods, where the number of required steps dramatically increases with n. Following this approach, we realize these gates with n up to 4, verifying the high efficiency of this geometric manipulation for quantum computation.

Geometric phase is of fundamental interest and has practical application in quantum computation. Here the authors observe continuous-variable geometric phase in a superconducting circuit and demonstrate a multi-qubit controlled phase gate protocol based on this geometric effect.