Implementation Of Quantum Algorithms Research Articles

Quantum circuit optimization of an integer divider

Efficient arithmetic operations in quantum circuits play a vital role in the implementation of quantum algorithms. Quantum circuits constructed exclusively using gates of the Clifford+T group are compatible with error detection and correction codes available in the quantum literature. However, the T gate, a member of this group, has a higher cost compared to other gates, making it crucial to minimize its usage to reduce circuit expenses. While the T gate cannot be entirely avoided since the Clifford group is not a universal set of gates, circuit optimization can effectively reduce the number of T gates required for implementation. In this work, we present a novel divider circuit for quantum computing that focuses on reducing the number of T gates while maintaining a reasonable number of qubits for this type of operation. To achieve this, we introduce variants of minor circuits, including a comparator and two types of subtractors. These circuits are based on published literature but undergo modifications to optimize their resource utilization for performing the division operation. The obtained results demonstrate that the proposed divider circuit outperforms other currently published divider circuits in terms of T gate usage, highlighting its efficiency and potential practicality in quantum algorithms.

Synthetiq: Fast and Versatile Quantum Circuit Synthesis

To implement quantum algorithms on quantum computers it is crucial to decompose their operators into the limited gate set supported by those computers. Unfortunately, existing works automating this essential task are generally slow and only applicable to narrow use cases.We present Synthetiq, a method to synthesize quantum circuits implementing a given specification over arbitrary finite gate sets, which is faster and more versatile than existing works. Synthetiq utilizes Simulated Annealing instantiated with a novel, domain-specific energy function that allows developers to leverage partial specifications for better efficiency. Synthetiq further couples this synthesis method with a custom simplification pass, to ensure efficiency of the found circuits. We experimentally demonstrate that Synthetiq can generate better implementations than were previously known for multiple relevant quantum operators including RCCCX, CCT, CCiSWAP, C√SWAP, and C√iSWAP. Our extensive evaluation also demonstrates Synthetiq frequently outperforms a wide variety of more specialized tools in their own domains, including (i) ‍the well-studied task of synthesizing fully specified operators in the Clifford+T gate set, (ii) ‍є-approximate synthesis of multi-qubit operators in the same gate set, and (iii) ‍synthesis tasks with custom gate sets. On all those tasks, Synthetiq is typically one to two orders of magnitude faster than previous state-of-the-art and can tackle problems that were previously out of the reach of any synthesis tool.

Enabling continuous deployment techniques for quantum services

AbstractEarly advances in quantum computing have provided new opportunities to tackle intricate problems in diverse areas such as cryptography, optimization, and simulation. However, current methodologies employed in quantum computing often require, among other things, a broad understanding of quantum hardware and low‐level programming languages, posing challenges to software developers in effectively creating and implementing quantum services. This study advocates the adoption of software engineering principles in quantum computing, thereby establishing a higher level of hardware abstraction that allows developers to focus on application development. With this proposal, developers can design and deploy quantum services with less effort, which is similar to the facilitation provided by service‐oriented computing for the development of conventional software services. This study introduces a continuous deployment strategy adapted to the development of quantum services that covers the creation and deployment of such services. For this purpose, an extension of the OpenAPI specification is proposed, which allows the generation of services that implement quantum algorithms. The proposal was validated through the creation of an application programming interface with diverse quantum algorithm implementations and evaluated through a survey of various developers and students who were introduced to the tool with positive results.

Decomposing (n+1)$(n+1)$‐Qubit Toffoli Gate with Shallow Circuit Depth and No Ancilla

AbstractCircuit depth optimization is crucial for implementing quantum algorithms in practical systems. The decomposition of ‐qubit Toffoli gate is continually optimized since this gate is a fundamental component for many quantum algorithms. Without any ancilla, ‐qubit Toffoli gate can be decomposed by standard gates with circuit depth . Here, the decomposition is further optimized and its circuit depth is reduced to . The decomposition is equivalent to ‐qubit Toffoli gate up to an overall phase and also does not need any ancilla.

Long-range entanglement between spin qubits in quantum dots by virtual photon process

Electron spin qubits in silicon quantum dots are an attractive candidate for large-scalable quantum computation. An essential step for quantum information processing based on spin qubits is to realize the spatially separated two-qubit gate and entanglement with high fidelity. Here, we consider two spin qubits coupled to a common superconducting resonator in circuit quantum electrodynamics. We investigate the long-range two-qubit iSWAP gate mediated by virtual microwave photons using a Gaussian smoothing pulse. We show that the entangling gate fidelity can reach [Formula: see text] under realistic experimental conditions and analyze the factors limiting gate fidelity. Moreover, we numerically demonstrate the generation of remote Bell entangled states of spin qubits with high fidelity. In addition, this spin–resonator architecture can be used to implement quantum algorithms using our scheme. These results pave the way for quantum information processing with spin qubits.

Grammar-aware sentence classification on quantum computers

Natural language processing (NLP) is at the forefront of great advances in contemporary AI, and it is arguably one of the most challenging areas of the field. At the same time, in the area of quantum computing (QC), with the steady growth of quantum hardware and notable improvements towards implementations of quantum algorithms, we are approaching an era when quantum computers perform tasks that cannot be done on classical computers with a reasonable amount of resources. This provides an new range of opportunities for AI, and for NLP specifically. In this work, we work with the Categorical Distributional Compositional (DisCoCat) model of natural language meaning, whose underlying mathematical underpinnings make it amenable to quantum instantiations. Earlier work on fault-tolerant quantum algorithms has already demonstrated potential quantum advantage for NLP, notably employing DisCoCat. In this work, we focus on the capabilities of noisy intermediate-scale quantum (NISQ) hardware and perform the first implementation of an NLP task on a NISQ processor, using the DisCoCat framework. Sentences are instantiated as parameterised quantum circuits; word-meanings are embedded in quantum states using parameterised quantum-circuits and the sentence’s grammatical structure faithfully manifests as a pattern of entangling operations which compose the word-circuits into a sentence-circuit. The circuits’ parameters are trained using a classical optimiser in a supervised NLP task of binary classification. Our novel QNLP model shows concrete promise for scalability as the quality of the quantum hardware improves in the near future and solidifies a novel branch of experimental research at the intersection of QC and AI.

Robust three-qubit search algorithm in Rydberg atoms via geometric control

Rydberg atoms possess long coherence time and inherent scalability, which makes it promising to implement quantum algorithms. An exact and robust quantum search algorithm (SA) is essential to some practical applications. Here we propose a multisolution three-qubit SA by employing quantum circuit and geometric operations, in which the target states can be successfully searched with the fidelity of at least 99.8$%$ and the geometric operators guarantee robustness against systematic errors. In particular, the geometric three-qubit gate operators employed reduce the implementation time and help to resist against the detrimental influence of decoherence. Moreover, our scheme can be straightforwardly extended to multiqubit cases. We have carried out numerical simulations based on the master equation to illustrate the superiority of our scheme. We consider that our study provides an alternative method for executing quantum SAs with high success probability.

Scalable algorithm simplification using quantum AND logic

Implementing quantum algorithms on realistic devices requires translating high-level global operations into sequences of hardware-native logic gates, a process known as quantum compiling. Physical limitations, such as constraints in connectivity and gate alphabets, often result in unacceptable implementation costs. To enable successful near-term applications, it is crucial to optimize compilation by exploiting the capabilities of existing hardware. Here we implement a resource-efficient construction for a quantum version of AND logic that can reduce the compilation overhead, enabling the execution of key quantum circuits. On a high-scalability superconducting quantum processor, we demonstrate low-depth synthesis of high-fidelity generalized Toffoli gates with up to 8 qubits and Grover’s search algorithm in a search space of up to 64 entries. Our experimental demonstration illustrates a scalable and widely applicable approach to implementing quantum algorithms, bringing more meaningful quantum applications on noisy devices within reach.

Hardware and software tools for teaching the basics of quantum informatics to students of specialized (high) schools

The article defines the criteria for choosing a cloud-based platform for mastering the basics of quantum informatics by students of a specialized (high) schools: cross-browser; intuitive interface; the possibility of free access; access without registration and simplified registration; the presence of a systematized reference system with examples; support for the development of the environment by the developer; support for working in a personal educational environment; support for working with quantum algorithms in graphical mode; automatic conversion of quantum algorithms from graphic format to program code text; support for the Ukrainian-language localization; availability of a mobile application; responsive design. The possibilities of platforms for implementing quantum algorithms from the following companies are analyzed: Microsoft, QuTech, Amazon Braket, IBM. The choice of the IBM Quantum cloud-based platform is justified. Work at IBM Quantum Composer and IBM Quantum Lab is described. Information about quantum operations and gates is presented: their designation in IBM Quantum Composer and IBM Quantum Lab, the gate matrix, and the purpose of the gate. An example of implementing quantum teleportation in the form of a circuit and program is given.

Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code

Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits. In our proposal, we use error-corrected two-qubit gates between GKP qubits and introduce a maximum likelihood decoding strategy for correcting shift errors in the two-GKP-qubit gates. Our proposed decoding reduces the total CNOT failure rate of the GKP qubits, e.g., from $0.87\%$ to $0.36\%$ at a GKP squeezing of $12$dB, compared to the case where the simple closest-integer decoding is used. Then, by concatenating the GKP code with the surface code, we find that the threshold GKP squeezing is given by $9.9$dB under the the assumption that finite-squeezing of the GKP states is the dominant noise source. More importantly, we show that a low logical failure rate $p_{L} < 10^{-7}$ can be achieved with moderate hardware requirements, e.g., $291$ modes and $97$ qubits at a GKP squeezing of $12$dB as opposed to $1457$ bare qubits for the standard rotated surface code at an equivalent noise level (i.e., $p=0.36\%$). Such a low failure rate of our surface-GKP code is possible through the use of space-time correlated edges in the matching graphs of the surface code decoder. Further, all edge weights in the matching graphs are computed dynamically based on analog information from the GKP error correction using the full history of all syndrome measurement rounds. We also show that a highly-squeezed GKP state of GKP squeezing $\gtrsim 12$dB can be experimentally realized by using a dissipative stabilization method, namely, the Big-small-Big method, with fairly conservative experimental parameters. Lastly, we introduce a three-level ancilla scheme to mitigate ancilla decay errors during a GKP state preparation.

Detailed Account of Complexity for Implementation of Circuit-Based Quantum Algorithms

In this review article, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware. In particular, some steps of the implementation, as the preparation of an arbitrary superposition state and readout of the final state, in most of the cases can surpass the complexity aspects of the algorithm itself. We present the complexity involved in the full implementation of circuit-based quantum algorithms, from state preparation to the number of measurements needed to obtain good statistics from the final states of the quantum system, in order to assess the overall space and time costs of the processes.

A polynomial time and space heuristic algorithm for T-count

An important part of reaping computational advantage from a quantum computer is to reduce the quantum resources needed to implement a desired quantum algorithm. Quantum algorithms that are too large to be practical on noisy intermediate scale quantum devices will require fault-tolerant error correction. This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more resources than the other gates in the gate set. More specifically, in this paper we consider the group of unitaries that can be exactly implemented by a quantum circuit consisting of the Clifford + T gate set. The Clifford + T gate set is a universal gate set and in this group, using state-of-the-art surface codes, the T gate is by far the most expensive component to implement fault-tolerantly. So it is important to minimize the number of T gates necessary for a fault-tolerant implementation. Our primary interest is to compute a circuit for a given n-qubit unitary U, using the minimum possible number of T gates (called the T-count of unitary U). We consider the problem COUNT-T, the optimization version of which aims to find the T-count of U. In its decision version the goal is to decide if the T-count is at most some positive integer m. Given an oracle for COUNT-T, we can compute a T-count-optimal circuit in time polynomial in the T-count and dimension of U. We give a provable classical algorithm that solves COUNT-T (decision) in time and space , where N = 2 n and c ⩾ 2. This gives a space-time trade-off for solving this problem with variants of meet-in-the-middle techniques. We also introduce an asymptotically faster multiplication method that shaves a factor of N 0.7457 off of the overall complexity. Lastly, beyond our improvements to the rigorous algorithm, we give a heuristic algorithm that outputs a T-count-optimal circuit and has space and time complexity poly(m, N), under some assumptions. In our heuristic algorithm we developed a novel way of pruning the search space. While our heuristic method still scales exponentially with the number of qubits (though with a lower exponent), there is a large improvement by going from exponential to polynomial scaling with m. We implemented our heuristic algorithm with up to 4 qubit unitaries and obtained a significant improvement in time. For all benchmark and random unitaries we studied, the T-count returned by our algorithm is at most the T-count of their circuits shown in previous papers.

Hardware and software tools for teaching the basics of quantum informatics to lyceums students

The article defines the criteria for choosing a cloud-oriented platformfor mastering the basics of quantum informatics by students of a specialized(high) school: cross-browser; intuitive interface; the possibility of free (free) access; access without registration and simplified registration; the presence of a systematized reference system with examples; support for the development of the environment by the developer; support for working in a personal educational environment; support for working with quantum algorithms in graphical mode; automatic conversion of quantum algorithms from graphic format to program code text; support for the Ukrainian-language locale; availability of a mobile application; responsive design. The possibilities of platforms for implementing quantum algorithms from the following companies are analyzed: Microsoft, QuTech, Amazon Braket, IBM. The choice of the IBM Quantum Cloud-based platform is justified. Work at IBM Quantum Composer and IBM Quantum Lab is described. Information about quantum operations and Gates is presented: their designation in IBM Quantum Composer and IBM Quantum Lab; the gate Matrix; and the purpose of the gate. An example of implementing quantum teleportation in the form of a scheme and program is given.

Implementing a quantum search algorithm with nonorthogonal states

The search algorithm is one of the most widely studied quantum algorithms, while its complete implementation in experiments is difficult and only a few experimental works have been reported. Based on Grover's algorithm, we propose a scheme of quantum search using nonorthogonal states and experimentally implement the entire scheme in a linear optical system. With this scheme, a large-sized search space can be encoded using only one qubit and the search probability of the target state is $100%$ in theory. The experimental setup and the operations for implementing this scheme are extremely simple. In our linear optical experiment, different target states are successfully found from a database of nine elements with all fidelities $&gt;0.99$, the state evolution from the initial state to a target state is studied, and the medium states and the final state are shown in a Bloch sphere. The scheme is general and can be easily realized in a wide range of quantum systems. This work may pave an avenue to implement quantum algorithms with nonorthogonal states.

Value of NMR relaxation parameters of diamagnetic molecules for quantum information processing: optimizing the coherent phase

Quantum computing is the science that studies the applications of quantum mechanics in computer science. Thus, a quantum computer is an entity which can store quantum information, which in turn is an innovative procedure that creates conditions to allow the implementation of quantum algorithms and simulations, wherein the decoherence is a key problem. Considering the unique qubits, the time of the coherence phase can be well measured by the time of transversal relaxation (T2). In this line, we study the PPN derivatives, PPN-F, PPN-ethyl and PPN-NH2, as candidates to carry out quantum information. Therefore, the structures were optimized at the B3LYP/6-311G(d,p) level; after the optimization, molecular dynamics (MD) simulations were performed and the structures obtained were selected by statistical inefficiency method to then obtain the relaxation parameters (T1 and T2). The modification in the PPN molecule increases the transverse relaxation rate phosphorus nuclear spins at most five times because of the hydrogen bonds. From our findings, the studied molecules showed excellent candidates for the processing of quantum information; however, it is important to rule out the PPN-NH2 molecule that has more significant values of T1 and T2, and thus, this compound stands out from the others studied.

Quantum circuit designs of carry lookahead adder optimized for T-count T-depth and qubits

Quantum circuits of arithmetic operations such as addition are needed to implement quantum algorithms in hardware. Quantum circuits based on Clifford+T gates are used as they can be made tolerant to noise. The trade-off of gaining fault tolerance from using Clifford+T gates and error-correcting codes is the high implementation overhead of the T gate. As a result, the T-count and T-depth performance measures have become important in quantum circuit design. Due to noise, the risk for errors in a quantum circuit computation increases as the number of gate layers (or depth) in the circuit increases. As a result, low depth circuits such as quantum carry lookahead adders (QCLA)s have caught the attention of researchers. This work presents two QCLA designs each optimized with emphasis on T-count and T-depth or qubit cost, respectively. In-place and out-of-place versions of each design are shown. The proposed QCLAs are compared against the existing works in terms of T-count and T-depth. The proposed QCLAs for out-of-place addition achieve average T-count savings of 54.34% and 37.21%, respectively. The proposed QCLAs for out-of-place addition achieve up to a 33.33% reduction in T-depth. The proposed QCLAs for in-place addition achieve average T-count savings of 65.31% and 30.63%, respectively. When compared to existing works, the proposed QCLAs for in-place addition achieves T-depth savings ranging from 33.33% to 95.56%.

Tomography of Qubit States and Implementation of Quantum Algorithms by Unipolar Pulses

The conventional technique for controlling the states of individual qubits and quantum registers is based on the use of high-frequency modulated pulses whose carrier frequency is close to the transition frequency between the ground states of “artificial atoms” and “molecules” (the Rabi technique). In this paper, an alternative concept for controlling superconducting qubits is developed that is based on the idea of fast excitation of a quantum system by solitary unmodulated pulses. The formation of entangled Bell states in a two-qubit superconducting register under the action of field pulses obtained by rapid single flux quantum (RSFQ) devices is demonstrated by numerical simulation. The tomography of quantum states is performed by solving the density matrix equation. It is shown that the technique of “unipolar pulses” allows one to speed up the formation of entangled states (at picosecond times) with a fidelity of 95–98%. The execution of the basic quantum algorithms is demonstrated: the Deutsch–Jozsa algorithm with an accuracy of more than 98% and Grover’s algorithm with an accuracy of 93%.

A Quantum Mechanics-Based Framework for EEG Signal Feature Extraction and Classification

Quantum machine learning (QML) is an emerging research field, which is devoted to devising and implementing quantum algorithms that could enable machine learning faster than that of classical computers. In this article, a hierarchic quantum mechanics-based framework is investigated to implement both the feature extraction and classification in the electroencephalogram (EEG) signal. First, the classical EEG signal dataset is prepared as a quantum state while the sign of the data point is preserved. The prepared quantum state is then evolved with the quantum wavelet packet transformation (QWPT) and the wavelet packet energy entropy (WPEE) feature is extracted as the input of the subsequent quantum classifier. We finally propose the improved quantum support vector machine with the arbitrary nonlinear kernel, which is employed to predict the label of the EEG signal. The complexity analysis indicates that the proposed framework provides exponential speedup over the same structured classical counterpart. Besides, the quantitative experimental results verify the feasibility and validity.

Reaction: Molecular Spins as Qubits

Floriana Tuna is a Leverhulme Trust Senior Research Fellow at the University of Manchester (UoM). She holds MSc and PhD degrees in chemistry from the University of Bucharest (1989) and National Academy of Romania (1997), respectively. She worked as a visiting DAAD fellow at the University of Heidelberg (Germany), a CNRS postdoctoral fellow at ICMCB Bordeaux (France), and a Marie Curie fellow at the University of Warwick (UK) before joining UoM in 2003. She received the Romanian Academy “Ilie Murgulescu” Prize for excellence in research in 2005 and has published over 300 high-impact papers. Her major interests are in coordination chemistry, molecular magnetism, and quantum information science.

An optimized quantum circuit for converting from sign–magnitude to two’s complement

Nowadays, one of the critical issues to implement quantum algorithms is the required number of elementary gates, qubits and delay. Current quantum computers and simulators are mainly prototypes, and there is a lack of computational resources. Therefore, it is necessary to optimize the quantum operations to reduce the necessary number of gates and qubits. This work presents a novel reversible circuit which is able to convert signed binary numbers to two’s complement of N digits in a quantum environment. The depth of the circuit is O(log N). It is based on the fastest out-of-place carry look-ahead addition quantum circuit currently available. This addition circuit has been adapted to make the conversion using the minimum number of gates and qubits, being faster than other adder circuits. A robust metric has been used to measure the quantum cost, delay, ancilla inputs and garbage outputs of the proposed converter. Moreover, it has been compared with others described in the literature.