Qubit Maps Research Articles

A computational study and analysis of Variational Quantum Eigensolver over multiple parameters for molecules and ions

AbstractMaterial discovery is a phenomenon practiced since the evolution of the world. The discovery of materials has led to significant development in varied fields such as Science, Engineering and Technology. Computationally simulating molecules has been an area of interest in the industry as well as academia. However, simulating large molecules can be computationally expensive in terms of computing power and complexity. Quantum computing is a recent development that can improve the efficiency in predicting properties of atoms and molecules which will be useful for material design. The Variational Quantum Eigensolver (VQE) is one such quantum algorithm used to calculate the ground state energy of molecules or ions. In this study, we have done a comparative analysis of the parameters that constitute the VQE algorithm. This includes components such as basis, qubit mapping, ansatz, and optimizers used. We have also developed a database consisting of 79 single atoms and their variations of oxidation states and 33 molecules with the data of their Hamiltonian and ground state energy and dipole moment.

Solving the B-SAT Problem Using Quantum Computing: Smaller Is Sometimes Better.

This paper aims to outline the effectiveness of modern universal gate quantum computers when utilizing different configurations to solve the B-SAT (Boolean satisfiability) problem. The quantum computing experiments were performed using Grover's search algorithm to find a valid solution. The experiments were performed under different variations to demonstrate their effects on the results. Changing the number of shots, qubit mapping, and using a different quantum processor were all among the experimental variables. The study also branched into a dedicated experiment highlighting a peculiar behavior that IBM quantum processors exhibit when running circuits with a certain number of shots.

Context-aware coupler reconfiguration for tunable coupler-based superconducting quantum computers

Abstract Crosstalk, caused by unwanted interactions from the surrounding environment, remains a fundamental challenge in existing superconducting quantum computers (SQCs). We propose a method for qubit placement, connectivity, and logical qubit allocation on tunable-coupler SQCs to eliminate unnecessary qubit connections and optimize resources while reducing crosstalk errors. Existing mitigation methods carry trade-offs, like increasing qubit connectivity or software-based gate scheduling. Our method, the Context-Aware COupler REconfiguration (CA-CORE) compilation method, aligns with application-specific design principles. It optimizes the qubit connections for improved SQC performance, leveraging tunable couplers. Through contextual analysis of qubit correlations, we configure an efficient coupling map considering SQC constraints. We then apply the SWAP-based Bidirectional Heuristic Search (SABRE) qubit mapping method and crosstalk-adaptive scheduling to further optimize the quantum circuit. Our architecture reduces depth by an average of 18% and 27%, and by up to 50% and 60%, compared to lattice and heavy-hex architectures, respectively. With crosstalk optimization through adaptive scheduling, we achieve performance improvements of 35%, 20%, and 160% on fully-enabled grid, lattice, and heavy-hex topologies, respectively.

Robust Qubit Mapping Algorithm via Double-Source Optimal Routing on Large Quantum Circuits

Qubit mapping is a critical aspect of implementing quantum circuits on real hardware devices. Currently, the existing algorithms for qubit mapping encounter difficulties when dealing with larger circuit sizes involving hundreds of qubits. In this article, we introduce an innovative qubit mapping algorithm, Duostra, tailored to address the challenge of implementing large-scale quantum circuits on real hardware devices with limited connectivity. Duostra operates by efficiently determining optimal paths for double-qubit gates and inserting SWAP gates accordingly to implement the double-qubit operations on real devices. Together with two heuristic scheduling algorithms, Limitedly Exhaustive Search and Shortest-Path Estimation, it yields results of good quality within a reasonable runtime, thereby striving toward achieving quantum advantage. Experimental results showcase our algorithm’s superiority, especially for large circuits beyond the NISQ era. For example, on large circuits with more than 50 qubits, we can reduce the mapping cost on an average 21.75% over the virtual best results among QMAP, t \(|ket\rangle\) , Qiskit, and SABRE. Besides, for mid-size circuits such as the SABRE-large benchmark, we improve the mapping costs by 4.5%, 5.2%, 16.3%, 20.7%, and 25.7%, when compared to QMAP, TOQM, t \(|ket\rangle\) , Qiskit, and SABRE, respectively.

Improving the performance of digitized counterdiabatic quantum optimization via algorithm-oriented qubit mapping

Improving the performance of digitized counterdiabatic quantum optimization via algorithm-oriented qubit mapping

Adaptive diversity-based quantum circuit architecture search

Quantum variational algorithms (VQAs) are highly promising to realize quantum advantages on near-term quantum devices. Existing VQAs based on a manually fixed quantum are computationally inefficient due to noise and the limited coupling maps of these devices. Previous work considers various quantum architecture search (QAS) algorithms to autodesign a quantum based on specific questions to improve the performance of VQAs. Compared to manual design, autodesign can more efficiently explore the large space of a possible and achieve better performance. However, two main challenges in utilizing QAS to design quantum circuits efficiently are the tremendous amount of space required for candidate quantum circuits, and the disconnection between quantum devices and autodesign in terms of qubit mapping and quantum noise. To address these issues, we propose an adaptive diversity-based quantum search algorithm to efficiently generate the optimal quantum circuit based on device qubit mapping and noise. By considering the diversity among different candidate circuits and adaptively adding circuit depths, our approach only needs to focus on a small optimization space at each iteration step. In addition, the synchronization of optimizing circuit structure and aligning qubit mapping enables us to generate quantum circuits while avoiding additional mapping overhead. We evaluate the performance of our algorithm on simulators and real quantum devices for quantum eigenvalue problems and classification tasks. Results demonstrate that quantum circuits generated by our method outperform both a fixed hardware-efficient and randomly generated quantum circuits in terms of final performance and resource-saving. Our algorithm provides a flexible way to efficiently generate excellent quantum circuits for significantly improving the performances of VQAs on near-term quantum devices. Published by the American Physical Society 2024

Shell-model study of 58Ni using quantum computing algorithm

This study presents a simulated quantum computing approach for the investigation into the shell-model energy levels of 58Ni through the application of the variational quantum eigensolver (VQE) method in combination with a problem-specific ansatz. The primary objective is to achieve a fully accurate low-lying energy spectrum of 58Ni. The chosen isotope, 58Ni is particularly interesting in nuclear physics through its role in astrophysical reactions while also being a simple but non-trivial nucleus for shell-model study, it being two particles outside a closed shell. Our ansatz, along with the VQE method are shown to be able to reproduce exact energy values for the ground state and first and second excited states. We compare a classical shell model code, the values obtained by diagonalization of the Hamiltonian after qubit mapping, and a noiseless simulated ansatz+VQE simulation. The exact agreement between classical and qubit-mapped diagonalization shows the correctness of our method, and the high accuracy of the simulation means that the ansatz is suitable to allow a full reconstruction of the full nuclear wave function.

QM-DLA: an efficient qubit mapping method based on dynamic look-ahead strategy

Quantum computing has already demonstrated great computational potential across multiple domains and has received more and more attention. However, due to the connectivity limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, most of the quantum algorithms cannot be directly executed without the help of inserting SWAP gates. Nevertheless, more SWAP gates lead to a longer execution time and, inevitably, lower fidelity of the algorithm. To this end, this paper proposes an optimized qubit mapping algorithm based on a dynamic look-ahead strategy to minimize the number of SWAP gates inserted. Firstly, a heuristic algorithm is proposed based on maximizing physical qubit connectivity to generate the optimal initial qubit mapping, which reduces the need for logical qubit shifts during subsequent SWAP gate insertion. Secondly, in the form of directed acyclic graphs, we identify quantum gates that violate the constraints of physical coupling and insert SWAP gates to remap qubits, thereby overcoming the limitations of qubit interactions. Finally, the optimal SWAP gate insertion strategy is built by comparing the cost of different SWAP gate insertion strategies through a multi-window look-ahead strategy to reduce the number of SWAP gates inserted. The experimental results show that the strategy in this paper decreases the number of SWAP gate insertions and significantly reduces the depth of quantum circuits when performing qubit mapping compared with state-of-the-art methods.

Optimal qubit mapping search for encoding classical data into matrix product state representation with minimal loss

Matrix product state (MPS) offers a framework for encoding classical data into quantum states, enabling the efficient utilization of quantum resources for data representation and processing. This research paper investigates techniques to enhance the efficiency and accuracy of MPS representations specifically designed for encoding classical data. Based on the observations that MPS truncation error depends on the pattern of the classical data, we devised an algorithm that finds optimal qubit mapping for given classical data, thereby improving the efficiency and fidelity of the MPS representation. Furthermore, we evaluate the impact of the optimized MPS in the context of quantum classifiers, demonstrating their enhanced performance compared to the conventional mapping. This improvement confirms the efficacy of the proposed techniques for encoding classical data into quantum states. MPS representation combined with optimal qubit mapping can pave a new way for more efficient and accurate quantum data representation and processing.

Qubit Mapping Based on Tabu Search

Qubit Mapping Based on Tabu Search

QuCloud+: A Holistic Qubit Mapping Scheme for Single/Multi-programming on 2D/3D NISQ Quantum Computers

Qubit mapping for NISQ superconducting quantum computers is essential to fidelity and resource utilization. The existing qubit mapping schemes meet challenges, e.g., crosstalk, SWAP overheads, diverse device topologies, etc., leading to qubit resource underutilization and low fidelity in computing results. This article introduces QuCloud+, a new qubit mapping scheme that tackles these challenges. QuCloud+ has several new designs. (1) QuCloud+ supports single/multi-programming quantum computing on quantum chips with 2D/3D topology. (2) QuCloud+ partitions physical qubits for concurrent quantum programs with the crosstalk-aware community detection technique and further allocates qubits according to qubit degree, improving fidelity, and resource utilization. (3) QuCloud+ includes an X-SWAP mechanism that avoids SWAPs with high crosstalk errors and enables inter-program SWAPs to reduce the SWAP overheads. (4) QuCloud+ schedules concurrent quantum programs to be mapped and executed based on estimated fidelity for the best practice. Experimental results show that, compared with the existing typical multi-programming study [ 12 ], QuCloud+ achieves up to 9.03% higher fidelity and saves on the required SWAPs during mapping, reducing the number of CNOT gates inserted by 40.92%. Compared with a recent study [ 30 ] that enables post-mapping gate optimizations to further reduce gates, QuCloud+ reduces the post-mapping circuit depth by 21.91% while using a similar number of gates.

Timing-Aware Qubit Mapping and Gate Scheduling Adapted to Neutral Atom Quantum Computing

As a less developed but potential quantum technology, neutral atoms (NA) can provide advantages including higher qubit connectivity, longer-range interactions, and much more native multi-control gates than superconductivity. Long-range interactions, however, prevent parallelism of interacting qubit pairs with their surrounding restriction zones. Therefore, the quantum program cannot be run directly on a neutral atom quantum computer (NAQC) unless compiled. The recent compiling study of NAQC applies simple layer-by-layer scheduling and does not consider the difference in gate duration. To address the above issues, we focus on the qubit mapping and quantum gate scheduling () problem of quantum circuits to meet hardware constraints of superconductivity and even neutral atoms. Our goal is to shorten the execution time to mitigate decoherence noise. We propose a block-game-like abstraction mechanism which is an abstract model of the problem and aware of the duration difference of gates and several other NA characteristics. Based on the abstraction, we propose a heuristic greedy algorithm (HGA) to solve the problem efficiently. To further speed up the execution of the circuit, we embed HGA into a Monte Carlo tree search (MCTS) framework to solve the problem, which consumes more compiling time but achieves a better result. Comparing our MCTS algorithm with the only recent algorithm for NAQC, the average speedup ratio is 1.75× for several quantum circuits collected from RevLib, and 1.18× for circuits from Qiskit Lib.

Geometry of phase-covariant qubit channels

We analyze the geometry on the space of non-unital phase-covariant qubit maps. Using the corresponding Choi-Jamiołkowski states, we derive the Hilbert-Schmidt line and volume elements using the channel eigenvalues together with the parameter that characterizes non-unitality. We find the shapes and analytically compute the volumes of phase-covariant channels, in particular entanglement breaking and obtainable with time-local generators.

Research on Qubit Mapping Technique Based on Batch SWAP Optimization

Research on Qubit Mapping Technique Based on Batch SWAP Optimization

Near-optimal circuit mapping with reduced search paths on IBM quantum architectures

Due to technological constraints in the quantum devices, two-qubit gates can be executed only if their qubits are physically connected (neighbours). If all the qubits of the two-qubit gates in a circuit cannot be kept adjacent to each other, then a remapping has to be performed. We insert swap gates between two adjacent qubits to update the mapping of qubits, increasing the number of basic operations. Generally, the mapping problem was addressed in terms of two sub-problems in the related works, the global ordering by initial mapping and the re-ordering of qubits (local ordering). We propose a technique where these two sub-problems are combined together; the need of local ordering is greatly reduced. We divide the circuit into blocks such that every block contains maximum gates and all the interacting qubits within the blocks are connected. Swap operations are performed between two consecutive blocks, and a series of swap operations form a path. The shortest route between two successive blocks is acquired using a breadth first search strategy. The main objective is to provide a near-optimal solution in reduced time. Experiments were conducted using the latest versions of the 5-qubit IBM Q devices, and the effects of qubit connectivities on the circuit cost was also investigated.

An Iterated Local Search Methodology for the Qubit Mapping Problem

The qubit mapping approach serves to transform a quantum logical circuit (LC) into a physical one that satisfies the connectivity constraints imposed by the noisy intermediate-scale quantum (NISQ) devices. The quality of the physical circuit generated by a mapping approach depends largely on the initial mapping, which specifies the correspondence between the qubits in the LC and the qubits on the NISQ device. There are a total of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n!$ </tex-math></inline-formula> different initial mappings for a qubit mapping problem with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> qubits, and among them, there is at least one initial mapping corresponding to the smallest physical circuit that this mapping approach can output. Finding such an initial mapping is very important for reliable computations on the NISQ device. To this end, we propose an iterated local search framework as well as a heuristic circuit mapper. In this framework, we perform multiple local searches on the space of initial mappings, and during each local search, several promising neighborhoods of the current initial mapping are generated and evaluated by invoking the circuit mapper in a forward or a backward manner. This framework provides a way for the qubit mapping approach to find the best physical circuit that it can produce, allowing it to trade time for circuit quality, which is necessary in the NISQ era. The experimental results demonstrate the stability, scalability, and effectiveness of this approach in reducing the number of additional gates. Moreover, although this approach is a multipass circuit mapping process, it can generate a good-quality physical circuit within half an hour, even for the circuit with more than 10 000 gates.

Moving quantum states without swap via intermediate higher-dimensional qudits

Quantum algorithms can be realized in the form of a quantum circuit. To map a quantum circuit for a specific quantum algorithm to quantum hardware, qubit mapping is an imperative technique based on the qubit topology. Due to the neighborhood constraint of qubit topology, the implementation of the quantum algorithm rightly, is essential for moving information around in a quantum computer. Swapping of qubits using a swap gate moves the quantum state between two qubits and solves the neighborhood constraint of qubit topology. Although, one needs to decompose the swap gate into three controlled-not gates to implement the swap gate efficiently, but unwillingly quantum cost with respect to the gate count and depth increases. In this paper, a formalism of moving quantum states without using swap operation is introduced. Moving quantum states through qubits have been attained with the adoption of temporary intermediate qudit states. This introduction of intermediate qudit states has exhibited a three times reduction in quantum cost with respect to the gate count and approximately two times reduction with respect to circuit depth compared to the state-of-the-art approach of the swap gate insertion. We also exhibit that the adoption of the intermediate qudit makes the approach sublimer than the existing works by obtaining a better fidelity. Furthermore, the proposed approach is generalized to any finite-dimensional quantum system.

Quantum algorithm for electronic band structures with local tight-binding orbitals

While the main thrust of quantum computing research in materials science is to accurately measure the classically intractable electron correlation effects due to Coulomb repulsion, designing optimal quantum algorithms for simpler problems with well-understood solutions is a useful tactic to advance our quantum “toolbox”. With this in mind, we consider the quantum calculation of a periodic system’s single-electron band structure over a path through reciprocal space. Previous efforts have used the Variational Quantum Eigensolver algorithm to solve the energy of each band, which involves numerically optimizing the parameters of a variational quantum circuit to minimize a cost function, constructed as the expectation value of a Hamiltonian operator. Traditionally, a unique Hamiltonian operator is constructed for each k-point, so that many cost functions, each with their own parameter space, must be optimized to generate a single band. Similarly, calculating higher bands than the first has traditionally involved modifying the cost function with additional overlap terms to ensure higher-energy eigenstates are orthogonal to those of lower bands. In this paper, we adopt a direct space approach, using a novel hybrid first/second-quantized qubit mapping which allows us to construct a single Hamiltonian, and a single cost-function, suitable for solving the entire electronic band structure. In contrast to previous approaches, the k-point and the band index are selected by additional parameters in our quantum circuit, rather than through modifications to the cost function. The result is a technically and conceptually simpler approach to band structure calculations on a quantum computer. Moreover, we expect that the tools developed herein will motivate new strategies for tackling highly-correlated materials beyond the grasp of classical computing.

Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps

We analyze the connections between the non-Markovianity degree of the most general phase-damping qubit maps and their legitimate mixtures. Using the results for image non-increasing dynamical maps, we formulate the necessary and sufficient conditions for the Pauli maps to satisfy specific divisibility criteria. Next, we examine how the non-Markovianity properties for (in general noninvertible) Pauli dynamical maps influence the properties of their convex combinations. Our results are illustrated with instructive examples. For P-divisible maps, we propose a legitimate time-local generator whose all decoherence rates are temporarily infinite.

A Parallelized Qubit Mapping Algorithm for Large-scale Quantum Circuits

Quantum computers are superior to existing classical supercomputers in terms of run time for specific tasks, and various studies on quantum computers are in progress. Despite this, there is a significant gap in technology between available technologies and actual quantum computers on the noisy intermediate-scale quantum-scale. Currently, various quantum algorithms have been implemented and verified using quantum simulations. Therefore, the runtime performance of a quantum circuit can be verified in the same environment as a real quantum machine. A quantum compiler compiles quantum circuits. When a quantum circuit is compiled, logical qubits in a quantum circuit should be mapped to physical qubits, called qubit mapping. As qubit mapping is an NP-Complete problem, the compilation time increases exponentially according to the number of qubits. Therefore, various studies on effective qubit mapping techniques have been developed to accelerate the execution time. This paper proposes a new parallelized Qubit mapping algorithm. The proposed method consists of three-step processes: one circuit is divided into several circuits; the SABRE enhanced algorithm is executed on each circuit in parallel and then merged. The performance was evaluated using 10 benchmarks. The experimental results revealed an acceleration of up to 6.42x and an average speed up of 4.8x, with an average overhead of 1.03x in terms of the number of gates obtained. The proposed method outperformed the well-known modern qubit-mapping algorithm in terms of the execution time with exponential speedup improvement.