QuASeR -- Quantum Accelerated De Novo DNA Sequence Reconstruction

In this article, we present QuASeR, a reference-free DNA sequence reconstruction implementation via de novo assembly on both gate-based and quantum annealing platforms. Each one of the four steps of the implementation (TSP, QUBO, Hamiltonians and QAOA) is explained with simple proof-of-concept examples to target both the genomics research community and quantum application developers in a self-contained manner. The details of the implementation are discussed for the various layers of the quantum full-stack accelerator design. We also highlight the limitations of current classical simulation and available quantum hardware systems. The implementation is open-source and can be found on https://github.com/prince-ph0en1x/QuASeR.Comment: 24 page

A CQM-based approach to solving a combinatorial problem with applications in drug design

The use of D-Wave's Leap Hybrid solver is demonstrated here in solving a Knapsack optimization problem: finding meal combinations from a fixed menu that fit a diner's constraints. This is done by first formulating the optimization problem as a Constrained Quadratic Model (CQM) and then submitting it to a quantum annealer. We highlight here the steps needed, as well as the implemented code, and provide solutions from a Chicken and Waffle restaurant menu. Additionally, we discuss how this model may be generalized to find optimal drug molecules within a large search space with many complex, and often contradictory, structures and property constraints.Comment: 10 pages, 2 table

The lower energy consumption in cryptocurrency mining processes by SHA-256 Quantum circuit design used in hybrid computing domains

Cryptocurrency mining processes always lead to a high energy consumption at considerably high production cost, which is nearly one-third of cryptocurrency (e.g. Bitcoin) price itself. As the core of mining process is based on SHA-256 cryptographic hashing function, by using the alternative quantum computers, hybrid quantum computers or more larger quantum computing devices like quantum annealers, it would be possible to reduce the mining energy consumption with a quantum hardware's low-energy-operation characteristics. Within this work we demonstrated the use of optimized quantum mining facilities which would replace the classical SHA-256 and high energy consuming classical hardware in near future

Scaling Advantage in Approximate Optimization with Quantum Annealing

Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected discrete optimization and quantum simulation problems. Nevertheless, despite numerous attempts, a computational quantum advantage in exact optimization using quantum annealing hardware has so far remained elusive. Here, we present evidence for a quantum annealing scaling advantage in approximate optimization. The advantage is relative to the top classical heuristic algorithm: parallel tempering with isoenergetic cluster moves (PT-ICM). The setting is a family of 2D spin-glass problems with high-precision spin-spin interactions. To achieve this advantage, we implement quantum annealing correction (QAC): an embedding of a bit-flip error-correcting code with energy penalties that leverages the properties of the D-Wave Advantage quantum annealer to yield over 1,300 error-suppressed logical qubits on a degree-5 interaction graph. We generate random spin-glass instances on this graph and benchmark their time-to-epsilon, a generalization of the time-to-solution metric for low-energy states. We demonstrate that with QAC, quantum annealing exhibits a scaling advantage over PT-ICM at sampling low energy states with an optimality gap of at least 1.0%. This amounts to the first demonstration of an algorithmic quantum speedup in approximate optimization.Comment: 11 pages, 6 figure

Quantum Advantage for All

We show that the algorithmic complexity of any classical algorithm written in a Turing-complete programming language polynomially bounds the number of quantum bits that are required to run and even symbolically execute the algorithm on a quantum computer. In particular, we show that any classical algorithm $A$ that runs in $\mathcal{O}(f(n))$ time and $\mathcal{O}(g(n))$ space requires no more than $\mathcal{O}(f(n)\cdot g(n))$ quantum bits to execute, even symbolically, on a quantum computer. With $\mathcal{O}(1)\leq\mathcal{O}(g(n))\leq\mathcal{O}(f(n))$ for all $n$, the quantum bits required to execute $A$ may therefore not exceed $\mathcal{O}(f(n)^2)$ and may come down to $\mathcal{O}(f(n))$ if memory consumption by $A$ is bounded by a constant. Our construction works by encoding symbolic execution of machine code in a finite state machine over the satisfiability-modulo-theory (SMT) of bitvectors, for modeling CPU registers, and arrays of bitvectors, for modeling main memory. The FSM is linear in the size of the code, independent of execution time and space, and represents the reachable machine states for any given input. The FSM may be explored by bounded model checkers using SMT and SAT solvers as backend. However, for the purpose of this paper, we focus on quantum computing by unrolling and bit-blasting the FSM into (1)~satisfiability-preserving quadratic unconstrained binary optimization (QUBO) models targeting adiabatic forms of quantum computing such as quantum annealing, and (2)~semantics-preserving quantum circuits (QCs) targeting gate-model quantum computers. With our compact QUBOs, real quantum annealers can now execute simple but real code even symbolically, yet only with potential but no guarantee for exponential speedup, and with our QCs as oracles, Grover's algorithm applies to symbolic execution of arbitrary code, guaranteeing at least in theory a quadratic speedup

Exploration of new chemical materials using black-box optimization with the D-wave quantum annealer

In materials informatics, searching for chemical materials with desired properties is challenging due to the vastness of the chemical space. Moreover, the high cost of evaluating properties necessitates a search with a few clues. In practice, there is also a demand for proposing compositions that are easily synthesizable. In the real world, such as in the exploration of chemical materials, it is common to encounter problems targeting black-box objective functions where formalizing the objective function in explicit form is challenging, and the evaluation cost is high. In recent research, a Bayesian optimization method has been proposed to formulate the quadratic unconstrained binary optimization (QUBO) problem as a surrogate model for black-box objective functions with discrete variables. Regarding this method, studies have been conducted using the D-Wave quantum annealer to optimize the acquisition function, which is based on the surrogate model and determines the next exploration point for the black-box objective function. In this paper, we address optimizing a black-box objective function containing discrete variables in the context of actual chemical material exploration. In this optimization problem, we demonstrate results obtaining parameters of the acquisition function by sampling from a probability distribution with variance can explore the solution space more extensively than in the case of no variance. As a result, we found combinations of substituents in compositions with the desired properties, which could only be discovered when we set an appropriate variance.Comment: 14pages, 4figures, 4table

Multilevel Combinatorial Optimization Across Quantum Architectures

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave's quantum annealer and IBM's gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution

Highly accurate quantum optimization algorithm for CT image reconstructions based on sinogram patterns

Computed tomography (CT) has been developed as a non-destructive technique for observing minute internal images of samples. It has been difficult to obtain photo-realistic (clean or clear) CT images due to various unwanted artifacts generated during the CT scanning process, along with limitations of back projection algorithms. Recently, an iterative optimization algorithm has been developed that uses the entire sinogram to reduce errors caused by artifacts. In this paper, we introduce a new quantum algorithm for reconstructing CT images. This algorithm can be used with any type of light source as long as the projection is defined. Suppose we have an experimental sinogram produced by a Radon transform. To find the CT image of this sinogram, we express the CT image as a combination of qubits. After the Radon transform of the undetermined CT image, we find the combination of the actual sinogram and the optimized qubits. The global energy optimization value used here can determine the value of qubits through a gate model quantum computer or quantum annealer. In particular, the new algorithm can also be used for cone-beam CT image reconstructions and will be of great help in the field of medical imaging.Comment: 16 Pages, 5 figures, 1 Tabl