arXiv subjects

Mehdi Sedighi

Publications and source records attributed to Mehdi Sedighi.

18 recordsLinked to original sources

arXiv2025

A Scalable Synthesis Algorithm for Reversible Functions

Reversible computation is an emerging technology that has gained significant attention due to its critical role in quantum circuit synthesis and low-power design. This paper introduces a transformation-based method for exact synthesis of reversible circuits. The proposed approach utilizes a novel adaptation of the Quine-McCluskey algorithm to eliminate input-output discrepancies in the truth table, transforming the permutation matrix into an identity matrix. Furthermore, a novel search space reduction technique is presented which, combined with the primary method, enables the synthesis algorithm to handle high-input reversible functions. This approach combines the influence of multiple control qubits on a target qubit, evaluating their collective impact. This aggregation can decrease the control qubit count within quantum gates. Consequently, it proves beneficial for applications like surface code error correction architectures as well as current Noisy Intermediate-Scale Quantum (NISQ) hardwares. Experimental results demonstrate significant improvements over the state-of-the-art exact synthesis methods, achieving up to 99% improvements in terms of the number of levels of T-gates.

quant-ph↗

arXiv2021

Low-Overhead Code Concatenation Approaches for Universal Quantum Computation

As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, two approaches for universal fault-tolerant quantum computation, mainly based on code concatenation, are proposed. The proposed approaches outperform code concatenation in terms of both number of qubits and code distance and has also significantly less resource overhead than code switching, magic state distillation and pieceable fault-tolerance at the cost of reducing the effective distance of the concatenated code for implementing non-transversal gates.

quant-ph↗

arXiv2020

A system architecture for parallel analysis of flux-balanced metabolic pathways

In this paper, a system architecture is proposed that approximately models the functionality of metabolic networks. The AND/OR graph model is used to represent the metabolic network and each processing element in the system emulates the functionality of a metabolite. The system is implemented on a graphics processing unit (GPU) as the hardware platform using CUDA environment. The proposed architecture takes advantage of the inherent parallelism in the network structure in terms of both pathway and metabolite traversal. The function of each element is defined such that it can find flux-balanced pathways. Pathways in both small and large metabolic networks are applied to the proposed architecture and the results are discussed.

q-bio.MN↗

arXiv2018

A Graph-Based Approach to Analyze Flux-Balanced Pathways in Metabolic Networks

An Elementary Flux Mode (EFM) is a pathway with minimum set of reactions that are functional in steady-state constrained space. Due to the high computational complexity of calculating EFMs, different approaches have been proposed to find these flux-balanced pathways. In this paper, an approach to find a subset of EFMs is proposed based on a graph data model. The given metabolic network is mapped to the graph model and decisions for reaction inclusion can be made based on metabolites and their associated reactions. This notion makes the approach more convenient to categorize the output pathways. Implications of the proposed method on metabolic networks are discussed.

q-bio.MN↗

arXiv2017

A Low-Overhead Hybrid Approach for Universal Fault-Tolerant Quantum Computation

As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, a hybrid approach is proposed which combines the code concatenation technique with the other mentioned approaches. The proposed approach outperforms code concatenation in terms of both number of qubits and error threshold and also significantly reduces the resource overhead of code switching, magic state distillation and pieceable fault-tolerance at the cost of reducing the effective distance of the concatenated code for implementing non-transversal gates.

quant-ph↗

arXiv2017

Geometry-Based Optimization of One-Way Quantum Computation Measurement Patterns

In one-way quantum computation (1WQC) model, an initial highly entangled state called a graph state is used to perform universal quantum computations by a sequence of adaptive single-qubit measurements and post-measurement Pauli-X and Pauli-Z corrections. The needed computations are organized as measurement patterns, or simply patterns, in the 1WQC model. The entanglement operations in a pattern can be shown by a graph which together with the set of its input and output qubits is called the geometry of the pattern. Since a one-way quantum computation pattern is based on quantum measurements, which are fundamentally nondeterministic evolutions, there must be conditions over geometries to guarantee determinism. Causal flow is a sufficient and generalized flow (gflow) is a necessary and sufficient condition over geometries to identify a dependency structure for the measurement sequences in order to achieve determinism. Previously, three optimization methods have been proposed to simplify 1WQC patterns which are called standardization, signal shifting and Pauli simplification. These optimizations can be performed using measurement calculus formalism by rewriting rules. However, maintaining and searching these rules in the library can be complicated with respect to implementation. Moreover, serial execution of these rules is time consuming due to executing many ineffective commutation rules. To overcome this problem, in this paper, a new scheme is proposed to perform optimization techniques on patterns with flow or gflow only based on their geometries instead of using rewriting rules. Furthermore, the proposed scheme obtains the maximally delayed gflow order for geometries with flow. It is shown that the time complexity of the proposed approach is improved over the previous ones.

quant-ph↗

arXiv2017

S-Restricted Compositions Revisited

An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed- form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to finding solutions to corresponding so-called interpreters which are linear homogeneous recurrence relations with constant coefficients. Then, we reduce interpreters to Diophantine equations. Such equations are not in general solvable. Thus, we restrict our attention to those S-restricted composition problems whose interpreters have a small number of coefficients, thereby leading to solvable Diophantine equations. The formalism developed is then used to study the integer sequences related to some well-known cases of the S-restricted composition problem.

math.CO↗

arXiv2016

Non-Uniform Code Concatenation for Universal Fault-Tolerant Quantum Computing

Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state distillation, code switching or code concatenation in order to achieve universality. In this paper we propose an alternative approach for universal fault-tolerant quantum computing mainly based on the code concatenation approach proposed in [PRL 112, 010505 (2014)] but in a non-uniform fashion. The proposed approach is described based on non-uniform concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code as well as the 5-qubit code with the 15-qubit Reed-Muller code, which lead to two 49-qubit and 47-qubit codes, respectively. These codes can correct any arbitrary single physical error with the ability to perform a universal set of fault-tolerant gates, without using magic state distillation.

quant-ph↗

arXiv2016

Quantum-Logic Synthesis of Hermitian Gates

In this paper, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in linear algebra is considered as the basis of the proposed synthesis method. The quantum circuit synthesis method derived from the Jacobi approach and its optimization challenges are described. It is shown that the proposed method results in multiple-control rotation gates around the y axis, multiple-control phase shift gates, multiple-control NOT gates and a middle diagonal Hermitian matrix, which can be synthesized to multiple-control Pauli Z gates. Using the proposed approach, it is shown how multiple-control U gates, where U is a single-qubit Hermitian quantum gate, can be implemented using a linear number of elementary gates in terms of circuit lines with the aid of one auxiliary qubit in an arbitrary state.

quant-ph↗

arXiv2015

One-Way Quantum Computer Simulation

In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state. The choices of bases for these measurements as well as the structure of the entanglements specify a quantum algorithm. As scalable and reliable quantum computers have not been implemented yet, quantum computation simulators are the only widely available tools to design and test quantum algorithms. However, simulating the quantum computations on a standard classical computer in most cases requires exponential memory and time. In this paper, a general direct simulator for 1WQC, called OWQS, is presented. Some techniques such as qubit elimination, pattern reordering and implicit simulation of actions are used to considerably reduce the time and memory needed for the simulations. Moreover, our simulator is adjusted to simulate the measurement patterns with a generalized flow without calculating the measurement probabilities which is called extended one-way quantum computation simulator (EOWQS). Experimental results validate the feasibility of the proposed simulators and that OWQS and EOWQS are faster as compared with the well-known quantum circuit simulators, i.e., QuIDDPro and libquantum for simulating 1WQC model.

cs.ET↗

arXiv2014

Decomposition of Diagonal Hermitian Quantum Gates Using Multiple-Controlled Pauli Z Gates

Quantum logic decomposition refers to decomposing a given quantum gate to a set of physically implementable gates. An approach has been presented to decompose arbitrary diagonal quantum gates to a set of multiplexed-rotation gates around z axis. In this paper, a special class of diagonal quantum gates, namely diagonal Hermitian quantum gates, is considered and a new perspective to the decomposition problem with respect to decomposing these gates is presented. It is first shown that these gates can be decomposed to a set that solely consists of multiple-controlled Z gates. Then a binary representation for the diagonal Hermitian gates is introduced. It is shown that the binary representations of multiple-controlled Z gates form a basis for the vector space that is produced by the binary representations of all diagonal Hermitian quantum gates. Moreover, the problem of decomposing a given diagonal Hermitian gate is mapped to the problem of writing its binary representation in the specific basis mentioned above. Moreover, CZ gate is suggested to be the two-qubit gate in the decomposition library, instead of previously used CNOT gate. Experimental results show that the proposed approach can lead to circuits with lower costs in comparison with the previous ones.

cs.ET↗

arXiv2013

A Quantum Physical Design Flow Using ILP and Graph Drawing

Implementing large-scale quantum circuits is one of the challenges of quantum computing. One of the central challenges of accurately modeling the architecture of these circuits is to schedule a quantum application and generate the layout while taking into account the cost of communications and classical resources as well as the maximum exploitable parallelism. In this paper, we present and evaluate a design flow for arbitrary quantum circuits in ion trap technology. Our design flow consists of two parts. First, a scheduler takes a description of a circuit and finds the best order for the execution of its quantum gates using integer linear programming (ILP) regarding the classical resources (qubits) and instruction dependencies. Then a layout generator receives the schedule produced by the scheduler and generates a layout for this circuit using a graph-drawing algorithm. Our experimental results show that the proposed flow decreases the average latency of quantum circuits by about 11% for a set of attempted benchmarks and by about 9% for another set of benchmarks compared with the best in literature.

quant-ph↗

arXiv2012

Depth-Optimized Reversible Circuit Synthesis

In this paper, simultaneous reduction of circuit depth and synthesis cost of reversible circuits in quantum technologies with limited interaction is addressed. We developed a cycle-based synthesis algorithm which uses negative controls and limited distance between gate lines. To improve circuit depth, a new parallel structure is introduced in which before synthesis a set of disjoint cycles are extracted from the input specification and distributed into some subsets. The cycles of each subset are synthesized independently on different sets of ancillae. Accordingly, each disjoint set can be synthesized by different synthesis methods. Our analysis shows that the best worst-case synthesis cost of reversible circuits in the linear nearest neighbor architecture is improved by the proposed approach. Our experimental results reveal the effectiveness of the proposed approach to reduce cost and circuit depth for several benchmarks.

quant-ph↗

arXiv2010

Reversible Circuit Synthesis Using a Cycle-Based Approach

Reversible logic has applications in various research areas including signal processing, cryptography and quantum computation. In this paper, direct NCT-based synthesis of a given $k$-cycle in a cycle-based synthesis scenario is examined. To this end, a set of seven building blocks is proposed that reveals the potential of direct synthesis of a given permutation to reduce both quantum cost and average runtime. To synthesize a given large cycle, we propose a decomposition algorithm to extract the suggested building blocks from the input specification. Then, a synthesis method is introduced which uses the building blocks and the decomposition algorithm. Finally, a hybrid synthesis framework is suggested which uses the proposed cycle-based synthesis method in conjunction with one of the recent NCT-based synthesis approaches which is based on Reed-Muller (RM) spectra. The time complexity and the effectiveness of the proposed synthesis approach are analyzed in detail. Our analyses show that the proposed hybrid framework leads to a better quantum cost in the worst-case scenario compared to the previously presented methods. The proposed framework always converges and typically synthesizes a given specification very fast compared to the available synthesis algorithms. Besides, the quantum costs of benchmark functions are improved about 20% on average (55% in the best case).

quant-ph↗

arXiv2010

Block-based quantum-logic synthesis

In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which contains $l$ qubits. In addition, a previously proposed quantum-logic synthesis method based on quantum Shannon decomposition is recursively applied to reach unitary gates over $l$ qubits. Then, the basic block is used and some optimizations are applied to remove redundant gates. It is shown that the exact value of $l$ affects the number of one-qubit and CNOT gates in the proposed method. In comparison to the previous synthesis methods, the value of $l$ is examined consequently to improve either the number of CNOT gates or the total number of gates. The proposed approach is further analyzed by considering the nearest neighbor limitation. According to our evaluation, the number of CNOT gates is increased by at most a factor of $\frac{5}{3}$ if the nearest neighbor interaction is applied.

quant-ph↗

arXiv2010

A Library-Based Synthesis Methodology for Reversible Logic

In this paper, a library-based synthesis methodology for reversible circuits is proposed where a reversible specification is considered as a permutation comprising a set of cycles. To this end, a pre-synthesis optimization step is introduced to construct a reversible specification from an irreversible function. In addition, a cycle-based representation model is presented to be used as an intermediate format in the proposed synthesis methodology. The selected intermediate format serves as a focal point for all potential representation models. In order to synthesize a given function, a library containing seven building blocks is used where each building block is a cycle of length less than 6. To synthesize large cycles, we also propose a decomposition algorithm which produces all possible minimal and inequivalent factorizations for a given cycle of length greater than 5. All decompositions contain the maximum number of disjoint cycles. The generated decompositions are used in conjunction with a novel cycle assignment algorithm which is proposed based on the graph matching problem to select the best possible cycle pairs. Then, each pair is synthesized by using the available components of the library. The decomposition algorithm together with the cycle assignment method are considered as a binding method which selects a building block from the library for each cycle. Finally, a post-synthesis optimization step is introduced to optimize the synthesis results in terms of different costs.

quant-ph↗

arXiv2010

Algebraic Characterization of CNOT-Based Quantum Circuits with its Applications on Logic Synthesis

The exponential speed up of quantum algorithms and the fundamental limits of current CMOS process for future design technology have directed attentions toward quantum circuits. In this paper, the matrix specification of a broad category of quantum circuits, i.e. CNOT-based circuits, are investigated. We prove that the matrix elements of CNOT-based circuits can only be zeros or ones. In addition, the columns or rows of such a matrix have exactly one element with the value of 1. Furthermore, we show that these specifications can be used to synthesize CNOT-based quantum circuits. In other words, a new scheme is introduced to convert the matrix representation into its SOP equivalent using a novel quantum-based Karnaugh map extension. We then apply a search-based method to transform the obtained SOP into a CNOT-based circuit. Experimental results prove the correctness of the proposed concept.

quant-ph↗

arXiv2010

A Novel Synthesis Algorithm for Reversible Circuits

In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer steps. To evaluate the proposed method, several circuits taken from the literature are used. The experimental results corroborate the expected findings.

quant-ph↗