Quantum computing method and system for optimizing a technical process involving the traveling salesman problem

Abstract

A quantum computing method and system optimize technical processes involving the Traveling Salesman Problem (TSP). The method initializes N quantum registers, each corresponding to a task position and comprising N qubits. A W state is generated in each register, representing an equally distributed superposition of quantum states. Controlled operations encode the technical costs of transitions between tasks as phase shifts between qubits in adjacent registers. Optionally, penalty phase shifts are applied to qubits in different registers corresponding to the same task. The state of the quantum registers is measured, and the process is repeated over multiple trials to identify the most frequently measured state, providing a target task sequence. The system includes quantum registers, a superposition generator, a phase encoder, a measurement unit, and a processor to perform the method. Applications include manufacturing, data transfer, and genome sequencing, optimizing technical costs such as energy expenditure, bandwidth consumption, and DNA segment overlap.

Description

[0001] QUANTUM COMPUTING METHOD AND SYSTEM FOR OPTIMIZING A TECHNICAL PROCESS INVOLVING THE TRAVELING SALESMAN PROBLEM

[0002] TECHNOLOGICAL FIELD

[0003] The present disclosure relates to the field of quantum computing. More particularly, the present disclosure relates to a method implemented at least partially on a quantum processor for optimizing a technical process.

[0004] BACKGROUND

[0005] The Traveling Salesman Problem (TSP) is a foundational optimization problem in which the objective is to determine the shortest route that visits a given set of locations once before returning to the starting point. Formally, the TSP can be represented as finding the minimal Hamiltonian cycle in a weighted graph, where nodes correspond to specific locations and edges represent the travel costs or distances between them. While the TSP is central to theoretical computer science and operations research, its real-world applications in technical processes span numerous fields that benefit from optimized routing and resource allocation.

[0006] In logistics and supply chain management, for instance, solving the TSP enables the design of cost-effective delivery and transportation routes, reducing fuel consumption and time. In manufacturing, the TSP framework is applied to optimize robotic path planning and minimize operational delays, thereby enhancing production efficiency. In the field of electronics, printed circuit board (PCB) manufacturing utilizes TSP-inspired solutions to streamline component placement and wiring, minimizing signal interference and material usage. Furthermore, in computational biology, the TSP is employed in genome sequencing, where it aids in identifying the optimal arrangement of DNA fragments for accurate sequence assembly, an essential step in de novo genome assembly.

[0007] Despite the straightforward definition of the TSP, it belongs to the NP-hard class of problems, meaning that solving it exactly is computationally intensive and infeasible for large instances. Conventional approaches include exact methods like branch andbound and heuristic techniques such as genetic algorithms, yet these often fall short for large datasets due to exponential growth in complexity.

[0008] Quantum computing, with its ability to evaluate multiple states simultaneously through superposition, introduces a transformative approach to solving NP-hard problems like the TSP. By leveraging quantum algorithms, it becomes possible to compute all potential paths in parallel and identify the shortest (or longest) path. This parallelism, achieved through quantum states and entanglement, positions quantum computing as a potent tool for tackling complex optimization challenges across industries, from logistics and manufacturing to cutting-edge biological research. This quantum framework for the TSP could reshape the approach to resource allocation and pathfinding problems across a wide array of technological fields.

[0009] GENERAL DESCRIPTION

[0010] The present disclosure introduces a quantum computing method and system designed to optimize technical processes involving the TSP. By leveraging the principles of quantum parallelism and superposition, the disclosed method enables the simultaneous evaluation of multiple potential solutions.

[0011] The present disclosure provides a computer-implemented method for improving a technical process comprising a plurality of N tasks to be sequentially performed in a task sequence and wherein transitioning between each two tasks is associated with a corresponding technical cost, by finding a target task sequence improving a process technical cost associated with transitioning between said tasks, using a quantum computer. The method comprises (a) initializing a set of N quantum registers, wherein each quantum register corresponds to a task position in the task sequence and comprises a plurality of N qubits and each qubit corresponds to a respective task in the technical process; (b) preparing a W state in each quantum register, wherein the W state is an equally distributed superposition of quantum states of the register, each having a single qubit in a 11) state, and all other qubits in a |0) state; (c) applying phase gates controlled by each pairs of qubits of adjacent registers corresponding to different tasks, so as to encode the technical costs of transitions between said tasks as phase shifts into an ancilla qubit, said phase shifts being a function of the technical costs of said transitions; (d) applying a unitary operation on the ancilla qubit to transfer said phase shifts into amplitudes so as to increase a probability of measuring states corresponding to improved process technical costs; (e) measuring the state of the quantum registers; (f)repeating steps (a)-(e) over a plurality of trials to identify a most frequently measured state thereby providing said target task sequence corresponding to tasks associated with the qubits in said most frequently measured state.

[0012] In addition to the above features, a computer implemented method for improving a technical process, according to the presently disclosed subject matter, can optionally comprise one or more of features / steps (i) to (xv) below, in any technically possible combination or permutation:

[0013] (i) identifying a plurality of most frequently measured states over the plurality of trials and selecting one of the most frequently measured states as the target task sequence.

[0014] (ii) The method of claim 2, wherein selecting one of the most frequently measured states comprises discarding task sequences that do not satisfy predefined constraints.

[0015] (iii) the technical process comprises a manufacturing process with a plurality of manufacturing stations and the technical cost comprises an energy expenditure associated with transitioning between the stations.

[0016] (iv) the technical process comprises a data transfer process with a plurality of nodes in a network and the technical cost comprises bandwidth consumption associated with routing the data between two nodes.

[0017] (v) the technical process comprises genome sequencing operation with a plurality of DNA segments and the technical cost comprises a likelihood of overlap between two DNA segments.

[0018] (vi) the technical process comprises travelling through a plurality of cities and the technical cost comprises a time, distance and / or fuel consumption associated with transitioning between said cities.

[0019] (vii) further comprising providing instructions to perform the technical process in the identified target task sequence.

[0020] (viii) applying the unitary operation on the ancilla qubit comprises applying a Hadamard gate on the ancilla qubit.

[0021] (ix) the phase shifts applied to encode the technical costs are inversely proportional to the technical costs.

[0022] (x) phase shifts Grm,rm+ienc°ding the technical costs for transitioning between two technical tasks rmand rm+1are provided according to: >

[0023]

[0024] where n is the number of technical tasks,

[0025]

[0026] is the technical cost for transitioning between task rmand task rm+1and D = max Drm m+1is the largest ofrm>rm+l

[0027] technical costs for transitioning between any of the tasks.

[0028] (xi) applying phase gates further comprises applying phase gates controlled by each pairs of qubits of different registers corresponding to the same task when said qubits are in the 11) state.

[0029] (xii) the penalty phase shifts are configured to attenuate the amplitudes of quantum states representing unallowed task sequences.

[0030] (xiii) the penalty phase shifts 0pare provided according to 0p= , where n

[0031]

[0032] is the number of technical tasks.

[0033] (xiv) the output quantum state after applying the unitary operation on the ancilla qubit is given by:

[0034] "

[0035]

[0036] ">

[0037] where

[0038]

[0039] is a register state in which all register qubits are in the |0) state except the n-th qubit in the 11) state, ©(ry, ... , rn) is the total phase accumulated for a given task sequence (ty, ...,rn).

[0040] (xv) further comprising:

[0041] (a) using a classical greedy algorithm to identify an initial task sequence;

[0042] (b) pruning from said initial task sequence one or more task transitions associated with technical costs that do not meet a predefined criteria thereby obtaining a sub -process including a sub-plurality of tasks;

[0043] (c) feeding said sub -process as input to the quantum algorithm to refine the initial task sequence.

[0044] The present disclosure provides also a quantum computing system for optimizing a technical process in accordance with the method previously described. Thesystem comprises: (a) a plurality of N quantum registers, each quantum register comprising a plurality of qubits, wherein each quantum register corresponds to a task position in the task sequence; and each qubit in the quantum register corresponds to a respective task in the technical process; (b) a superposition generator configured to generate a W state in each quantum register, wherein the W state is an equally distributed superposition of quantum states of the register, each having a single qubit in a ll) state and all other qubits in a |0) state, (c) a phase encoder configured to apply phase gates controlled by each pairs of qubits of adjacent registers corresponding to different tasks, so as to encode the technical costs of transitions between said tasks as phase shifts into an ancilla qubit, said phase shifts being a function of the technical costs of said transitions; a phase to amplitude converter configured to apply a unitary operation on the ancilla qubit to transfer said phase shifts into amplitudes so as to increase a probability of measuring states corresponding to improved process technical costs; a measurement unit configured to measure the states of the quantum registers; a processor configured to: (i) repeat the operation of the superposition generator, the phase encoder, the phase to amplitude converter and the measurement module over a plurality of trials; and (ii) identify a most frequently measured quantum state as a target task sequence corresponding to tasks associated with the sequence of qubits in the most frequently measured quantum state.

[0045] The controller may be configured to perform a preprocessing step of pruning an initial task sequence generated by a classical greedy algorithm, by removing transitions (edges) based on their technical costs. The pruned initial task sequence may be provided as an input technical process to the method herein described. This preprocessing step simplifies an original technical process (which may be represented as a graph) by creating a sub-process (sub-graph) with a reduced complexity which is subsequently processed by the quantum algorithm.

[0046] In the present disclosure, the following terms and their derivatives can be understood in view of the below explanations:

[0047] The terms circuits and gates refer to the field of quantum computation. Quantum computation is built upon the manipulation of qubits through quantum circuits. These circuits consist of quantum gates that perform operations on qubits.

[0048] A Hadamard gate is one of the most fundamental quantum gates. It transforms a qubit from a definite classical state, |0) or |1), into a superposition of both states. Mathematically, the Hadamard gate operates as follows:> >

[0049] >

[0050]

[0051] By applying the Hadamard gate, a qubit is placed in an equal superposition, where there is an equal probability of measuring the qubit in either the |0) or |1) state.

[0052] A Pauli-X gate is analogous to the classical NOT gate, which inverts the state of a qubit:

[0053] DO)=ID

[0054] » = |0)

[0055] This gate may be used for quantum algorithms that require bit-flip operations. When used in conjunction with other gates, it forms the basis of more complex quantum logic.

[0056] Controlled gates introduce entanglement between qubits, a purely quantum phenomenon that has no classical equivalent. The Controlled-NOT (CNOT) gate is one of the most widely used controlled gates. It operates on two qubits: a control qubit and a target qubit. The operation of the CNOT gate is conditional on the state of the control qubit: If the control qubit is in the |0) state, the target qubit remains unchanged. If the control qubit is in the |1) state, the target qubit is flipped (i.e., X operation). This gate may be used in generating entanglement, where the states of qubits become interdependent.

[0057] Phase gates are a class of gates that introduce a phase shift to the qubit quantum state. These gates are described by the following operations:

[0058]

[0059] These gates may be used in quantum algorithms where phase relationships between quantum states must be finely tuned.

[0060] A Controlled-Controlled Phase (CCP) gate (also referred to as phase gate controlled by two qubits) is a three-qubit operation where two qubits act as control qubits and the third qubit (the target qubit) undergoes a phase shift if the control qubits are both in the |1) state. This operation is a direct extension of the Controlled Phase (CP) gate and can be used to encode phase shifts in a quantum system.Phase kickback refers to the transfer of phase information into the amplitude probabilities of a qubit state through a sequence of quantum operations. Specifically, the process may involve applying a Hadamard gate, a phase gate introducing a phase shift (e.g., (|)), and another Hadamard gate. This results in the encoding of phase information ((|>) into the relative probabilities of the qubit states in the computational basis.

[0061] A technical process may refer to a sequence of discrete tasks or operations, arranged in a manner where transitioning between tasks incurs a quantifiable cost. In the present disclosure and in the claims scope, any technical process involves technical means and produces a technical effect. A technical process may encompass structured set of technical operations or technical tasks that can be modeled as a weighted graph, where the nodes represent tasks or stations, and the edges represent transitions between them with associated costs. The process may be considered as involving the Traveling Salesman Problem (TSP) optimization when identifying a sequence of tasks that minimizes or maximizes an aggregate cost while satisfying practical constraints such as task dependencies or resource limitations. Technical processes can be grouped into categories based on their application domains and include, but are not limited to:

[0062] Manufacturing processes including for example one or more technical tasks such as assembly, quality control, material handling, packaging, or transportation between manufacturing stations, where the associated technical costs may include energy consumption, time, or resource utilization.

[0063] Network and data transfer processes including for example one or more technical tasks such as routing data packets, accessing servers or nodes, or transferring data between network components, where the associated technical cost may be measured in terms of bandwidth consumption, latency, or computational overhead.

[0064] Biological sequencing processes such as aligning biological data (e.g. DNA fragments, RNA sequences or protein structures) to achieve an optimal arrangement based on specific criteria. The tasks in such processes may include individual sequence fragments, and the transitions between these tasks may correspond to the relationships between fragments, such as overlaps, alignment scores, or structural similarities. The costs associated with these transitions may be determined by factors such as mismatch penalties, gaps, insertions, or deletions introduced during the alignment or ordering process.Logistical and routing processes including for example one or more technical tasks such as planning travel itineraries, delivery routes, or supply chain logistics, where transitions represent the movement between locations and the costs involve time, distance, or fuel consumption.

[0065] The term "improving" a process technical cost may refer to optimizing the total technical cost associated with transitioning between all tasks in the technical process. Optimization can take the form of minimizing or maximizing the technical cost, depending on the specific problem being addressed (also referred to as “optimization type”). For example, in a shortest route problem, the optimization may minimize the total cost, such as time, distance, or energy consumption. Conversely, in a longest route problem, the goal may be to maximize the total cost, such as overlap between DNA fragments in a genome sequencing problem or the total utility in a resource allocation problem. The method described herein applies to problems requiring optimization in either direction, as the quantum algorithm evaluates all possible task sequences in parallel, enabling the identification of a target task sequence that provides an improved (e.g. the best / optimized) outcome for the technical cost.

[0066] BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to better understand the subject matter that is disclosed herein and to exemplify how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which:

[0068] Fig- 1 is a graph representing a technical process involving the TSP according to embodiments of the present disclosure.

[0069] Fig- 2 is a flow chart diagram illustrating generally a method for optimizing a technical process involving the Traveling Salesman Problem (TSP) according to embodiments of the present disclosure.

[0070] Fig- 3 illustrates a quantum circuit useful in a method for improving a technical process according to embodiments of the present disclosure.

[0071] Fig. 4 illustrates a quantum circuit useful in a method for improving a technical process according to embodiments of the present disclosure.Fig. 5 illustrates a quantum circuit useful for implementing a state preparation step in a method for improving a technical process according to embodiments of the present disclosure.

[0072] Fig- 6 illustrates an exemplary computing environment in which the disclosed technology may be implemented.

[0073] Fig- 7 illustrates an exemplary system for implementing the disclosed technology.

[0074] DETAILED DESCRIPTION OF EMBODIMENTS FIG. 1 a graph illustrating a technical process that may be optimized using a quantum computing method, as described hereinbelow. The technical process may include a plurality of N tasks to be sequentially performed once in a given order i.e. a task sequence. The technical process can be represented as a graph, where each technical task is depicted as a vertex and each transition between tasks is depicted as an edge. Each task transition may be associated with a technical cost which may differ depending on a direction of the transition. These costs may include parameters such as energy expenditure, bandwidth consumption, or travel distance depending on the type of technical process. A target task sequence having a global optimized cost may be determined using methods disclosed herein. The global cost may for example be defined as a sum of the costs of each task transition.

[0075] Referring to FIG. 1, the technical process may comprise a plurality of tasks or stations, designated as technical tasks 1, 2, 3, and 4. Transitions between these tasks are represented as paths, explicitly labelled as follows: 12 (transition from task 1 to task 2), 13 (transition from task 1 to task 3), 14 (transition from task 1 to task 4), 23 (transition from task 2 to task 3), 24 (transition from task 2 to task 4), and 34 (transition from task 3 to task 4). Each transition is associated with a measurable technical cost, which may differ depending on the direction of the transition. For instance, the cost of transitioning from task 1 to task 2 may not be the same as transitioning from task 2 to task 1. A goal of the methods described herein may be to identify a target task sequence that completes all tasks in an optimal sequence which optimizes the aggregate technical cost across all transitions. Each task corresponds to a specific task or operation within the technicalprocess, and the transitions represent the relationships or interactions between these tasks.

[0076] In a manufacturing context, each step may represent a distinct manufacturing station or operation, such as assembly, quality control, packaging, or storage. The transitions may represent for example the energy expenditure required to move materials or components between stations. In a context of data transfer, the tasks may represent nodes within a communication network, such as servers, routers, or data centers. Transitions between tasks may represent the bandwidth consumption required for routing data packets between nodes. In genome sequencing applications, the tasks may correspond to DNA fragments or segments. Transitions between tasks may represent a likelihood of overlap between two DNA segments. For travel -related applications, the tasks may correspond to a plurality of locations to be visited, and the transitions may represent the technical costs associated with traveling between them. These costs may include time, distance, or fuel consumption.

[0077] FIG. 2 illustrates generally a quantum computing method 100 according to embodiments of the present disclosure. The method 100 is configured for improving a technical process comprising a plurality of N tasks that are to be sequentially performed once in a given task sequence. Transitioning between each two tasks is associated with a corresponding technical cost and the total cost of the given task sequence is referred to as process technical cost. The method 100 is configured for determining a target task sequence reducing a process technical cost using a quantum computer. A task sequence may include an ordered list of the technical tasks of the technical process (i.e. task X in first position of the task sequence, task Y in second position of the task sequence, etc.). As such, the method 100 can be understood as a quantum algorithm for improving a technical process involving the Traveling Salesman Problem (TSP).

[0078] In a first step S100, the method may include initializing a set of N quantum registers. Each quantum register may be mapped to a task position (i.e. first position, second position...) in the task sequence and may comprise a plurality of N qubits. For example, a first register may correspond to a first position in the task sequence, a second register to a second task position in the task sequence, etc. Each qubit may be mapped to a respective task of the technical process.In a further step S200, the method may include a state preparation step for preparing a space that contains all task sequences. The state preparation step may include generating a W state in each of the N quantum registers. The W state is an equally distributed superposition of quantum states of the register, each having a single qubit in a |1) state, and all other qubits in a |0) state. More explanation about W state generation is provided hereinbelow with reference to FIG. 5.

[0079] For the sake of convenience and clarity in the subsequent calculations, we use the following notations:

[0080] Ri represents the ithregister, qij are the qubits of Ri

[0081]

[0082] <

[0083] The quantum state can be written: \i ) =

[0084]

[0085] 0 | / ?2) ■■■ 0 l^n)

[0086] The output superposition state of Ri after the state preparation step can be written:

[0087]

[0088] Where

[0089]

[0090] represents the register state |00. .1. .00), in which all register qubits are in the 10) state except the jthqubit being in the 11) state.

[0091] Thus, the output state for n registers can be written:

[0092]

[0093] Wherein the index rk(where k=l,2,.. ,,n) denotes the position of the single ‘ 1’ qubit within the kthregister (i.e. mapping which the task is at the kthposition). Each tuple (?i, r2, ...,rn) specifies a configuration (i.e. a given task sequence) in which each register has exactly one qubit set to ‘ 1’, and the specific qubit that is ‘ 1’ in register k is the rk-th qubit.

[0094] In some embodiments, the state preparation step may include applying an Hadamard gate on an ancilla qubit. In some embodiments, applying of the Hadamard gate on the ancilla qubit may be performed at a further step.Therefore, the state becomes:

[0095] > > > >

[0096]

[0097] In some embodiments (not shown on FIG. 2), the method may include at this stage a step of attenuating unallowed task sequences by introducing penalty phase shifts. For example, the method may include applying phase gates controlled by each pairs of qubits of different registers corresponding to the same task when said qubits are in the |1) state. This may allow to penalize task sequences including the same task at two different positions in the task sequence (i.e. no transition to a different task). For example, the penalty phase shifts 0pmay be provided according to 0p

[0098]

[0099] . More

[0100]

[0101] details about the penalties are provided hereinbelow with reference to FIG. 4.

[0102] In a further step S300, the method may include a data embedding step of encoding the technical costs of transitions between the tasks as phase shifts into an ancilla qubit. The encoding step may include applying CCP gates controlled by each pairs of qubits from adjacent (i.e. consecutive) registers corresponding to different tasks into the ancilla qubit as target qubit. The phase shifts may be a function of the technical costs of the transitions between the tasks corresponding to said qubit pairs. The CCP gates may be controlled so as to apply a phase shift to the 11) state of the ancilla qubit when both controlling qubits of said qubit pair are in the 11) state. Therefore, the phases for each transition in the technical process (i.e. each edge in the path) are accumulated in the ancilla qubit. More details on the data embedding step are provided herein below with reference to FIG. 3.

[0103] For a pair of adjacent registers m and m+1, if the rm-th qubit of the m-th register and the rm+1-th qubit of the (m+l)-th register are both in the ‘1’ state, a phase shift ^rm,rm+1is imparted to the ancilla qubit. These phase shifts 0rm,rm+1candiffer for different pairs of indices (rm, rm+1) allowing the encoding of transition technical costs into the quantum state. In other words, 0rm,rm+1isaparameter that determines how much phase is added to the ancilla when a particular qubit (identified by rm) in one register and another particular qubit (identified by rm+1) in the neighboring register are both set to ‘1’ i.e. when transitioning from the rm-th task to the rm+1-th task. In some embodiments, the phase shifts applied to encode the technical costs are proportional tothe technical costs such that a task sequence with a lower total cost carries a lower total phase.

[0104] In some embodiments, the phase shifts may be scaled and / or set inversely proportional to the technical cost. For example, the phase shifts may be set as follows:

[0105]

[0106] where n is the number of technical tasks, Drm rm+iis the technical cost for transitioning between task rmand task rm+1and D = max Drm rm+iis the largest of technical costsrm>rm+l

[0107] for transitioning between any of the tasks.

[0108] The total phase 0(7i, ... , rn) associated with a given configuration / task sequence (r1;...,rn) is the sum of the individual phase contributions 0rm,rm+1over all pairs of adjacent registers m and m+1. It can be written formally:

[0109]

[0110] The state after the data encoding state may be written:

[0111]

[0112] In a further step S400, the method 100 may include a step of transferring the phase shifts into amplitudes so as to increase a probability of measuring states corresponding to improved process technical costs (i.e. low or high depending on the optimization type). For example, step S400 may include applying a unitary operation such as an Hadamard gate on the ancilla qubit.

[0113] In the embodiment in which a Hadamard gate is used to transfer of the phase shifts into amplitude, the final state can be written as follows:

[0114] <> "

[0115]

[0116] In the final state formula, when the technical costs are encoded as phase shifts inversely proportional to the technical cost, the amplitude of the left term: [(1 +eL0(ri r"-))|eri... ern0) is amplified while the amplitude of the right term (1 —

[0117]

[0118] " attenuated.

[0119] In a further step S500, the final state is measured.

[0120] In a further step S600, the steps S100 to S500 are iterated over a plurality of trials to identify a most frequently measured state thereby providing said target task sequence corresponding to tasks associated with the qubits in said most frequently measured state. In some embodiments, the method may further comprise identifying a plurality of most frequently measured states over the plurality of trials and selecting one of the most frequently measured states as the target task sequence. In some embodiments, selecting one of the most frequently measured states comprises discarding task sequences that do not satisfy predefined constraints. For example, this may enable discarding task sequences which are not allowable.

[0121] In a further step (not shown), the method may include providing instructions to perform the technical process in the identified target task sequence. The instructions may be provided to the same or a different computer controlling the technical process. Alternatively, the instructions may be displayed to an operator. In some embodiments, the method may further include performing the technical process.

[0122] FIG. 3 illustrates a quantum circuit useful for implementing a method for improving a technical process according to embodiments of the present disclosure such as method 100 described hereinabove. The quantum circuit may include a plurality of N registers (Ri) 10 each including a plurality of N qubits (qij), a plurality of state preparation circuits 20 for preparing a W state in each of the registers 10, a Hadamard gate 25 for preparing the ancilla qubit in a |+> state, a plurality of CCP gates 30 applied to an ancilla qubit 15 and controlled by pairs of qubits belonging to adjacent registers. The quantum circuit may further include a unitary gate 40 applied to the ancilla qubit and measurement gates for measuring the qubits. As illustrated and explained with reference to the description of the method 100, the CCP gates 30 may be controlled by qubits corresponding to different tasks and belonging to adjacent registers.

[0123] FIG. 4 illustrates an optional step S250 of applying penalties to unallowed task sequences in embodiments of the method of the present disclosure. For the sake of conciseness and to avoid redundancy, elements in FIG. 4 that are identical to orcorrespond to elements already described in FIG. 3 are referred to by the same reference numerals. Detailed descriptions of these elements are not repeated, and reference is made to the relevant description provided for FIG. 3. Step S250 may be performed after or before the state preparation step S200. Step S250 may be performed after or before the encoding step S300. Step S250 may include applying CCP gates 30’ into the ancilla qubit 15, said CCP gates 30’ being controlled by pairs of qubits of different registers 10 corresponding to the same task when said qubits are in the |1) state. In other words, the CCP gates 30’ are configured to be controlled by qubits having the same position in different registers and to shift the phase of the ancilla qubit 15.

[0124] This may allow penalizing states representing task sequences in which the same task is performed at two different positions in the task sequence. The penalty phase shifts may be configured to attenuate the amplitudes of quantum states representing unallowed task sequences after the phase to amplitude transfer. In some embodiments, wherein the penalty phase shifts 0pis constant and provided according to 0P= where n is the

[0125]

[0126] number of technical tasks.

[0127] If the penalty phase contribution in a task sequence is defined as

[0128]

[0129] <<<

[0130] Where 6rm rqis 1 if rm= rqand 0 otherwise. This sum accounts for all register pairs that have the same 1 qubit index.

[0131] The state after the penalty step can be written:

[0132]

[0133] And the final state after the encoding becomes

[0134] <

[0135]

[0136] "

[0137] With the total phase contribution 0Tbeing the sum of the penalty phase and the previously defined sum of phase shifts:->0 = ©(r-L, ...,rn) + Qpf , ...,rn~)

[0138] It is noted that when attempting to find a task sequence that maximizes the technical cost, if the phase shift applied to the ancilla qubit is inversely proportional to the technical cost associated with a transition between tasks, amplitudes of states corresponding to higher technical costs in the final quantum state are amplified. This arises because the phase-to-amplitude conversion step translates the encoded phase information into amplitude probabilities. For inversely proportional encoding: smaller phase shifts (associated with higher technical costs) result in higher amplitudes for those states in the final quantum state. Larger phase shifts (associated with lower technical costs) result in decreasing the amplitudes of less optimal states. In the final quantum state equation, the left term (corresponding to higher amplitudes) represents task sequences with higher technical costs, thereby prioritizing these sequences during the measurement phase.

[0139] FIG. 5 illustrates a quantum circuit useful in a state preparation step of the method according to embodiments of the present disclosure. As explained previously, the state preparation step may prepare a space containing all task sequences. The state preparation step may include generating a W state in each of the N quantum registers. The W state is an equally distributed superposition of quantum states of the register, each having a single qubit in a 11) state, and all other qubits in a |0) state.

[0140] Preparing the W state (the “W block”) may include applying an X gate 29 to the first qubit qi,i flipping it into the |1) state. A controlled unitary gate cU 27 may be applied between each pair of adjacent qubits in the quantum register, wherein each qubit acts as a control for the application of the gate on the subsequent qubit. In other words, the controlled unitary (CU) gate 27 may be applied to the ithqubit, where the operation is controlled by the (i l )thqubit in the register. In order to achieve a uniform 1 superposition of W states in each register, the phases may be set to: 6 = , where c is the index of the control qubit in the register and n is the number of qubits in each register. The controlled unitary gate 27 may be a general phase gate that has three phases: cU^O,^,^. For instance, (p, A , may be set to 0 and the cU gate 27 may be a cRy gate. For instance a first cU gate 27 with a phase of % controlled by the first qubit qi,i may be applied on the second qubit qi,2, a second cU gate 27 with a phase of 1 / 3 controlled by the second qubit qi,2 may be applied on the third qubit qi,3 and a third cUgate 27 with a phase of Yi controlled by the third qubit q 1,3 may be applied on the fourth qubit qi,4.

[0141] CNOT gates 26 may thereafter be applied to the (i-l)thqubit, where the operation is controlled by the ithqubit in the register. In other words, a first CNOT gate 26 may be applied on the first qubit qi,i and controlled by the second qubit qi,2. Similarly, a second CNOT gate 26 may be applied between the second and third qubits qi,2, qi,3.. A third CNOT gate 26 may thereafter be applied between the third and fourth qubits qi,3, qi,4. This allows preparing the W state in the quantum register.

[0142] In general, the W state for a register of n qubits can be written

[0143]

[0144] Where

[0145]

[0146] represents the register state |00. .1. .00), in which all register qubits are in the 10) state except the jthqubit being in the 11) state.

[0147] FIG. 6 and the following discussion are intended to provide a brief, general description of an exemplary computing environment in which the disclosed technology may be implemented. Although not required, the disclosed technology is described in the general context of computer executable instructions, such as program modules, being executed by a personal computer (PC). Generally, program modules include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Moreover, the disclosed technology may be implemented with other computer system configurations, including handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. The disclosed technology may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0148] With reference to FIG. 6, an exemplary system for implementing the disclosed technology includes a general purpose (classical) computing device in the form of an exemplary conventional PC 1100, including one or more processing units 1110, a system memory 1120, and a system bus 1130 that couples various system componentsincluding the system memory 1120 to the one or more processing units 1110. The system bus 1130 may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and / or a local bus using any of a variety of bus architectures. The exemplary system memory 1120 includes read only memory (ROM) 1122 and random access memory (RAM) 1127. A basic input / output system (BIOS) 1125, containing the basic routines that help with the transfer of information between elements within the PC 1100, is stored in ROM 1122. As shown in FIG. 6, the system memory 1120 stores computer-executable instructions for performing any of the disclosed techniques (e.g., sending instructions to quantum computer for initializing the set of registers, preparing a W state, applying phase gates, applying unitary operation on the ancilla qubit, measuring, etc.) in respective memory portions (shown generally as executable software 1129 for performing any embodiment of the disclosed techniques)).

[0149] The exemplary PC 1100 further includes one or more storage devices 1140, such as a hard disk drive for reading from and writing to a hard disk, a magnetic disk drive for reading from or writing to a removable magnetic disk, and / or an optical disk drive for reading from or writing to a removable optical disk (such as a CD-ROM or other optical media). Such storage devices can be connected to the system bus 1130 by a hard disk drive interface, a magnetic disk drive interface, and / or an optical drive interface, respectively. The drives and their associated computer readable media provide nonvolatile storage of computer-readable instructions, data structures, program modules, and other data for the PC 1100. Other types of computer-readable media which can store data that is accessible by a PC, such as magnetic cassettes, flash memory, digital video disks, CDs, DVDs, RAMs, NVRAMs, ROMs, and the like, may also be used in the exemplary operating environment. As used herein, the terms storage, memory, and computer-readable media do not include or encompass propagating carrier waves or signals per se.

[0150] A number of program modules may be stored in the storage devices 1140, including an operating system, one or more application programs, other program modules, and program data. Storage of results of quantum measurements and instructions for obtaining such measurements (and / or instructions for performing any embodiment of the disclosed technology) can be stored in the storage devices 1140. A user may enter commands and information into the PC 1100 through one or more inputdevices 1150 such as a keyboard and a pointing device such as a mouse. Other input devices may include a digital camera, microphone, joystick, game pad, satellite dish, scanner, or the like. These and other input devices are often connected to the one or more processing units 1110 through a serial port interface that is coupled to the system bus 1130, but may be connected by other interfaces such as a parallel port, game port, or universal serial bus (USB). A monitor 1180 or other type of display device is also connected to the system bus 1130 via an interface, such as a video adapter. Other peripheral output devices 1160, such as speakers and printers (not shown), may be included. In some cases, a user interface is displayed so that a user can input a circuit for synthesis, and verify successful synthesis.

[0151] The PC 1100 may operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1190. In some examples, one or more network or communication connections 1170 are included. The remote computer 1190 may be another PC, a server, a router, a network PC, or a peer device or other common network node, and typically includes many or all of the elements described above relative to the PC 1100, although only a memory storage device 1195 has been illustrated in FIG. 6. The personal computer 1100 and / or the remote computer 1190 can be connected to a logical a local area network (LAN) and a wide area network (WAN). Such networking environments are commonplace in offices, enterprise wide computer networks, intranets, and the Internet.

[0152] When used in a LAN networking environment, the PC 1100 is connected to the LAN through a network interface. When used in a WAN networking environment, the PC 1100 typically includes a modem or other means for establishing communications over the WAN, such as the Internet. In a networked environment, program modules depicted relative to the personal computer 1100, or portions thereof, may be stored in the remote memory storage device or other locations on the LAN or WAN. The network connections shown are exemplary, and other means of establishing a communications link between the computers may be used.

[0153] With reference to FIG. 7, an exemplary system for implementing the disclosed technology includes computing environment 1200, The environment includes one or more quantum processing unit(s) 12210 including one or more monitoring / measuring device(s). The quantum processing unit(s) execute quantum circuits that are providedby a classical processing unit 1220. The quantum circuits are downloaded into or used to program or configure the quantum processing unit(s) 1210 (e.g., via control lines (quantum bus) 1270). Procedures according to any of the disclosed embodiments (e.g. a high-level description of the set of gate sequences to be applied to perform the presently disclosed technology) are stored in a memory 1230.

[0154] With reference to FIG. 7, the high-level description of a quantum software may be translated into sets of gates (e.g., a sequence of quantum circuits). Such high-level descriptions may be stored, as the case may be, on one or more external computers 1260 outside the computing environment 1200 utilizing one or more memory and / or storage device(s) 1265, then downloaded as necessary into the computing environment 1200 via one or more communication connection(s) 1240. Quantum circuits (according to any of the disclosed embodiments) are coupled to the quantum processor 1310.

[0155] The quantum processing unit(s) can be one or more of, but are not limited to: (a) a superconducting quantum computer; (b) an ion trap quantum computer; or (c) a topological quantum computer using e.g. Majorana zero modes. The sets of gates (e.g., using any of the disclosed embodiments) can be sent into (or otherwise applied to) the quantum processing unit(s) via control lines 1270 at a controller 1250 of the classical processor 1220. In the illustrated example, the desired quantum computing process is implemented with the aid of one or more controllers 1250 that are specially adapted to control a corresponding one of the quantum processor(s) 1210. The classical processor 1220 can further interact with measuring / monitoring devices (e.g., readout devices) 1280 to help control and implement the desired quantum computing process (e.g., by reading or measuring out data results from the quantum processing units once available, etc.)

[0156] Having described and illustrated the principles of the disclosed technology with reference to the illustrated embodiments, it will be recognized that the illustrated embodiments can be modified in arrangement and detail without departing from such principles. For example, the method described herein does not require the quantum registers to directly correspond to the sequential order of the tasks in the technical process. Instead, the quantum registers may represent the tasks using a mapping function that establishes a correspondence between the tasks and the qubits in the registers. Also, the described quantum algorithm may not be limited to providing amethod for solving the Traveling Salesman Problem (TSP) but also extends to a variety of related optimization problems. These include tasks where the goal may be to minimize or maximize measurable costs associated with transitions between nodes, tasks, or segments. Such problems may involve additional constraints, such as multiple vehicles, dependencies between tasks, or maximizing alignment scores, making them broader yet structurally similar to the TSP. Also, elements of the illustrated embodiments shown in software may be implemented in hardware and vice-versa. Also, the technologies from any example can be combined with the technologies described in any one or more of the other examples. It will be appreciated that procedures and functions such as those described with reference to the illustrated examples can be implemented in a single hardware or software module, or separate modules can be provided. The particular arrangements above are provided for convenient illustration, and other arrangements can be used.

Claims

CLAIMS:

1. A computer-implemented method for improving a technical process comprising a plurality of N tasks to be sequentially performed in a task sequence and wherein transitioning between each two tasks is associated with a corresponding technical cost, by finding a target task sequence improving a process technical cost associated with transitioning between said tasks, using a quantum computer, the method comprising:(a) initializing a set of N quantum registers, wherein each quantum register corresponds to a task position in the task sequence and comprises a plurality of N qubits and each qubit corresponds to a respective task in the technical process;(b) preparing a W state in each quantum register, wherein the W state is an equally distributed superposition of quantum states of the register, each having a single qubit in a |1) state, and all other qubits in a |0) state; (c) applying phase gates controlled by each pairs of qubits of adjacent registers corresponding to different tasks, so as to encode the technical costs of transitions between said tasks as phase shifts into an ancilla qubit, said phase shifts being a function of the technical costs of said transitions;(d) applying a unitary operation on the ancilla qubit to transfer said phase shifts into amplitudes so as to increase a probability of measuring states corresponding to improved process technical costs;(e) measuring the state of the quantum registers;(f) repeating steps (a)-(e) over a plurality of trials to identify a most frequently measured state thereby providing said target task sequence corresponding to tasks associated with the qubits in said most frequently measured state.

2. The method of claim 1, further comprising identifying a plurality of most frequently measured states over the plurality of trials and selecting one of the most frequently measured states as the target task sequence.

3. The method of claim 2, wherein selecting one of the most frequently measured states comprises discarding task sequences that do not satisfy predefined constraints.

4. The method of any one of claims 1 to 3, wherein the technical process comprises a manufacturing process with a plurality of manufacturing stations and the technical cost comprises an energy expenditure associated with transitioning between the stations.

5. The method of any one of claims 1 to 3, wherein the technical process comprises a data transfer process with a plurality of nodes in a network and the technical cost comprises bandwidth consumption associated with routing the data between two nodes.

6. The method of any one of claims 1 to 3, wherein the technical process comprises genome sequencing operation with a plurality of DNA segments and the technical cost comprises a likelihood of overlap between two DNA segments.

7. The method of any one of claims 1 to 3, wherein the technical process comprises travelling through a plurality of cities and the technical cost comprises a time, distance and / or fuel consumption associated with transitioning between said cities.

8. The method of any one of the preceding claims, further comprising providing instructions to perform the technical process in the identified target task sequence.

9. The method of any one of the preceding claims, wherein applying the unitary operation on the ancilla qubit comprises applying a Hadamard gate on the ancilla qubit.

10. The method of any one of claims 1 to 9, wherein the phase shifts applied to encode the technical costs are inversely proportional to the technical costs.

11. The method of claim 10, wherein phase shifts Grm,rm+ienc°ding the technical costs for transitioning between two technical tasks rmand rm+1are provided according to:>where n is the number of technical tasks, Drm m+1is the technical cost for transitioning between task rmand task rm+1and D = max Drm m+1is the largest of technical costsrm>rm+lfor transitioning between any of the tasks.

12. The method according to any one of claim 1 to 11, wherein applying phase gates further comprises applying phase gates controlled by each pairs of qubits of different registers corresponding to the same task when said qubits are in the 11) state.

13. The method of claim 12, wherein the penalty phase shifts are configured to attenuate the amplitudes of quantum states representing unallowed task sequences.

14. The method of any one of claims 1 to 13, wherein the penalty phase shifts 0pare provided according to 0p= , where n is the number of technical tasks.

15. The method of claim 9, wherein the output quantum state after applying the unitary operation on the ancilla qubit is given by:<<"where \erk) is a register state in which all register qubits are in the |0) state except the rk-th qubit in the 11) state, 0(rx, ... , rn) is the total phase accumulated for a given task sequence (r1;...,rn).

16. The method of any one of the preceding claims, further comprising:(a) using a classical greedy algorithm to identify an initial task sequence;(b) pruning from said initial task sequence one or more task transitions associated with technical costs that do not meet a predefined criteria thereby obtaining a sub-process including a sub-plurality of tasks;(c) feeding said sub-process as input to the quantum algorithm to refine the initial task sequence.

17. A quantum computing system for optimizing a technical process comprising a plurality of N tasks to be sequentially performed in a task sequence, wherein transitioning between each two tasks is associated with a corresponding technical cost, the system comprising:(a) a plurality of N quantum registers, each quantum register comprising a plurality of qubits, wherein each quantum register corresponds to a task position in the task sequence; and each qubit in the quantum register corresponds to a respective task in the technical process;(b) a superposition generator configured to generate a W state in each quantum register, wherein the W state is an equally distributed superposition of quantum states of the register, each having a single qubit in a 11) state and all other qubits in a |0) state.(c) a phase encoder configured to:i) apply phase gates controlled by each pairs of qubits of adjacent registers corresponding to different tasks, so as to encode the technical costs of transitions between said tasks as phase shifts into an ancilla qubit, said phase shifts being a function of the technical costs of said transitions;(d) a phase to amplitude converter configured to apply a unitary operation on the ancilla qubit to transfer said phase shifts into amplitudes so as to increase a probability of measuring states corresponding to improved process technical costs;(e) a measurement unit configured to measure the states of the quantum registers;(f) a processor configured to:i) repeat the operation of the superposition generator, the phase encoder, the phase to amplitude converter and the measurement module over a plurality of trials; andii) identify a most frequently measured quantum state as a target task sequence corresponding to tasks associated with the sequence of qubits in the most frequently measured quantum state.

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