US-12626174-B2 - Method of driving a quantum computer to find one or more states of interest of a network

US12626174B2US 12626174 B2US12626174 B2US 12626174B2US-12626174-B2

Abstract

There is presented a method of driving a quantum computer to find one or more states of interest of a network. In one example, the network comprising a plurality of players. The method determines a set of adjacent graphs by determining, for each graph, whether each of the other graphs are adjacent. The method defines a cost function associated with a Hamiltonian operator of the quantum computer; the cost function comprising a set of parameters determined by analysing the utilities of vertices in the set of adjacent graphs. The method further comprises outputting a plurality of control signals for driving the quantum computer wherein the control signals are associated with the set of parameters and comprise: one or more control signals for controlling the states of qubits in the quantum computer; and, one or more control signals for controlling the entanglement of qubits in the quantum computer.

Inventors

Samuel Douglas Palmer
Pablo Martin
Samuel Mugel
Roman Oscar Orús

Assignees

MULTIVERSE COMPUTING SL

Dates

Publication Date: 20260512
Application Date: 20211227
Priority Date: 20211221

Claims (19)

1 . A method of driving a quantum computer to find one or more states of interest of a network, the quantum computer comprising a quantum system; the network comprising a plurality of players wherein: a set of different configurations for the network are represented by a set of a plurality of graphs; each player is associated with a different vertex in a set of vertices for the plurality of graphs; each of the one or more states of interest respectively corresponds to one of the graphs; each graph comprises: i. the plurality of players; and ii. a set of connections representing edges between the vertices, wherein: each connection connects two vertices; iii. a different set of connections to any of the other graphs in the set of graphs; for each graph, a corresponding set of utilities defines a net payoff between the players having a connection in the respective graph; the method comprising using a processor to: I) determine a set of adjacent graphs by determining, for each graph, whether each of the other graphs are adjacent by: defining another graph to be adjacent if the connections between the two graphs differ by one; II) define a cost function associated with a Hamiltonian operator of the quantum computer; the cost function comprising a set of parameters determined by analysing the utilities of the vertices in the set of adjacent graphs wherein: A. a transition between adjacent graphs is determined as viable or non-viable wherein a viable transition occurs if: iv. a connection is added between the vertices and: 1. the utility of at least one of the said vertices is increased; and 2. the utility of the other of the said vertices is increased or remains the same; or v. a connection is removed between the vertices and: 1. the utility of one of the said vertices is increased; B viable transitions between adjacent graphs increase the energy of the quantum system; C. non-viable transitions between adjacent graphs lower the energy of the quantum system, the method further comprising: III) outputting a plurality of control signals for driving the quantum computer; the control signals associated with the set of parameters and comprising: one or more control signals for controlling the states of qubits in the quantum computer; and, one or more control signals for controlling the entanglement of qubits in the quantum computer; the method further comprising running the quantum computer using the control signals.
2 . The method of claim 1 wherein the step of determining a set of adjacent graphs comprises deterministically constructing adjacent graphs using the definition of adjacency in claim 1 , and as such appropriately adding or removing an edge from a graph.
3 . The method of claim 2 wherein the determining of adjacent graphs is used to determine player information; the player information comprising: i) a set of numerical values for each player, each numerical value associated with one of a plurality of player states, each player state being associated with a graph, f(G, P), where G is the graph and P is the player; ii) an adjacency between player states based on a graph adjacency.
4 . The method of claim 3 wherein the player information is stored in a binary matrix.
5 . The method of claim 4 wherein the cost function comprises a quadratic unconstrained binary optimisation cost function, QUBO.
6 . A method as claimed in claim 5 , wherein the QUBO is a first QUBO, the method further comprising determining cycles of states in a supernetwork by forming a second QUBO from summing terms in the first QUBO associated with increasing the quantum system energy according to a cycle topology.
7 . The method as claimed in claim 5 wherein at least one of the parameters comprising a cost of making a transition between two adjacent graphs; wherein determining the cost of making a transition comprises: determining, for each of the players, the player state; determining, for each of the players between the two graphs, the change in utility; determining whether each change in utility is positive or negative.
8 . The method as claimed in claim 7 wherein determining whether each change in utility is positive or negative comprises: reading an entry from the binary matrix with respect to the player state; and determining, from the read entry, that the transition between the two adjacent graphs is viable or non-viable.
9 . The method as claimed in claim 8 wherein reading the entry comprises matrix multiplying the binary matrix with canonical basis vectors.
10 . The method as claimed in claim 8 further comprising, for the two players associated with a viable transition: determining a player state column index and player state row index of the binary matrix for the respective read entry associated with that player.
11 . The method as claimed in claim 10 , wherein the canonical basis vectors are: a) predetermined; or, b) determined by mapping a player state to a canonical basis vector.
12 . The method as claimed in claim 1 wherein the set of parameters comprises a set of terms that increase the energy of the quantum system for any one or more of the following: a transition associated with edge removal is beneficial for either player but the edge transition is determined as a non-viable transition; a transition associated with edge removal is not beneficial for either player but the edge transition is determined as a viable transition; a transition associated with edge addition is beneficial for both players but the edge transition is determined as a non-viable transition; a transition associated with edge addition is beneficial for either player but the edge transition is determined as a viable transition; a transition associated with edge addition is not beneficial for either player but the edge transition is determined as a viable transition.
13 . The method as claimed in claim 1 wherein the set of parameters comprises: a. a first set of terms which represent counts of the number of viable transitions from each graph to any other adjacent graph; wherein each of the terms in the set increases the energy of the quantum system when any of: a transition is determined as a viable edge addition, but the edge is being removed; a transition is determined as a viable edge removal, but the edge is being added; b. a second set of terms which increase the energy of the quantum system for graph states with a number of viable transitions that is different from the predetermined number of viable transitions of the graph states of interest.
14 . A method as claimed in claim 1 further comprising: populating a QUBO matrix with data associated with the set of parameters; deriving the control signals from the QUBO matrix.
15 . A method as claimed in claim 1 wherein the quantum computer comprises a quantum annealer.
16 . An apparatus comprising a computer system comprising the processor for running the method as described in claim 1 .
17 . The apparatus as claimed in claim 16 further comprising the quantum computer.
18 . The apparatus as claimed in claim 17 wherein the quantum computer comprises a quantum annealer.
19 . A computer readable medium comprising program code that, when run, gives effect to the method of claim 1 .

Description

FIELD OF THE INVENTION The present invention is in the field of quantum computing, in particular, but not limited to, using a quantum annealer for finding a solution to a network problem. BACKGROUND The study of networks is a key area of study in many fields, and it is largely inspired by empirical findings of real-world networks such as social networks, biological networks, technological networks, financial networks, brain networks, climate networks and computer networks, among others. The formation and evolution of networks has been studied from a theoretical perspective throughout the literature. In particular, Jackson and Watts (“The evolution of Social and Economic Networks” Journal of Economic Theory, vol. 106, issue 2, October 2002) provided theoretical results in this field. Previously, stable configurations of a network have been attempted by using a Markov Chain Monte Carlo process. However, analysing the formation and evolution of these networks in practise is a very complex task, because the number of possible configurations in the network grows exponentially with the number of nodes and types of links. As a result, the computational resources that are needed to model the system also grow exponentially with the size of the network. For this reason, modelling the behaviour and assessing the robustness and stability of a network is an intractable task for classical computers for more than a few players. SUMMARY There is presented a method of driving a quantum computer to find one or more states of interest of a network, the quantum computer comprising a quantum system; the network comprising a plurality of players wherein: a set of different configurations for the network are represented by a set of graphs; each player is associated with a different vertex in a set of vertices; each of the one or more states of interest respectively corresponds to one of the graphs; each graph comprises: the plurality of players; and, a set of connections representing edges between the vertices, wherein: each connection connects two vertices; a different set of connections to any of the other graphs in the set of graphs; for each graph, a corresponding set of utilities defines a net payoff between the players having a connection in the respective graph. The method comprising using a processor to: I) determine a set of adjacent graphs by determining, for each graph, whether each of the other graphs are adjacent by: defining another graph to be adjacent if the connections between the two graphs differs by one; II) define a cost function associated with a Hamiltonian operator of the quantum computer; the cost function comprising a set of parameters determined by analysing the utilities of the vertices in the set of adjacent graphs wherein: a transition between adjacent graphs is determined as viable or non-viable wherein a viable transition occurs if: a connection is added between the vertices and: the utility of at least one of the said vertices is increased; and, the utility of the other of the said vertices is increased or remains the same; or, a connection is removed between the vertices and: the utility of one of the said vertices is increased; viable transitions between adjacent graphs increase the energy of the quantum system; non-viable transitions between adjacent graphs lower the energy of the quantum system. The method further comprising: outputting a plurality of control signals for driving the quantum computer; the control signals associated with the set of parameters and comprising: one or more control signals for controlling the states of qubits in the quantum computer; and, one or more control signals for controlling the entanglement of qubits in the quantum computer. The method may be adapted according to any step or feature described herein, including, but not limited to, any one or more of the following options listed in the summary. In some circumstances, when the quantum computer is run using the control signals, a state of interest is not found. A network may be any collection of two or more nodes that form a graph. In examples presented herein each node may represent a different player. A collection of different graphs with similar or the same internal nodes may form a supernetwork. The network may comprise a set of vertices and directed or undirected edges. These edges may be weighted or unweighted. The method may be configured such that the step of determining a set of adjacent graphs comprises deterministically constructing adjacent graphs using the definition of adjacency in claim 1, and as such appropriately adding or removing an edge from a graph. The method may be configured such that the determining of adjacent graphs is used to determine player information; the player information comprising: a set of numerical values for each player, each numerical value associated with one of a plurality of player states, each player state being a associated with a graph, f(g, p); an adjacency between