Abstract
In order to function reliably, a classical computer suppresses quantum uncertainty while a quantum computer harnesses uncertainty to provide additional computational resource. Both classical and quantum computers operate in a background dependent deterministic framework and process information in a step-by-step fashion. A quantum gravity computer, on the other hand, has indefinite causal structure caused by the interplay between general relativity and quantum mechanics and cannot be modeled as a step-by-step process. It does not ‘compute’ in the traditional sense but still processes information according to rules. Such a computer has greater power than a step computer and should have application to simulating systems where both quantum mechanics and general relativity re important, such as the early stages of our Universe. It may also serve as the model for the operation of the human brain, giving rise to such faculties as understanding, free will, and creativity.
Claims
1. A device which operates upon physicalized information using both the principles of quantum mechanics and general relativity.
2. The device as claimed in claim 1, device that operates upon information without recourse to step-wise computation.
3. The device as claimed in claim 1, device that operates upon information that cannot be simulated by a step-by-step computer or algorithm and, is not subject to the limitations of the halting problem.
4. A device that operates upon information comprising: a matrix of processing elements without definite position in space-time, capable of superposition, entanglement and communication with other elements through a multiplicity of quantum paths; and. input means to quantum excite selected elements of said processing matrix; and output means capable of performing an action upon sufficient accumulation of space-time separation of the superposed processing elements.
5. The device as claimed in claim 4, further comprising a computer composed of functional elements which are capable of manipulating qubits and the displacing mass in operation so that the result of the action of the element on the qubit is sensitive to both quantum and gravitational factors.
6. The device as claimed in claim 4 further comprising a processing system that can implement a watch dog function which is not subject to modelling by combination of state with the function which is subject to the watchdog.
7. The device as claimed in claim 4, further comprising a combination of human neurons and computer chip technology so designed as to be able to solve non-computable problems.
8. A processing system comprising: a matrix of quantum elements capable of interacting with one or more superposed entangled electromagnetic data signals in response to the presence of one or more, optionally superposed entangled control signal, arranges such that they modulate the space-time metric based on status of the matrix elements, a means for varying one or more control signals and, a means for output of information based on the status of the matrix.
9. The system as claimed in 8 where the other signal is a light
10. The system as claimed in 8 where the modulation the space-time metric is accumulated over a number of successive runs of processing.
11. The system as claimed in 8 where the processing matrix is laid out in a linear, interdigitated fashion.
12. The system as claimed in 8 where the processing matrix is laid out in a three-dimensional convoluted fashion.
13. The system as claimed in 8 comprising means by which the process can be approximately simulated on a classical or quantum computer.
14. (canceled)
15. The system as claimed in claim 8, comprising a computer like device where computation is sensitive to both the laws of quantum mechanics and general relativity.
6. The system as claimed in claim 8, comprising a means for teaching biological or synthetic neurons to learn through differential stimulus to a response.
17. (canceled)
18. The device as claimed in claim 4, wherein the output means is by way of a quantum measurement process.
Description
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0063] FIG. 1 Proof that the Halting Function cannot exist (in a step computer)
[0064] FIG. 1a Mathematical Object with no concept of time, for illustration purposes
[0065] FIG. 1b No combination feature
[0066] FIG. 2 Spacetime, cause and effect diagram
[0067] FIG. 3 Quantum gravity gate
[0068] FIG. 3a quantum gravity no-op (QGNO) gate
[0069] FIG. 4 Metric distortion during processing
[0070] FIG. 5 Topology of a quantum gravity computer
[0071] FIG. 6 Measurement Gate
[0072] FIG. 7 Quantum Circuit equivalency
[0073] FIG. 8 Distributed Measurement
[0074] FIG. 9 Two input quantum gravity gate
[0075] FIG. 10 Conceptual layout
[0076] FIG. 11 No causal paradox
[0077] FIG. 12 Neural Network of a quantum gravity computer
[0078] FIG. 13 Configuration of the system
[0079] FIG. 14 Process of operation of a QGC
[0080] FIG. 15 Collapse mechanism of a QGC
[0081] FIG. 16 Error Correction in a QGC
[0082] FIG. 17 Plan Elevation of one implementation of a QGC
[0083] FIG. 18 Side Elevation of one implementation of a QGC
[0084] FIG. 19 Biological QGC
DETAILED DESCRIPTION
[0085] The logical building blocks of a quantum gravity computer will be described along with the differences between quantum and quantum gravitational computing such that a person skilled in the art could make the necessary modifications to any quantum computer to enable it to perform quantum gravity computation. Several embodiments of devices optimized for quantum gravity computation will be described including a proposed graphene-based room temperature optical quantum gravity computer.
[0086] The existence of a halting function was a fundamental question in mathematics at the turn of the 20th century and the proof that no such function could exist has defined the limits of computation since Alan Turing and Alonzo Church prove it in 1935-36. FIG. 1 illustrates a visual proof that the halting function cannot exist on a step computer. First assume that halt does exist and construct a procedure 101 that performs this function, label this ‘Halt’. No attempt to specify the procedure is required as its existence will be disproven. The halting procedure 101 takes another program as input 102 and predicts if that program will halt if run on an input 103. Halting means that the computer stops and indicates it has reached a conclusion True (T) or False (F).
[0087] To disprove the existence of Halt, proceed as follows. Construct a new algorithm K 108 that takes Halt's output as its input and does the following
1. if Halt outputs “loop”(L, 104) then K halts 107,
2. otherwise if Halt outputs “halt” (H, 105) K loops forever 106.
[0088] Since K is a program, let us use K 108 as the two inputs to K 109 which are input to Halt 102, 103.
[0089] If Halt says that K halts then K itself would loop forever. If Halt says that K loops then K will halt. In either case Halt gives the wrong answer for K. Thus, Halt cannot work in all cases. There is an input that causes any solution Halt to fail, Paradox!
[0090] The only resolution of the paradox is that the Halt function cannot exist. The proof holds for all general computational systems equivalent to a Turing machine which we have characterized as step computers. That is to say computers which have a progression of states and transition rules from state to state.
[0091] There have been a number of attempts to avoid the paradox and reinstate a halt function. One solution is to construct a computer programming language that does not permit infinite loops, either by ensuring there is no construct in the language that will permit an open-ended loop 106 or by constructing a compiler that bounds checks programs to ensure that there is no infinite loop case. These solutions fail. By Rice's theorem it is impossible to construct a computer system that guarantees any non-trivial property of another program—in this case bounds checking is non-trivial and a compiler is non-trivial. If a language cannot enter an infinite loop it is not Turing complete and will not compute certain functions. Thus, attempts to escape the Turing limit are either faulty or result in limited computing systems. On a practical note all computing systems that purport to avoid the halting problem must eventually run on firmware and ultimately a hardware machine and that machine cannot be guaranteed not to fall into an infinite loop.
[0092] In a quantum gravity computer, a different approach is taken to removing the looping problem. The essence of the loop problem is that there exists a deterministic step-by-step procedure that will return the system to the same state in the future. (This is how the infinite loop 106 works). A way to side-step this problem is by removing the idea of the step-by-step evolution of state. This might seem impossible but there are many mathematical objects for which there is no concept of step or time. By way of analogy, the equation y=2x is an object that performs a ‘computation’ but does not do so with any concept of step or time; y is simply equal to two times x. There is no moment in time where this is not so, and a later point when it is. Thus, time steps do not need to form an integral part of the derivation of one piece of information from another. This does not mean there are no rules that govern the relationships. A QGC is not chaos. It is a different approach to manipulating information. We should state that unlike our analogy above a QGC does perform calculations which evolve over time however, they are not rigidly and deterministically step-by-step procedures.
[0093] In a system which cannot proceed step-by-step it becomes possible to introduce a watchdog to prevent looping. The simplest model is a two-entity model with a mutual watchdog. FIG. 1b illustrates two elements 110 and 111 which each process information and provide a watchdog function to the other 113. In normal step computers this model can be combined and modelled as a single process 112. To prove this is possible we can see it is simple to run a step from 110 and then a step from 111 on the third machine 112. The combined system cannot be guaranteed to halt and therefore the mutual watchdog function fails. However, a non-step computer cannot be combined and modelled by a third as it lacks definite state to permit interleaving.
[0094] This ability to process information without necessarily relying on step-by-step computation stems from features of our device. Firstly, there may be no matter of fact as to the state of the system at any time. The Kochen-Specker theorem shows that the state of a Boson (spin particle) has no matter of fact until measured. Secondly the causal structure cannot be statically modelled. Thus, in such a device it may be impossible to specify a state or determine that you have returned to that state at a later time because there is no meaning to ‘later time’ and no matter of fact to state. While these concepts might seem fanciful on a macroscopic level and in conflict with the causal structure of general relativity, all that is needed for a QGC to compute hitherto non-computable functions is a brief departure from macroscopic determinism. We will now describe how such a departure could be engineered.
[0095] FIG. 2 Illustrates schematically a block of spacetime in a general relativistic framework with two light cones centered on points in the grid, the first labelled 204. We should immediately say that blocks of spacetime do not exist in Relativistic Quantum Mechanics (RQM) but they are a useful notion to setup our understanding: The grid should be imagined as fuzzy and in flux. In FIG. 2 the dimensions x 201, y 202 and t 203 of space-time are illustrated while z must be imagined. A grid of processing elements is arranged in this space. The light cones from those elements indicate the degree to which different areas of spacetime are ‘time-like’ and ‘space-like’ separated and therefore the causal connection between computational elements. (Space-like and time-like regions of a light cone are illustrated at 401 of FIG. 4). The center of the cone 204 represents some arbitrary small region in space-time at which we have placed a processing element. The elements can communicate along light cones using encoded light pulses. Each processing element might be imagined as a small microprocessor of around the size of a grain of sand, able to receive and send encoded light pulses, through polarization, time bucket or other quantum optical encoding scheme. These microprocessors would also need the ability to maintain quantum coherence and entanglement of the photonic inputs and outputs they process. Such processors can be created in principle using, for example, Linear Optics Quantum Computation (LOQC) elements or indeed any arbitrary quantum optical device including the non-linear devices described in the introduction. We will describe methods to make such processing units later, and such units can be as simple as a single logic gate or as complex as a commercial microchip without loss of generality to the design.
[0096] Elements that are time-like separated 205, 206, 207 & 208 are causally connected to element 204 as they fall within the past or future light cone of 204. In the case of 205 & 206 this is a cause relationship and 207 and 208 is an effect relationship. Thus 205 & 206 may form inputs to the operation performed by 204 and the output of this operation may form an input to elements 207 and 208.
[0097] In a classical computer there may be regions that are space—like separated—not causally connected. At the dock speeds present in a modern-day computer it is possible for a signal to be still in flight along a wire at the time when the next calculation is to be performed. If a calculation is dependent on such a signal the computer must be organized to wait for that signal before calculation is undertaken. For this reason, modern computers distribute a dock signal and synchronization information that ensures computational elements ° wait' until they are within the light cone of a previous computation. In the language of this diagram sufficient time t 203 is allowed to pass before a computation is made so that all relevant inputs fall within the light cone of a processing element.
[0098] We will shortly see that the introduction of relativistic quantum mechanics confuses this picture and destroys the dean notion of space-time and cause and effect.
[0099] FIG. 3 Illustrates schematically the operation of a quantum gravity gate 310 implemented using optical elements. (It is possible to construct a universal quantum gate from linear optical elements). This gate is a simple quantum gravitational gate and conceptually similar to the Hadamard gate for purely quantum computation. A photon 301 enters the apparatus from the left and is split into two paths by a beam splitter 302, a straight path 303 and a reflected path 304. The photon is now in a superposition of states traversing path 303 and 304 simultaneously. The mirror 305 serves simply to redirect the photon to the gate 307. The gate at 307 could make any arbitrary quantum computation action but in this instant, we will assume it performs a quantum no operation (no-op) and outputs this on 310. The gate is gravitationally active: It will move a mass 308 to one of two optional positions depending on input to the gate. The mass moves to the upper location if the 303 photon arrives earlier than the 306 photon path-time bucket encoding. When the mass 308 moves it will distort spacetime by emitting gravitational waves 309 that will change the metric and therefore the length of the two paths 303 and 306. In this diagram the paths have been shown as of distinctly different lengths to illustrate the concept, but they can be redrawn so that the paths 303 and 306 are similar in length. Tiny variations in the metric of space time will affect whether a photon travelling along 303 appears before or after the expected arrival of 306. It might be thought this causes a paradox. If photon 303 arrives first the mass is moved to the downward location and shortens spacelike paths in the lower half of the diagram. However, this means that the 303 photon arrives after the 306 photon. In a general relativistic frame this is not the case because the modification to the metric spreads as a gravitational impulse wave 309 at the speed of light in all directions. However, quantum mechanical considerations introduce uncertainty and it is therefore impossible to say with certainty whether the inputs to the gate are not affected by the mass displacement. This might appear, at first site, as a ridiculous statement, an output having effects on the inputs. However, there is no restriction on this in principle. If time is uncertain we cannot be sure of the causal relationship. There might be a concern that such a causal relationship would introduce grandfather paradoxes and therefore render the gate ineffective or illegal in some way. However, quantum mechanics is probabilistic. According to David Deutsch although a grandfather paradox does occur in a digital system it does not occur in a probabilistic system. Changing the probability of you killing your grandfather does not render your existence impossible (and therefore paradoxical), only less likely. Therefore, this simplest of gates, a quantum gravity gate or a relativistic quantum gate is introduced as a building block for our QGC.
[0100] In FIG. 3a we generalize the model a little further by replacing the Michaelson beam splitter apparatus with a Hadamard gate 312. This gate modifies the base states of |0> and |1> to a superposition of |0> and |0> and |1> with equal probability. The QG no-op gate 310 of FIG. 3a, which had been imagined as a time-bin encoded photon timing operation in FIG. 3 can be implemented by any quantum gravity no-op (QGNO) gate. The only function of the QGNO gate is to move some mass based on the operation of the gate without making any appreciable modification to the quantum state. It is an open question whether no appreciable modification means no modification at all or a modification that is sufficiently small s to permit the quantum operation to continue with the application of quantum error correction. We must assume that some element of the mass movement causes information to leak from the quantum gate into the environment and this leads to some level of decoherence or broader entanglement. This puts a limit on the fidelity of the system in the absence of error correction. We further replace the ‘wires’ of FIG. 3 (301, 303, 306, 310) with a relationships (311, 313, 314) in FIG. 3a implying no time wise relationship and no one-to-one mapping. This is because the movement of mass can modify the spacetime metric thus modifying the causal relationship between logical elements. It is possible that the output of a gate could also function as an input to the same gate, either directly or via an intermediary gate.
[0101] FIG. 4 represents a gate depicted in the light cone diagram coordinates of FIG. 2. The diagram has been rotated relative to FIG. 3 so that time now flows in the vertical direction. (Changing coordinates is a common feature of discussions of this topic.) Again, the diagram shows only two dimensions of space 402, 403 and one of time 404, given the drawing is on a flat piece of paper one of the spatial directions is shown through the common perspective practices of space-time illustrations. In the embodiment described, processing is performed using light and therefore propagation of signals follows the extremes 405 of the light cones 401. Gates and their corresponding mass displacements are depicted as vertical structures 406 & 407, showing that they do not move in space and are present throughout time. It might be imagined that some signals have problems propagating ‘thru’ objects however one must remember there is an additional unillustrated dimension of space available to use. As each gate 406 operates it moves mass 407 into superposition 408, 409 and mass causes the metric to distort illustrated by the tilting of light cones. In general relativity, the metric tensor (abbreviated to the metric) captures all the geometric and causal structure of spacetime being used to define notions such as time, distance, volume, curvature, angle, and separating the future and the past. It is simply depicted as light cones in this diagram. It can now be seen that the performance of subsequent gates depends both on the signals that arrive and the metric. This is because changes in a gates state moves mass (strictly speaking also energy and momentum.) This change in the causal structure of space-time means that some signals may be brought into the past causal light cone of future events and therefore become causes, whilst if things go the other way they would cease to be causes. At a larger scale it can be imagined that the very order of gates is uncertain. Cause and effect and certainty of causal structure are not preserved in this construct. Despite this it is possible to manipulate information according to well defined rules.
[0102] In the figure we can see that once the gate has operated and switched the light cones 401 become uncertain. Light cone 410 is tilted towards mass 407 whilst light cone 411 is less affected as it is further from mass 410. After operation of the gate 406 at time 412 the masses are placed into superposition 408 and 409. This causes light cones to have uncertainty and appear ‘fuzzy’ 413, 414 & 415. The fuzzy light cone at 414 is separated so we can see its alternate 415. Tracing the causal line from gate 406 to gate 407 we can see a distinct difference in the arrival times of signals Lit 415 depending on the switching state of gate 406. If gate 407 operates based on time buckets the gate will operate based on the uncertainty.
[0103] FIG. 5 Illustrates the general arrangement of a quantum gravity computer using optical switches such as graphene dots or tryptophan molecules. The upward direction 503 represents time while x 501 and y 502 represent two spatial dimensions and the slices represent equal time slices. (Note this is a convenience and there is no such thing as an equal time slice in a quantum gravity computer due to uncertainty in the metric.) A z dimension is not illustrated and for this diagram is not necessary as we imagine that the processing system is similar to a two-dimensional silicon chip. At each slice the first two labelled 504, 505 in our illustration the quantum dot—gates 506 have an element in a superposition—507 labels the left element of the two possible states. These superposed elements each cause a different metric distortion. The future light cones 508 and 509 are therefore defined by whether element 507 is in the left or right position. Since this is uncertain the future light cones from this gate can affect different groupings of dots in future time periods in an uncertain basis, Cone 508 only affects the bottom left quantum dot on the chip substrate while cone 509 affects two dots. The metric distortions are exaggerated for illustration purposes, in a real chip the quantum dots would be far more densely packed and the metric distortions needed for different causal relationships would be small. The substrate system can be silicon wafer technology that will support graphene on silicon so that part, or all of the graphene can be suspended above the silicon wafer. The graphene can flex or move in response to excitation signals putting it into physical superposition. Each graphene dot is influenced by an electrical circuit allowing the strength of optical coupling to other elements to be adjusted.
[0104] FIG. 6 illustrates the QGC equivalent of the ‘measurement’ gate in a quantum computer for a QGC. In a regular quantum computer an element is provided which does not obey the normal mechanics of other gates in the system. It is an irreversible measurement mechanism 602 and application to the quantum state results in a collapse from the superposed 0|1 601 state to either |0> or |1> 603 with a given probability—usually 50:50. This is essentially an external process applied to the quantum computation. In the QGC this measurement process is replaced with a gravitational gate 606. AH gates within a QGC will act as gravitational gates because any change in state or superposition of states will affect the metric tensor. However, a QGG is a special gate that amplifies the quantum superposition to a level that will self-collapse in a human scale time frame, typically 100 ms to 7 seconds when taken with other gates. Thus, an input 604 will drive the gate 606 into a superposition 607, 608 gravitational waves will propagate and the gate will make some output 609. If sufficient mass is involved 605 having a critical mass according to E.sub.g then the single gate will self-collapse and make an irreversible output 609. In this case the gate is identical to the measurement gate of quantum mechanics save for the fact that it is no longer an ‘external’ effect but rather consistent with the operational model.
[0105] FIG. 7 Illustrates the QGC equivalent of a circuit in a standard quantum computer. In a QGC all elements in 701 can (and must be) replaced by a gravitationally active gates 702. In order to preserve the quantum computer operation, the computational gates are replaced with low mass action elements 703 operating on inputs I, 704 and giving outputs O, 705 and the measurement gates are high mass action elements 703 with a larger mass. This generalizes the QC to a QGC but at the expense of the ability to implement deterministic algorithms. Power is achieved by implementing new forms of ‘algorithm’ available to QGCs the most readily implementable being a deep learning QG neural network.
[0106] FIG. 8 Illustrates the distribution of measurement elements in a QGC so that the self-collapse is formed from more than one gate mass. The summing of metric distortions from individual gates 807 will reach the critical E.sub.g level in some time T. The measurement gate described in FIG. 6, 801, 802, 803 is affected by the accumulation of metric distortions from a set of QGGs 804, 805, 806. This location of space-time 807 now has sufficient distortion to modify the metric above the critical E.sub.g limit.
[0107] FIG. 9 Illustrates the QG equivalent of a general two input quantum computer gate. Inputs 901 and 902 are processed by 903 to form outputs 905 and 906. We may replace the general gate 903 with a general GQ gate 908 Provided that the system is subcritical WRT E.sub.g mass will be moved 904 and modifications to the metric will start to propagate 907.
[0108] FIG. 10 Illustrates the arrangement of a conceptual QGC as described by Lucien Hardy so as to allow the reader to understand how a point in space-time can be both in existence and uncertain at the same time. A computation element 1001 is located in space time. It receives signals from four GPS satellites 1002-1005. The computation element can calculate its position x, y, z, t with respect to the satellites (for which it might have a flight plan) and therefore knows its own location in space and time. However, from the point of view of the observer 1006 x, y, z and t might be uncertain or there might not even be a matter of fact as to what they are. For example, the computational element might be the subject of a calculation which puts t into two places at the same time—a ‘cat’ state. Thus, we could not run a computation to determine what happens next to this system because there is no matter of fact as to the starting state of the system. Never-the-less the system could follow rules. Plotting observations of the state along the t axis would show the system appears to evolve over time.
[0109] FIG. 11 Illustrates a state which may occur within a QGC. Elements form a causal rings where an element may be its own cause. Element 1101 affects element 1102 which in turn effects element 1103 which is an input to element 1101. In a classical system such a ring would be unremarkable as it is assumed that time flows during operation such that each gate affects the next at successive time intervals but in a QG system this cannot be guaranteed and gates may respond to outputs in arbitrary time order, gate outputs may be their own input. In a quantum system—as opposed to a classical system—this does not result in grandfather paradoxes as cause and effect relationships are probabilistic. The grandfather paradox occurs if an effect travels back in time and deletes its cause—killing one's grandfather, for example. If an effect travels back in time and affects the probability of a cause it is permitted. Another paradox commonly used to argue against time reordering of cause and effect is the Shakespeare paradox. A person memorizes the works Shakespeare, travels back in time and dictates the works to him: The works spring from nowhere! The Shakespeare paradox is a false paradox. It is perfectly permitted to travel back in time and create a cause of a subsequent effect: It simply offends common sense. Much of quantum theory offends common sense and this is not a reason for forbidding it. In the Orch-OR system a limit is placed on the mass that can be in superposition for a time t. Macro paradoxes such as the Shakespeare paradox and Schrodinger's Cat are forbidden (or rendered vanishingly unlikely) without affecting the micro paradox of superposition—how can something be in two places at the same time . . .
[0110] FIG. 12 Illustrates a neural network inspired construction of a QGC. In a neural network each computational element is linked to other elements according to a topology. There are commonly layers—including hidden layers and feed forward and backward paths. In such networks wiring defines the allowed paths along which signals may pass. In a preferred embodiment of a QGC one or more of these ‘layers’ is replaced by a maximally-connected network. Quantum signals which encounter this network may spread out and couple to any node via long 1203 or short 1202 paths. It can be modelled as a one to many (all) network, a portion of which is drawn in FIG. 12. As this network increases the number of ‘connections’ that would need to be drawn increases greater than exponentially so only a small number of elements are illustrated. The quantum information spreads over this network depending on many factors including the coupling sensitivity of the nodes, their separation and the excitation state of nodes in the network. A classical description of this can be found in reference Silva of which the following is a short excerpt.
[0111] Within a complex dynamic network, there are two topologies: a static structural topology that describes all the possible connections within the network and a dynamic functional topology that establishes how a signal propagates through the static topology. Functional topologies are subsets of the structural topology and vary depending on the functional connectivity, internal dynamics of individual vertices, and the specific stimulus to the network. In other words, cells that are physically connected need not necessarily signal each other. Having said this, though, in cellular neural circuits and networks, structure and function influence each other, and the states of cells and the connections between them may change with time as a function of plasticity mechanisms.
[0112] Because this is a dynamic emergent network there is no particular need to perform a specific function at each node. All that is needed is that there is some arbitrary function at each node that receives input photons and emits output photons according to some relationship between the input photons: coupling, frequency, phase, polarization, time arrival or similar quantum encoded state. In this quantum gravity implementation there is no matter of fact as to the state of the network, no fixed causal structure and any excited state of a node may be in superposition and entangled with the excitation state of another node. Learning and programming occur by making some change to the function of each node again modifying relationship between the input photons, coupling, frequency, phase, polarization, time arrival or similar quantum encoded state.
[0113] FIG. 13 illustrates the standard MNIST data set for testing Al 1301. Hand written characters are input to the QGC neural network by setting an input layers based on a pixel array 1302 to 1303. The QGC neural network will form a dynamic pattern based on the input letter 1304—trivially this might be a triangle between three elements but in general will be a complex stable dynamic pattern. This stable pattern can be recognized to provide the output of the system. A benefit of using a dynamic stable pattern is that long lived qubits are not needed. The system can be trained to collapse reaching the E.sub.g threshold once a recognition event has occurred.
[0114] FIG. 14 Describes the process by which a quantum gravity computer generates an output. It should be noted that numbering, time or step sequence might not have significance as this is not a step computer and so these operations could occur simultaneously or in any order. Statistically an output emerges and conceptually those statistics match, to some extent, a procedural description. A procedural explanation will now be given taking note of this caveat A quantum computation is executed 1401. The qubit states will be modified by the operation of gates and these state changes will move a certain mass-energy resulting in distortion of the space-time metric. In an optimal QGC a mechanism is provided to amplify the gravitational effect of the qubit movement using proteins that flex and move appreciable mass dependent on their state 1402. This might be by opening a gate and allowing electrons to flow from one capacitor to another or by modifying a protein such as redopsin which will fold to a dramatically different topography based on the energy of a single electron in the molecule. Thus, the superposed qubit state may result in a superposed space-time metric 1403. Further quantum computation may occur where, due to the modified space-time metric the cause and effect relationship of inputs to gates may be in question 1404. Thus, the computation is in a state where there can be no matter of fact as to what state or program has been executed. Quantum computation results in qubits becoming entangled with each other and thus so-called Bell states or EPR states are established. Qubits have modified the metric of space-time in an entangled manner. This is an unstable state 1405, regions of the system if summed together in a particular way would exceed the E.sub.g limit. However, there is no arbiter to decide how the sum should be made and so the system has an intrinsic instability. This state is rather like the super-critical state in crystallization or freezing. At some point either the system becomes so super critical that it must collapse to a state or a small perturbation of imperfection triggers collapse 1406. This collapse is complex—orchestrated we say 1407—as the nature of the collapse in one area affects the nature of the collapse in others in a non-local fashion. Once sufficient collapse has occurred to bring the system under its critical limit the system returns to computation and a readout can be made 1408. Based on the nature of the readout and normal neural network learning mechanisms the weights of the quantum computing structure are modified to reinforce 1409 good behavior.
[0115] FIG. 15 illustrates the condition in which gates occupy regions of space 1501-4 and are entangled by relationships indicated by dashed lines 1505. The metric will be affected by the state of gates within a certain region and metric modifications occur at the speed of light such that certain regions such as 1500 may be affected by the metric distortions of gates in regions 1501 and 1503. And certain other regions 1507 may be affected by the gravitational distortions of gates in many regions 1501-4. One can immediately see that the distinctions of regions is an arbitrary conceptual overlay and has no true meaning other than to provide a way in which to model the system. A given point in space time Will be subject to elements within its past (uncertain and superposed) light cone. It is also worth noting that entanglement effects 1505 are independent of space-time light cones. Two qubits might be outside each other's light cones yet quantum entangled. The modulation of space-time by the quantum superposed states results in areas of space-time having incompatible metrics. Space-time at the large scale appears smooth and linear. It cannot maintain two contradictory curvatures. Thus, regions of space-time become unstable and superpose different states. These superpositions are very complex as they are affected by both the metric variation and by logical constraints imposed by the entanglement of different qubits. This forms a super-critical 1406 energy state FIG. 14 in which the system must collapse into a single state but it is unclear as to how the state should collapse—and impossible to model on a quantum computer. Because there are regions which are space-like separated that contain entangled qubits there can be no causal process by which to model the collapse and there can be no mater of fact about the state prior to collapse that would allow us to form an input to a Turing algorithm to model the process. However, the constraints of space-time mean the state ‘must’ collapse and so it does in step 1407. The state can be imagined to crystalize out and metric state of each region becomes sufficiently certain. This means that the location of masses is once again certain to the degree required to be sub-critical and looking at these masses allows us to ‘see’ the result of the ‘computation’. Of course, neither of these two words is correct. The locations of masses might be the position of a finger or the state of certain photons on the retina. Rather than considering that the state has been read out it is more correct to say the state has been imposed upon the world. There is no requirement in this system for full collapse. Only sufficient collapse is required to bring the system within sub-critical limits again. Thus, the system may display a variety of oscillatory modes as it transitions from super-critical to subcritical state and back to super-critical again.
[0116] FIG. 16 Illustrates the standard Shor code 1601 for quantum error correction. A full explanation can be found at https://en.wikipedia.org/wiki/Quantum_error_correction. Implementing this in quantum logic allows for an error corrected store of quantum information that can be manipulated without errors increasing that swamp the result. In our system quantum error correction is an emergent property of the dynamic network. A stable pattern will emerge that cycles around the triangle 1602, 1603, 1604. The diagram is much simplified as one to two orders of magnitude more nodes are required for implementation but the conceptual idea is illustrated. The pattern would not stable if errors accumulated and it would dissipate. Stable patterns are the only ones that emerge because they are intrinsically error correcting.
[0117] FIG. 17 Illustrates a layout for the QGC implementation. A series of quantum gravity gates (QGG)—somewhat equivalent to neural network nodes—are deposited onto a substrate which is organized into a series of interlocking fingers or a snaking paths. The QGG elements are formed of graphene tuned to a particular wavelength and spaced along the finger so that they coherently transport energy along a finger. Portions of graphene compound move with respect to the substrate when excited. At the end of each finger a connecting element transports energy from one finger to the next and computation occurs in the other direction along an adjacent finger, Quantum resonant gravity gates (nodes) are laid out along the snaking paths 1701, 1702, 1703. The nodes are able to communicate most readily with each other along the main pathways but are entangled 1704 and gravitationally effective laterally 1705. The nodes of the quantum gravity computer are not wired as a conventional computer might be, rather the gates are simply placed at the correct interval and computation occurs because of quantum resonant coupling between gates. Such coupling is inspired by the mechanism in photosynthesis. The arrows show interconnection between nodes schematically but should show influence between every node—the strength of coupling diminishing degree at farther distance.
[0118] Photons are introduced to the end of the substrate 1 706 and take ‘all’ paths through the matrix of gates. The dynamics of the network processes information. (ref Functional Topology of the Complex Dynamic Geometric Networks, Silva for detailed explanation). Photons may be of the same frequency as is given out by oxygen respiration of mitochondria i.e. blue light.
[0119] The graphene gates can be addressed from the silicon chip below and differing charges put onto them to effect different processing. This can be to implement weights for memory and learning. Equally as the gates process information they affect the charge in the SiO2 section which can be read to determine the state of the graphene dot.
[0120] By looping the computational structure back on itself a calculation that proceeds along the interdigitated path can be near its origin topographically despite being topologically distant. The processing elements at the nodes are made from Graphene Quantum Dots but could be made from different molecules such as tryptophan, redopsin or even linear optical processing elements,
[0121] According to the Penrose OR hypothesis once sufficient metric uncertainty is generated space-time can no longer bifurcate into the many possibilities and a spontaneous self-measurement of the superposed gravitational states occurs. It is not possible to make a procedural calculation of this collapse and in our system the mass superposition is distributed across many entangled elements. The best way to visualize the collapse process is as a phase transition: The system crystalizes.
[0122] FIG. 18 illustrates a side view of the graphene on silicon system. A computer circuit 1802 is created on a substrate 1801, Graphene on silicon is deposited on silicon areas insulated by SiO2 areas. A top wave guide 1804 is placed on pillars over the graphene connection layer 1803. Standard chip fabrication technology can be used to construct the system.
[0123] FIG. 19 illustrates a quantum gravity computer built from neurons 1801. Neurons can be grown in the laboratory from stem cells or microtubules can be synthesized in the laboratory from tubulin. Tubulin will self-assemble into microtubules in an aqueous solution and tubulin will preferentially assemble if subjected to electromagnetic radiation at the appropriate frequencies. One benefit of building biological quantum gravity computers is theft matrixes are generally three dimensional. Three-dimensional chip technology is still a technology in its infancy. They can also be constructed at large scale due to fact they self-assemble or grow organically.
[0124] It can be seen from the diagram that light cones 1803, 1804 superposed on biological human neuron allow uncertainty at the edge of light cones within the same neuron. In this diagram we have superposed the scale of time on the y direction of space shown vertically. This can be done without difficulty since the speed of light c is a constant and we imagine processing occurs along the length of the microtubule fibers within the neurons in the vertical axis so that time wrt processing elapses along the y axis 1802. In order to use neurons as a computational element it is necessary to input and output signals from the bundle of neurons or microtubules. This can be done through electrical stimulation and recording or optical stimulation and either optical or electrical recording.
[0125] To facilitate this one or more fiber optic cables 1807 is inserted through the wall of the neuron into the microtubule and one or more triaxial probes 1805, 1806 are inserted through the wall of the neuron into the microtubule. Signals are inserted and measured and the neuron arrangement can be trained to process signals. Neurons self-train in that they do not require a reward mechanism over and above attention. Positive reinforcement for training is achieved through providing differential stimulus for a ‘good’ response or a ‘bad’ response. Neurons automatically work out how to learn based on unlabeled reinforcement information.
[0126] Note that in this QGC we have constrained the physical location of the dots in space and are allowing the time dimension to carry the bulk of the uncertainty. In a biological quantum computer, the substrate is flexible and typically formed of strands which float in an aqueous medium. This is the model that microtubules form in a neuron with MAP flexible proteins forming the quantum gravitational gates. These gflex proteins™ have three main functions: they are controlled optical switches, they move mass based on their state, they provide for coherent energy transfer between elements. Example gflex proteins include Tryptophan and Redopsin.
