Holographic quantum dynamics simulation

Abstract

The present invention is entitled Holographic Quantum Dynamics Simulation. The present invention provides a quantum computer controller, which receives a quantum circuit including circuit slices. The first slice includes a causal cone of a first system qubit line at a fully evolved level of the circuit. The i-th slice contains all gates within the causal cone of the system qubit line that reaches the fully evolved level in slice i, and the gates are not within the causal cone of the system qubit line that reaches the fully evolved level in slice i‑j. The controller causes the i-th slice to be executed using physical qubits; causes the physical qubits that have evolved along the system qubit line to the fully evolved level via the execution of the i-th slice to be reinitialized and reintroduced onto the system qubit line at the base level of the i+m-th slice; and causes the quantum computer to execute the i+m-th slice using the physical qubits.

Description

Technical Field

[0001] Various embodiments relate to performing quantum circuits by a quantum computer. For example, various embodiments relate to performing quantum circuits by a quantum computer with efficient qubit usage. Background Art

[0002] Recent quantum computing hardware will only have access to a limited number (10 to 100) of qubits (quantum bits), and is also strongly limited by noise and gate errors. The relatively small number of noisy qubits makes it difficult to effectively solve complex problems that are very challenging to solve using classical computing devices. Through much effort, ingenuity, and innovation, many deficiencies of such systems have been addressed by developing solutions constructed according to embodiments of the present invention, and many examples of such solutions are described in detail herein. Summary of the Invention

[0003] Various embodiments provide methods, quantum computers, computing entities (e.g., classical computing entities), systems, computer program products, etc. According to one aspect, a quantum computer can execute a quantum circuit by efficiently using the physical qubits of the quantum computer. In an exemplary embodiment, a controller of the quantum computer receives a quantum circuit including a plurality of circuit slices. The quantum computer includes a controller, a qubit management system, and a plurality of physical qubits. The first slice of the plurality of circuit slices includes the past causal cone of a first system qubit line at the fully evolved level of the quantum circuit. The i-th slice of the plurality of circuit slices is defined to include all gates that are not within the causal cone of any system qubit line of the quantum circuit that reaches the fully evolved level of the quantum circuit in slice i - j, where 0 ≤ j < i is an integer, but now these gates can be executed by activating one or more physical qubits that have reached the fully evolved level during the execution of slice i - 1, have optionally been measured, and are reset to a system qubit line at the base level in slice i. For example, the i-th slice can include all gates within the causal cone of a system qubit line that reaches the fully evolved level of the quantum circuit via the execution of slice i that is not within the causal cone of the system qubit line, and the system qubit line reaches the fully evolved level in slice i - j, where 0 < j < i is an integer. The controller causes the i-th slice of the quantum circuit to be executed using the physical qubits of the quantum computer; causes the physical qubits that evolve as the system qubits fully evolved via the execution of the i-th slice to be optionally measured, and re-initialized and re-introduced to the system qubit line at the base level in slice i + m, where m is a positive integer; and causes the quantum computer to execute the i + m-th slice of the quantum circuit using the physical qubits.

[0004] According to another aspect, a method is provided. In an exemplary embodiment, the method includes receiving, by a controller of a quantum computer, a quantum circuit including a plurality of circuit slices. The quantum computer includes a qubit management system and a plurality of physical qubits. A first slice of the plurality of circuit slices includes a causal cone of a first system qubit line at a fully evolved level of the quantum circuit. The i-th slice of the quantum circuit is defined to include all gates that are not within the causal cone of any system qubit line of the quantum circuit that reaches the fully evolved level of the quantum circuit in slice i-j, where 0 < j < i is an integer, but now these gates can be executed by activating one or more physical qubits that have reached the fully evolved level during the execution of slice i-1, have optionally been measured, and are reset to a system qubit line at the base level of slice i. The method further includes causing, by the controller, the i-th slice of the quantum circuit to be executed using the physical qubits of the quantum computer; optionally measuring, by the controller, the physical qubits that evolve as system qubits fully evolved via the execution of the i-th slice, and re-initializing and re-introducing them to the system qubit line at the base level of slice i+m, where m is a positive integer; and causing, by the controller, the quantum computer to execute the i+m-th slice of the quantum circuit using the physical qubits.

[0005] In an exemplary embodiment, executing the i-th slice of the quantum circuit includes executing all gates for which the incoming and outgoing lines are located within the i-th slice so as to propagate the system qubits forward in time. In an exemplary embodiment, the quantum circuit includes at least one ancilla line, and executing the i-th slice of the quantum circuit includes interacting one or more system qubits at the bottom of the i-th slice with at least one ancilla line via a unitary gate so as to introduce an initial correlation between the one or more system qubits at the bottom of the i-th slice and the system qubits at the bottom of one or more other slices. In an exemplary embodiment, the quantum circuit encodes interactions dominated by a Hamiltonian characterized by local interactions. In an exemplary embodiment, the system qubit lines correspond to degrees of freedom associated with a segment of a simulated physical domain. In an exemplary embodiment, executing the i-th slice of the quantum circuit includes evolving the degrees of freedom according to an operator. In an exemplary embodiment, the operator is a Hamiltonian. In an exemplary embodiment, the physical domain is one of a one-dimensional physical domain, a two-dimensional physical domain, or a three-dimensional physical domain. In an exemplary embodiment, the quantum circuit simulates the dynamics of the evolution of quantum states defined on a lattice representing a physical domain. In an exemplary embodiment, the method further comprises performing one or more measurements of at least one physical qubit in the plurality of qubits to determine a value corresponding to at least one degree of freedom within the physical domain. In an exemplary embodiment, at least one system qubit wire of the quantum circuit extends through a plurality of slices of the quantum circuit.

[0006] According to yet another aspect, a computing entity is provided. In an exemplary implementation, the computing entity communicates with a controller of a quantum computer. The quantum computer includes a qubit management system and a plurality of physical qubits. The computing entity is configured to cause the controller to control elements of the quantum computer to receive, by the controller, a quantum circuit comprising a plurality of circuit slices. A first slice of the plurality of circuit slices includes a causal cone of a first system qubit line at a fully evolved level of the quantum circuit. An i-th slice of the plurality of circuit slices is defined to include all gates that are not within the causal cone of any system qubit line of the quantum circuit that reaches the fully evolved level of the quantum circuit in slice i - j, where 0 < j < i is an integer, but that can now be executed by activating one or more physical qubits that had reached the fully evolved level during the execution of slice i - 1, have optionally been measured, and have been reset to a system qubit line at a ground level in slice i. The computing entity is further configured to cause the controller to control elements of the quantum computer to cause the quantum computer to execute the i-th slice of the quantum circuit using the physical qubits; cause the quantum computer to initialize a physical qubit that evolves along at least one system qubit line to fully evolve to a system qubit line at a ground level of the i + m-th slice of the quantum circuit via execution of the i-th slice, where m is a positive integer; and cause the quantum computer to execute the i + m-th slice of the quantum circuit using the physical qubits.

[0007] In an exemplary embodiment, executing the i-th slice of the quantum circuit includes executing all gates for which the incoming and outgoing wires are located within the i-th slice so as to propagate the system qubits forward in time. In an exemplary embodiment, the quantum circuit includes at least one auxiliary wire, and executing the i-th slice of the quantum circuit includes interacting one or more system qubits at the bottom of the i-th slice with at least one auxiliary qubit via a unitary gate so as to introduce an initial correlation between the one or more system qubits at the bottom of the i-th slice and the system qubits at the bottom of one or more other slices. In an exemplary embodiment, the quantum circuit encodes interactions governed by a Hamiltonian operator characterized by local interactions. In an exemplary embodiment, the system qubit wires correspond to degrees of freedom associated with a segment of a simulated physical domain. In an exemplary embodiment, executing the i-th slice of the quantum circuit includes evolving the degrees of freedom according to an operator. In an exemplary embodiment, the operator is a Hamiltonian operator. In an exemplary embodiment, the physical domain is one of a one-dimensional physical domain, a two-dimensional physical domain, or a three-dimensional physical domain. In an exemplary embodiment, the quantum circuit simulates the dynamics of the evolution of a quantum state defined on a lattice representing the physical domain. In an exemplary embodiment, the computing entity is further configured to cause the controller to control elements of the quantum computer to cause the quantum computer to perform one or more measurements of at least one physical qubit in the plurality of qubits to determine a value corresponding to at least one degree of freedom in the physical domain. In an exemplary embodiment, at least one system qubit wire of the quantum circuit extends through a plurality of slices of the quantum circuit. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Having thus generally described the invention, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and in which:

[0009] Figure 1 Schematic diagrams of exemplary systems according to exemplary embodiments are provided.

[0010] Figure 2 A schematic diagram of an exemplary domain divided into segments according to an exemplary embodiment is provided.

[0011] Figure 3A and Figure 3B Schematic diagrams of exemplary quantum circuits and slices of exemplary quantum circuits are provided according to exemplary embodiments.

[0012] Figure 4 Flowcharts are provided that illustrate various processes, procedures, and / or operations performed by a quantum computer for executing quantum circuits with efficient qubit usage.

[0013] Figure 5A schematic diagram of an exemplary user computing entity that may be used in accordance with the exemplary embodiments is provided.

[0014] Figure 6 A schematic diagram of an exemplary quantum computer that may be used in accordance with exemplary embodiments is provided. DETAILED DESCRIPTION

[0015] The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which some but not all embodiments of the present invention are shown. In fact, the present invention can be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; on the contrary, these embodiments are provided so that the present disclosure meets applicable legal requirements. Unless otherwise indicated, the term "or" (also represented as " / ") is used herein in both alternative and combined senses. The terms "illustrative" and "exemplary" are used for examples without indication of quality level. Unless otherwise indicated, the terms "substantially" and "approximately" refer to within engineering and / or manufacturing limits and / or within the user's measurement capabilities. Throughout the content, similar reference numerals refer to similar elements.

[0016] I. Overview

[0017] Computing the dynamical properties of electronic and magnetic materials can be used to predict many of their technologically important physical properties, such as light absorption and emission spectra, AC conductivity, magnetic susceptibility, magnetoresistance, spin dynamics, and many others. Classical simulation of the dynamics of correlated quantum systems is extremely challenging due to the rapid growth of entanglement entropy, which limits state-of-the-art simulation methods such as the time-dependent density matrix renormalization group (DMRG) to very short time scales.

[0018] Very generally, the memory and simulation time resources for simulating the dynamics of quantum systems traditionally grow exponentially in the size of the system or the resulting simulation time. In contrast, the advent of programmable quantum computers enables a variety of polynomial-time algorithms for simulating quantum materials, which provides an exponential reduction in the resources required to perform these simulations. However, near-term quantum computing hardware will only have access to a limited number (10 to 100) of quantum bits (qubits) and will also be strongly limited by noise and gate errors.

[0019] Various embodiments of the present invention provide methods, apparatus, computing entities, computer program products, systems, etc. for executing quantum circuits with efficient qubit usage, such that relatively small numbers of potentially noisy qubits can be used to solve complex problems that may be very difficult and / or intractable to solve via classical computing devices.

[0020] In various embodiments, a quantum computer uses only a limited number of "physical qubits" to implement a large width circuit on a large number of "system qubits" (e.g., qubits evolved along the system qubit wires of the circuit). First, the causal cone of the quantum circuit output of the leftmost system qubit wire is identified, which contains a subset of the system qubit wires and at least one auxiliary qubit. For example, the causal cone of the first system qubit wire at the fully evolved level is identified and used to define the first slice 140A, such as Figure 3A For a given qubit in a circuit, we can define its causal cone as the set of all qubits from which the given qubit can be reached by tracing a line from the past to the future, leaving each gate through any line flowing out of the gate. By this definition, Figure 3A The causal cone for the qubits at the top of system qubit lines 1 and 2 is shown to contain all qubits below and to the left of the dashed line (e.g., boundary 146) (including qubits entering along system qubit lines 1-5, and all qubits entering along auxiliary lines).

[0021] The quantum computer has enough physical qubits to process the complete circuit contained within this causal cone. Figure 3A and Figure 3B If desired, evolve along these system qubit lines to the full evolution level of the quantum circuit (e.g., at the output of the cone, at Figure 3B The qubits labeled A and B in the circuit are measured, reinitialized, and looped back to the base level of the circuit, where they can be used to expand the causal cone to one slice to the right of the initial cone to include more system qubits at the circuit output [in this case, the 3rd and 4th qubits from the left at the top of the circuit, labeled C and D]. This process can be repeated to process and / or execute more slices of the circuit until all slices of the quantum circuit have been processed and / or executed. At this point, the entire quantum circuit has been faithfully executed and all expected measurement results for the fully evolved level of the circuit have been obtained.

[0022] In various embodiments, a quantum circuit is defined. In various embodiments, the quantum circuit includes a plurality of system qubit wires. In an exemplary embodiment, the physical system or domain being modeled and / or simulated is discretized onto a lattice using any suitable technique (e.g., a close binding description of the material). Each point in the lattice contains a finite number (e.g., at most d s) of quantum degrees of freedom. For example, the domain being modeled and / or simulated may be a one-dimensional, two-dimensional, or three-dimensional physical system and / or domain (e.g., at least a portion of a physical material), and each system qubit wire may represent, model, simulate, and / or correspond to the evolution (e.g., in time) of quantum degrees of freedom, physical locations, and / or particles within the system and / or domain. For example, a system qubit wire of a quantum circuit may simulate the evolution (e.g., in time) of one or more characteristics of a corresponding segment within a system and / or domain. For example, a quantum circuit may simulate the dynamics of the evolution of the quantum state of a particle within a physical domain. In various embodiments, a domain may not be a physical domain, and a domain may be more than three-dimensional. For example, a domain may correspond to the spread of a disease through a geographic region, logistics operations in a geographic region, a financial index, and / or other one-dimensional or multi-dimensional domains.

[0023] In various embodiments, the time evolution and / or interaction between segments of a domain (and / or positions and / or particles and / or corresponding degrees of freedom within a segment) is simulated and / or modeled via an operator. For example, a domain may be divided into segments. If the dimension of the domain is d, then the dimension of each segment is d-1. In various embodiments, the operator is a Hamiltonian operator. In various embodiments, the operator is a local operator. When H(t)=∑ k h k (t), the operator H(t) is a local operator where k indexes consecutive (e.g., spatially adjacent) d-1-dimensional segments of the d-dimensional lattice, and each operator term h k (t) acts on the lattice sites contained in the bins of distances up to a positive integer p from the bin. For example, if the system and / or domain is a one-dimensional system and / or domain, then the bins are zero-dimensional (e.g., corresponding to specific points within the system and / or domain), and each operator term h k (t) acts on at most p neighboring points in the system and / or domain. For example, Figure 2 An exemplary one-dimensional system and / or domain 200 is shown that has been divided into a plurality of segments 202 (e.g., 202.1, 202.2, 202.3, 202.4, 202.k). In an exemplary embodiment, where p = 2, h1(t) may act on the degrees of freedom associated with segments 202.1, 202.2, and 202.3, but not on the degrees of freedom in segment 202.4. In another exemplary embodiment, if the domain is a three-dimensional domain, the segments are two-dimensional (e.g., planes), and each operator term h k (t) acts in a two-dimensional segment and acts on degrees of freedom / points that are at most p segments away from segment k. For example, the operator term h k (t) does not act on every degree of freedom, position, and / or particle in the domain. For example, the operator h k (t) Geometric local interactions can be encoded.

[0024] In various embodiments, the quantum circuit includes one or more auxiliary lines. In various embodiments, each auxiliary qubit (e.g., a qubit evolving along an auxiliary line) prepares for correlations between various qubit lines (and / or degrees of freedom of the domain represented thereby) existing in an initial state corresponding to one or more initial characteristics of the domain over a segment of the domain. For example, when a system qubit (e.g., a physical qubit evolving along system qubit line 120) is passed through unitary gate 112 (see Figure 3A and Figure 3B ) interacts with auxiliary qubits (e.g., physical qubits evolving along auxiliary line 110), the auxiliary qubits impart correlations between initial states of various degrees of freedom in various segments. In an exemplary embodiment, at an initial time t=0, the auxiliary qubits (e.g., qubits evolving along the auxiliary lines) generate matrix product states between the degrees of freedom in various segments of the domain. In various embodiments, each system qubit is first initialized onto a system qubit line and then enters a correlated state by interacting with one or more auxiliary qubits via a unitary gate. The system qubit then continues to evolve along the system qubit line by gating with other system qubits (e.g., qubits evolving along other system qubit lines) to simulate the time evolution of the simulated system and / or domain under a local Hamiltonian.

[0025] In various embodiments, a slice of a quantum circuit is defined. As described above, the quantum circuit includes a plurality of system qubit wires extending from a base level of the quantum circuit corresponding to time t=0 to a fully evolved level corresponding to time t=T. Each of these quantum wires involves one or more degrees of freedom of a segment of a simulated system and / or domain. The system qubit wire may pass through one or more slices of the quantum circuit.

[0026] In various embodiments, from Figure 3B The quantum circuit is executed slice by slice 140, starting with the first slice 140A on the left, and moving from left to right through each successive slice 140. For example, first, all gates within the first slice 140A (the triangular region) are executed, and any desired measurements of the qubits at the output (e.g., the fully evolved level 136) of that slice 140A are made. Then, having reached the fully evolved level 136 (e.g., Figure 3B The physical qubits at the top of the slices labeled A and B in FIG. 140 are reset (e.g., reinitialized) and inserted into the bottom of the system qubit line (e.g., base level 130) in the next slice 140. The gates within slice 140 are then executed according to the time order of the circuit (e.g., red gates are executed first, and then blue gates are executed in ascending order from bottom to top). Figure 3BIn the example of , the gates executed at this point in the program are shown in light colors. Then the physical qubit that has reached the top of this second slice 140B (at Figure 3B The gates 112, 122 (marked C and D in FIG. 1 ) are reset (e.g., reinitialized) and inserted back into the bottom of the third slice 140. At this point, the gates in the third slice may be executed, and the process continues through all slices 140 from left to right until all gates 112, 122 have been executed and all measurements 150 have been made.

[0027] In various embodiments, each slice of a quantum circuit starts at a base level of the quantum circuit and extends diagonally across the system qubit wires of the quantum circuit to a fully evolved level. For example, if the quantum circuit simulates and / or models the evolution of a system and / or domain from time t=0 to time t=T, then the base level of the quantum circuit corresponds to time t=0 and the fully evolved level corresponds to time t=T. In various embodiments, the i=1 slice is defined such that at least one system qubit wire evolves from the base level to the fully evolved level and must exclusively contain a complete causal cone of at least one system qubit wire at the fully evolved level. The causal cone is defined by identifying all system qubits at the base level, which can be identified by following the steps of Figure 3A and Figure 3BThe arrow direction shown connects to the fully evolved qubit by passing through the line of the gate. For example, the system qubit that reaches the fully evolved level in i=1 slice evolves from the base level to the fully evolved level without interacting and / or evolving with any system qubit wire that starts at the base level of i>1 slice. In various embodiments, i>1 slices may be defined recursively. For example, for i≥1, the i+1 slice may be identified by bringing the system qubit wire directly to the right side of the system qubit wire at the fully evolved level of the i-th slice of the quantum circuit, and then identifying the causal cones of those system qubit wires directly to the right side of the system qubit wire at the fully evolved level of the i-th slice. The system qubit wires immediately to the right of the system qubit wire at the fully evolved level of the i-th slice include system qubit wires directly connected by gates at the fully evolved level. For any non-negative integer j, the portion of the identified causal cone that does not intersect with slice ij is slice i+1. For example, a system qubit line that reaches a fully evolved level in slice i>1 evolves to the fully evolved level without interacting and / or evolving with any system qubit line that begins at and / or extends from the base level of slice i+j, where j is a positive integer. Executing slice i>1 may include interacting and / or evolving with one or more system qubit lines that begin at and / or extend from the base level of slice ij, where j is a positive integer. In general, for a system qubit line that reaches a fully evolved level in slice i, it may be gated with a system qubit line originating from (e.g., at the base level of a quantum circuit) any one of slices in slice ij, where j is any non-negative integer, without being gated with a system qubit line originating from (e.g., at the base level of a quantum circuit) any one of slices in slice i+j.

[0028] In various embodiments, the quantum circuit is executed slice by slice. For example, a quantum computer may execute a first slice of the quantum circuit such that one or more system qubit wires are initialized at the base level of the first slice, and at least one system qubit wire is evolved to the fully evolved level of the first slice. A second slice of the quantum circuit may then be executed such that one or more system qubit wires are initialized at the base level of the second slice, and at least one system qubit wire is evolved to the fully evolved level of the second slice. A third slice of the quantum circuit may then be executed, and so on, until each slice of the quantum circuit has been executed.

[0029] In various embodiments, one or more characteristics of a qubit may be measured at various points in the evolution of the qubit along the corresponding qubit trace to determine the corresponding position and / or one or more characteristics of a particle of the domain at the corresponding time. For example, when a physical qubit evolving along a system qubit line reaches a fully evolved level of a quantum circuit, one or more measurements may be made to determine one or more characteristics of a position and / or particle corresponding to the system qubit line at time t=T. In various embodiments, once a physical qubit has evolved along a system qubit line to the fully evolved level of slice i, and any desired measurements have been made, it may be initialized and reintroduced at the base level of slice i+1 to evolve along another system qubit line.

[0030] In various embodiments, execution of quantum circuits in a slice-by-slice manner allows for recycling of physical qubits. For example, by executing quantum circuits in a slice-by-slice manner, physical qubits of a quantum computer can be initialized along multiple system qubit lines of different slices. Thus, fewer physical qubits are required to fully execute the quantum circuit. Thus, embodiments enable quantum circuit modeling and / or simulation of complex systems to be performed using a relatively small number of qubits.

[0031] II. Exemplary System Architecture

[0032] Figure 1 A schematic diagram of an exemplary system that can be used according to an exemplary embodiment is provided. In various embodiments, the system includes a user computing entity 10 and a quantum computer 30. In various embodiments, the quantum computer 30 includes a controller 500, a plurality of qubits, and one or more qubit management systems. In various embodiments, the user computing entity 10 can communicate with the controller 500 of the quantum computer 30 via wired or wireless communication. In various embodiments, the user computing entity 10 can communicate directly with the controller 500, or can communicate with the controller 500 via one or more networks 20.

[0033] In various embodiments, the user computing entity 10 is configured to allow a user (e.g., via a user interface of the user computing entity 10) to provide input to the quantum computer 30, and to receive, view, and / or perform similar processing on output from the quantum computer 30. The user computing entity 10 may communicate with the quantum computer 30 (e.g., the controller 500) via one or more wired or wireless networks 20. In various embodiments, the quantum computer 30 may be a trapped ion quantum computer, a nuclear magnetic resonance quantum computer, a superconducting quantum computer, a photonic quantum computer, and / or other types of quantum computers.

[0034] In various embodiments, the controller 500 is configured to control one or more qubit management systems of the quantum computer 30 so as to manipulate and / or evolve one or more qubits of the quantum computer 30 in a desired manner. For example, the controller 500 may be configured to execute one or more quantum circuits by causing one or more qubit management systems to manipulate and / or evolve one or more qubits in a manner indicated and / or defined by the quantum circuit. For example, the one or more qubit management systems may include a thermal control system (e.g., a cryogenic cooling system), a vacuum system (e.g., a pressure control system), a qubit confinement system (e.g., in the case of a trapped ion quantum computer, an ion trap and a voltage source connected to the ion trap), one or more gate systems (e.g., in the case of a trapped ion quantum computer, a laser and corresponding optical devices), a measurement system (e.g., in the case of a trapped ion quantum computer, including optical devices, photodetectors, etc.), etc. By causing one or more qubit management systems to manipulate and / or evolve one or more qubits according to the quantum circuit, the quantum computer 30 may perform calculations, simulations, generate models, etc.

[0035] The user computing entity 10 may provide (e.g., transmit) a quantum circuit, an executable code portion encoding the quantum circuit (e.g., a computer executable instruction, command set, etc.), and / or a request for execution of one or more quantum circuits, so that the controller 500 of the quantum computer 30 receives the quantum circuit, the executable code portion encoding the quantum circuit, and / or the request. The quantum computer 30 may then execute the quantum circuit, and may determine, measure, and / or similarly process the execution result of the quantum circuit in response to receiving the quantum circuit, the executable code portion encoding the quantum circuit, and / or the request to execute the quantum circuit. The quantum computer 30 may then provide (e.g., transmit) the execution result of the quantum circuit and / or the processing result of the execution result of the quantum circuit, so that the user computing entity 10 receives the execution result of the quantum circuit and / or the processing result of the execution result of the quantum circuit. The user computing entity 30 may then use the execution result of the quantum circuit and / or the processing result of the execution result of the quantum circuit as input to one or more programs, cause the execution result of the quantum circuit and / or the processing result of the execution result of the quantum circuit to be displayed via a user interface of the user computing entity 10, cause the execution result of the quantum circuit and / or the processing result of the execution result of the quantum circuit to be stored in a computer-readable memory, etc.

[0036] III. Exemplary Quantum Circuits

[0037] In various embodiments, a quantum circuit is a model of a quantum computation, where a quantum computation is a series of quantum gates. In various embodiments, a quantum circuit is divided into a plurality of slices. Executing the quantum circuit includes executing the slices serially. Figure 3A and Figure 3B A schematic diagram of an exemplary quantum circuit 100 is provided. The quantum circuit 100 includes a plurality of system qubit wires 120 (e.g., 120A, 120B). The quantum circuit 100 includes a plurality of levels, starting from a base level 130, at which each system qubit wire begins with an initialization step and extends through a plurality of levels to a fully evolved level 136. As used herein, a system qubit is a physical qubit 555 of a quantum computer 30 that evolves along a system qubit wire 120. It should be noted that due to the qubit reuse scheme described herein, a single physical qubit 555 can play the role of multiple different system qubits at various points in the algorithm. For example, a single physical qubit 555 can be continuously reintroduced onto multiple system qubit wires after reaching a fully evolved state of a previous system qubit wire.

[0038] In various embodiments, the multiple levels between the base level 130 and the fully evolved level 136 may include a unitary circuit level 132. In various embodiments, the quantum circuit 100 includes one or more auxiliary wires 110. As used herein, an auxiliary qubit is a physical qubit 555 of the quantum computer 30 that evolves along the auxiliary wire 110. In various embodiments, the unitary circuit level 132 includes the interaction of the auxiliary wire 110 with the system qubit wire 120. For example, the auxiliary qubit may interact with the system qubit evolving along the system qubit wire 120, for example, via a gate 112 (e.g., 112A, 112B). The interaction of the auxiliary qubit and the system qubit via the gate 112 may place the system qubit in a state that corresponds to and / or approximates an initial state of a position and / or particle corresponding to the corresponding system qubit wire 120. For example, the interaction of the auxiliary qubit with the system qubit may place the system qubit in a state that approximates the lowest energy state of the Hamiltonian. Intermediate levels 134 (e.g., 134A, 134B) may correspond to the temporal evolution and / or interaction between adjacent positions and / or particles within a domain, as described by an operator (e.g., a Hamiltonian). For example, intermediate levels 134 of system qubit wire 120 may include interaction gates 122 (e.g., 122A, 122B) resulting in temporal evolution and / or interaction between physical qubits evolving along other system qubit wires. In various embodiments, physical qubits 555 evolving along auxiliary wire 110 will not be reused compared to physical qubits 555 evolving along system qubit wire 120.

[0039] In various embodiments, quantum circuit 100 may include making one or more measurements 150 (e.g., 150A, 150n). For example, measurement 150 may indicate one or more properties of a position and / or particle within a domain at a corresponding time. For example, if measurement 150A is made at the fully evolved level 136 on a first physical qubit evolving along first system qubit wire 120A, measurement 150A indicates one or more properties corresponding to a first position or particle at time t=T. Quantum circuit 100 may include various measurements at different levels 134, 136 within the circuit and / or along different system qubit wires 120, as appropriate for the computation modeled by quantum circuit 100.

[0040] Quantum circuit 100 has an implied time ordering whereby all system qubit (i.e. vertical) lines 120 extend from bottom (past) to top (future), and auxiliary (i.e. horizontal) lines 110 extend from left (past) to right (future). The directions are given by Figure 3A and Figure 3B The arrows on a subset of the lines in are indicated, but the direction exists in a similar way for all lines.

[0041] In various embodiments, quantum circuit 100 is divided into and / or includes a plurality of slices 140 (e.g., 140A, 140B, ..., 140n). Compared to system qubit wire 120, slices 140 of quantum circuit 100 extend diagonally from base level 130 to full execution level 136. For example, slice boundaries 146 (at Figure 3A and Figure 3B140i) may intersect one or more system qubit wires 120. For example, the i-th slice 140i of the quantum circuit 100 may correspond to a base-level qubit set 142i (e.g., 142A, 142B) and a fully evolved-level qubit set 144i (e.g., 144A, 144B). The base-level qubit set 142i includes at least one system qubit wire 120, and the fully evolved-level qubit set 144i includes at least one system qubit wire 120. However, the base-level qubit set 142i and the fully evolved-level qubit set 144i may not have any overlap. For example, the fully evolved-level qubit set 144i of the i-th slice 140i may not include any of the system qubit wires 120 in the base-level qubit set 142i of the i-th slice 140i. In other words, the system qubit line 120 may start at the base level 130 in the base level set 142i of the i-th slice and may reach the fully evolved qubit set 144(i+j) of the i+j-th slice 140(i+j), where j is a positive integer. For example, the i-th slice 140i extends diagonally across the intermediate levels 134 (e.g., 134A, 134B) to the fully evolved level 136.

[0042] In an exemplary embodiment, for i>1, the base level qubit set 142i and the fully evolved level qubit set 144i include the same number of system qubit wires 120. In an exemplary embodiment, for i, j>1, the base level qubit set 142i of the i-th slice and the base level qubit set 142j of the j-th slice include the same number of system qubit wires 120. In an exemplary embodiment, the fully evolved level qubit set 144A of the first slice 140A includes the same number of system qubit wires 120 as the fully evolved level qubit set 144i of the i-th slice 140i. In various embodiments, the base level qubit set 142A of the first slice 140A includes a greater number of system qubit wires 120 than the base level qubit set 144i of the i-th slice 140i. In an exemplary embodiment, base-level qubit set 142A of first slice 140A includes the minimum number of system qubit wires 120 required to fully evolve at least one system qubit wire 120 of base-level qubit set 142A. For example, first slice 140A may be the only slice 140 where there is overlap between base-level qubit set 142A and fully evolved level qubit set 144A.

[0043] In various embodiments, quantum circuit 100 is a dynamics simulation of the evolution of the quantum state |ψ(0)> Circuits and / or algorithms of the type described herein, in which quantum states are represented as matrix product states (MPS) with bond dimension χ, processed by geometrically local (possibly time-dependent) operators in the form of Hamiltonian operators H(t). Here T represents the time-ordered product. MPS can represent any pure or mixed quantum state for sufficiently large bond dimension χ. Classical computational methods for MPS generally require computational time and memory resources that scale polynomially on the bond dimension χ, typically limiting them to short-time dynamics and to one-dimensional or quasi-one-dimensional systems. In contrast, various embodiments enable exponentially reduced bond dimension χ dependence of quantum computing resources, enabling computations to be performed for a larger range of quantum states, longer time scales, and higher dimensional (e.g., two-dimensional and three-dimensional) materials and / or domains.

[0044] In various embodiments, the domain to be simulated and / or modeled is approximated by a discrete grid with a finite number of quantum degrees of freedom ds per site, using any standard orbital basis for electron correlation orbitals (e.g., a tight-binding description). Various embodiments are agnostic to the specific choice of orbital basis. Various embodiments simulate and / or model the local Hamiltonian H(t) = ∑ k h k (t) the resulting temporal dynamics, where as used herein, the term “local” means that for each term, h k (t) acts on a lattice site contained in a segment that is at a distance from the segment k at most a positive integer p.

[0045] The dynamics are simulated over a range of time intervals t∈[0,T] of a system or domain discretized onto a lattice of integer linear and cross-sectional dimensions L×A, with an accuracy of ~∈, various implementations require Physical qubits and quantum circuit depth Here, L is the number of lattice points / sites in the direction along which the lattice is divided into segments, and A is the number of lattice points / sites contained within each segment. In an exemplary embodiment, the system and / or domain is divided into segments along its longest dimension, which makes the algorithm more efficient. For example, the segments can be cut orthogonally and / or transversely to the longest dimension of the system and / or domain.

[0046] In various embodiments, quantum circuit 100 divides the physical qubits into The qubits, which move along the system qubit line, are prepared in some fixed initial state and iteratively interact with N a˜O(log2χ) register interactions for additional auxiliary lines. Strategic use of opportunistic measurements and serially resetting and reusing physical qubits along one or more system qubit lines enables various embodiments to simulate very large systems with a relatively small number of qubits.

[0047] In various embodiments, quantum circuits may be defined, generated, and / or determined as follows. In various embodiments, the continuous time evolution of the quantum state of the position and / or particle of a domain through the Hamiltonian operator is decomposed into discrete quantum circuits of N-level (e.g., 130, 132, 134, 136) disjoint terms acting on p segments of the simulated system and / or domain. In various embodiments, this decomposition of the time evolution is performed using various standard methods. For example, in an exemplary embodiment, the Trotter-Suzuki formula is used. to perform the decomposition, where (This equation represents only the simplest Trotter decomposition, but generalizes directly to higher-order versions of the Trotter-Suzuki decomposition.) The initial matrix product state can be defined and / or determined, and a tensor in left normal form can be extracted from it In various embodiments, the interaction between auxiliary qubits (e.g., qubits evolving along auxiliary qubit wire 110) and system qubits (e.g., qubits evolving along system qubit wire 120) can be based on tensors extracted from and / or determined by the initial matrix product state of the domain Without loss of generality, we assume that the tensor is in left normalized form such that are isometric and can be solved by a unitary circuit U acting on the auxiliary qubit and the system qubit V is implemented, where the system qubits are initialized to a fixed initial state |0> (at the base level 130). In an exemplary embodiment, the unitary circuit U V , tensor and a fixed initial state |0>satisfies In various embodiments, the unitary circuit U V Generated by a priori knowledge of the state or by variable optimization parameterizing a series of circuits, e.g., to variable-approximate the lowest energy state of the Hamiltonian of the material and / or domain being modeled and / or simulated. In various embodiments, the result is a quantum circuit 100, which can then be partitioned into a plurality of slices 140.

[0048] In various embodiments, the time-evolving quantum circuit 100 is configured to have N a = O(log2χ) auxiliary qubits, which are connected along (LA log2ds ) The system qubit interaction of the system qubit line 120, which is composed only of Physical qubit representation. The quantum circuit is divided into a plurality of slices 140, each slice having a fully evolved hierarchical qubit set 144, which includes O(pA log2 d s ) system qubit wires and a series of quantum gates to realize U V AND operation For example, Figure 3A and Figure 3B The exemplary quantum circuit 100 shown corresponds to A=1, d s =2 and p=2.

[0049] The quantum circuit 100 may then be executed. In various embodiments, each level of the first slice 140A is executed in order from the base level 130, then the unitary circuit level 132, then the intermediate level 134 (e.g., the first intermediate level 134A, then the second intermediate level 134B, etc.) across each level until the fully evolved level 136 is reached. For example, each physical qubit evolved along the system qubit line 120 of the base level qubit set 142A of the first slice 140A is initialized to a fixed initial state |0>. Then, the physical qubits evolved along the auxiliary line 110 are initialized, and the unitary circuit U is implemented. V The circuits of are applied to the physical qubits evolving along auxiliary wire 110 and the physical qubits evolving along system qubit wire 120 of first slice 140A at gates 112 (e.g., 112A, 112B). Interactive gates 122 (e.g., 122A, 122B) are executed by each intermediate level 134 until a fully executed level 136 is reached. In various embodiments, interactive gates 122 implement physical qubits evolving along system qubit wire 120 of first slice 140A. Once the first slice 140A has been fully executed, the physical qubits evolved along the system qubit wires 120 of the fully evolved level qubit set 144A of the first slice are reset and initialized onto the system qubit wires 120 of the base level qubit set 142B of the second slice 140B.

[0050] For i>1, the i-th slice can be executed by resetting the physical qubits evolved along the system qubit wire 120 of the fully evolved level qubit set 144(i-1) of the i-th slice, so that these physical qubits are initialized to a fixed initial state |0> at the base level 130 of the i-th slice 140i (e.g., on the system qubit wire 120 of the base level qubit set 142i of the i-th slice 140i). The unitary circuit gate 112 of the i-th slice 140i is executed at the unitary circuit level 132 of the i-th slice. The interactive gate 122 of the first intermediate level 134A is then executed to implement The remaining intermediate levels 134 are then executed in sequence as slice 140i traverses the system qubit wire 120 initialized in the previous slice 140(ij) until reaching the fully evolved level 136. The process may then be repeated for the i+1th slice 140(i+1) until all slices have been fully executed.

[0051] This procedure provides access to any measurable quantity of the time evolving state by measuring the desired observable quantity on the physical qubits evolving along the system qubit wire 120 at the fully evolved level 136 before resetting the physical qubits for reuse in the next slice. To measure an observable quantity at an intermediate time, execution of the quantum circuit 100 can simply be interrupted and the measurement of the desired observable quantity on the physical qubit performed at the desired time (e.g., at the intermediate level 134 corresponding to the desired time).

[0052] IV. Exemplary System Operation

[0053] Figure 4A flow chart is provided showing various processes, procedures and / or operations performed by a quantum computer 30 for executing a quantum circuit with effective qubit usage. Beginning at step / operation 302, a quantum circuit 100 is defined, and a slice 140 of the quantum circuit is determined and / or defined. In an exemplary embodiment, the quantum circuit 100 and / or the slice 140 of the quantum circuit may be defined by a user computing entity 10 (e.g., automatically (e.g., by a machine user) or via user interaction with a user interface) and / or by a controller 500 of a quantum computer 30. In an exemplary embodiment, the quantum circuit 100 may be defined by a user computing entity 10, and is provided such that the controller 500 of the quantum computer 30 receives the quantum circuit 100 and defines the slice 140 of the quantum circuit. In an exemplary embodiment, the quantum circuit 100 and the slice 140 of the quantum circuit are defined by the user computing entity 10, and are provided such that the controller 500 of the quantum computer 30 receives the quantum circuit 100 with the slice 140 of the quantum circuit already defined. For example, a user computer entity may provide a quantum circuit 100 with slices 140 of the quantum circuit defined. The controller 500 may then receive (e.g., at the processing device 505, via the communication interface 520) the quantum circuit 100 with its slices 140 defined. In various embodiments, n slices 140 of the quantum circuit 100 are defined.

[0054] At step / operation 304, physical qubits to be evolved along the system qubit wires of the first slice 140A are initialized (e.g., physical qubits to be evolved along the system qubit wires 120 of the base level qubit set 142A of the first slice 140A). For example, the base level 130 of the first slice 140A may be executed. For example, the controller 500 (e.g., via the processing device 505, the driver component element 515, etc.) may cause one or more qubit management systems 550 to manipulate the physical qubits 555 of the quantum computer 30 so that the physical qubits are initialized onto the system qubit wires 120 of the base level qubit set 142A of the first slice 140A and onto the auxiliary wires 110. For example, the index i is initialized at 1, and the base level 130 of the i-th slice is executed.

[0055] At step / operation 306, the unitary circuit level 132 of the i-th slice is executed. For example, the controller 500 (e.g., via the processing device 505, the driver component element 515, etc.) may cause one or more qubit management systems 550 to manipulate the physical qubits 555 of the quantum computer 30 so that the unitary circuit level 132 of the i-th slice is executed. For example, the unitary U may be transferred across the unitary circuit level 132 of the i-th slice. VApplied to the physical qubits evolving along the auxiliary line 110 and the system qubit line 120. For example, the unitary circuit gate 112 can be applied to the physical qubits evolving along the auxiliary line 110 and the physical qubits evolving along the system qubit line 120 of the i-th slice.

[0056] At step / operation 308, a circuit that applies the time evolution of the system qubit wire 120 of the i-th slice is executed. For example, the intermediate levels 134 of the i-th slice are executed in sequence. For example, the first intermediate level 134A may be executed, followed by the second intermediate level 134B, and so on, until the complete evolutionary level 136 of the i-th slice is achieved. In various embodiments, the controller 500 (e.g., via the processing device 505, the driver component element 515, etc.) may cause one or more qubit management systems 550 to manipulate the physical qubits 555 of the quantum computer 30 so that the interactive gates 122 are executed according to the intermediate levels 134 of the quantum circuit 100.

[0057] At step / operation 310, any desired measurement results of the fully evolved qubit set 144i corresponding to the i-th slice are captured. For example, the controller 500 (e.g., via the processing device 505, the driver component element 515, etc.) can cause one or more qubit management systems 550 to manipulate the physical qubits 555 of the quantum computer 30 so that any desired measurement results of the physical qubits 555 that have evolved (e.g., along the system qubit line 120) to the fully executed level 136 of the i-th slice are captured. Step / operation 310 can, but does not have to, begin after completing step 308, and can, for example, be implemented simultaneously with step / operation 308 so that measurements can be made at the intermediate circuit level 134.

[0058] At step / operation 312 , the controller 500 (eg, via the processing device 505 , etc.) may determine whether the index i is equal to n, ie, the number of slices of the circuit. When it is determined at step / operation 312 that the index i is not equal to n, the process proceeds to step / operation 314 .

[0059] At step / operation 314, the physical qubits that are to be evolved along the system qubit wire 120 of the full execution level qubit set 144i of the i-th slice are reset so that they can be initialized in the base level 130 of the (i+1)-th slice 140(i+1). For example, the controller 500 (e.g., via the processing device 505, the driver component element 515, etc.) can cause one or more qubit management systems 550 to manipulate the physical qubits 555 of the quantum computer 30 so that the physical qubits that are to be evolved along the system qubit wire 120 of the full execution level qubit set 144i of the i-th slice are reset so that they can be initialized to the system qubit wire of the base level qubit set 142(i+1) of the (i+1)-th slice. For example, once the physical qubits have been fully evolved along the system qubit wire 120 (e.g., reaching the fully evolved level 136), the physical qubit 555 can be reinitialized to another system qubit wire starting from a subsequent slice of the quantum circuit. In this way, physical qubits may be reused within an execution of a quantum circuit 100 to reduce the total number of physical qubits 555 required to execute the quantum circuit.

[0060] At step / operation 316, the controller 500 increments the index i. For example, the controller (eg, via the processing device 505, etc.) may increment the index i to a value of i+1. For example, the index i may be incremented and the next slice may be performed.

[0061] When the index i=n (the number of slices of the quantum circuit 100) is determined by the controller 500 at step / operation 312, the process continues to step / operation 318. At step / operation 318, the execution of the quantum circuit 100 is determined to be complete, and the controller 500 may provide the results of the execution of the quantum circuit 100. For example, the controller 500 (e.g., by the processing device 505 via the communication interface 520, etc.) may provide the measurement results captured during the execution of the quantum circuit 100. For example, the controller 500 may provide the results of executing the quantum circuit 100 so that the user computing entity 10 receives the results of executing the quantum circuit 100. The user computing entity 10 may then use the results as input to one or more processes (e.g., to analyze the results of executing the quantum circuit, etc.), cause at least a portion of the results of executing the quantum circuit 100 to be displayed and / or provided via a user interface of the user computing entity 10 (e.g., via the display 416), cause at least a portion of the results of executing the quantum circuit 100 to be stored in a memory (e.g., memory 422, 424), etc.

[0062] V. Technical Advantages

[0063] Various embodiments use quantum computers with a relatively small number of potentially noisy qubits to provide a technical solution to the technical problem of simulating the dynamics of a domain under the influence of a local operator (e.g., a local Hamiltonian). For example, various embodiments allow the use of a certain number of qubits (e.g., 1 to 500 qubits, 10 to 100 qubits, 20 to 50 qubits, etc.) to simulate the dynamics of a physical domain (e.g., a much larger physical domain) under the influence of a local operator (e.g., a local Hamiltonian) that is computationally very expensive and / or difficult to handle using classical computing means. In various embodiments, dividing a quantum circuit into slices and executing the slices sequentially allows the reuse of physical qubits along various qubit traces, thereby reducing the number of physical qubits required to perform a calculation (e.g., execute a quantum circuit). Various embodiments effectively reduce the dimensionality of the system and / or domain being simulated. For example, in an exemplary embodiment, only a small number (independent of the length L) may be used. x ) to simulate a physical quantum bit of length L x In another example, in an exemplary embodiment, a one-dimensional system with L y proportional (which can be chosen to be two lengths L x , L y The smaller / shorter of x Unrelated multiple qubits to simulate two-dimensional systems and / or dimensions L x , L y Thus, embodiments provide improvements to the capabilities of quantum computers by using fewer qubits to perform complex calculations.

[0064] VI. Exemplary User Computing Entities

[0065] Figure 5 An illustrative schematic diagram of an exemplary user computing entity 10 that can be used in conjunction with embodiments of the present invention is provided. In various embodiments, the user computing entity 10 is configured to allow a user (e.g., via a user interface of the user computing entity 10) to provide input to the quantum computer 30, and to receive, view, and / or perform similar processing on output from the quantum computer 30.

[0066] like Figure 5As shown, the user computing entity 10 may include an antenna 412, a transmitter 404 (e.g., a radio component), a receiver 406 (e.g., a radio component), and a processing element 408, which provides signals to the transmitter 404 and receives signals from the receiver 406. The signals provided to the transmitter 404 and the receiver 406, respectively, and received from the transmitter and the receiver may include signaling information / data according to the air interface standard of the applicable wireless system to communicate with various entities such as the controller 500 of the quantum computer 30. In this regard, the user computing entity 10 may be capable of operating using one or more air interface standards, communication protocols, modulation types, and access types. More specifically, the user computing entity 10 may operate according to any of a plurality of wireless communication standards and protocols. In certain embodiments, the user computing device 10 may operate in accordance with a variety of wireless communication standards and protocols, such as General Packet Radio Service (GPRS), Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 2000 (CDMA2000), CDMA2000 1X (1xRTT), Wideband Code Division Multiple Access (WCDMA), Global System for Mobile Communications (GSM), Enhanced Data Rates for GSM Evolution (EDGE), Time Division Synchronous Code Division Multiple Access (TD-SCDMA), Long Term Evolution (LTE), Evolved Universal Terrestrial Radio Access Network (E-UTRAN), Evolution Data Optimized (EVDO), High Speed ​​Packet Access (HSPA), High Speed ​​Downlink Packet Access (HSDPA), IEEE 802.11 (Wi-Fi), Wi-Fi Direct, 802.16 (WiMAX), Ultra Wideband (UWB), Infrared (IR) protocol, Near Field Communication (NFC) protocol, Wibree, Bluetooth protocol, Wireless Universal Serial Bus (USB) protocol, and / or any other wireless protocol.

[0067] Via these communication standards and protocols, the user computing entity 10 may communicate with various other entities using concepts such as Unstructured Supplementary Service Message / Data (USSD), Short Message Service (SMS), Multimedia Message Service (MMS), Dual Tone Multi-Frequency Signaling (DTMF), and / or Subscriber Identity Module Dial Pad (SIM Dial Pad). The user computing entity 10 may also download changes, add-ons, and updates, such as to its firmware, software (e.g., including executable instructions, applications, program modules), and operating system.

[0068] According to one embodiment, the user computing entity 10 may include location determination aspects, devices, modules, functional accessories and / or similar words used interchangeably herein. For example, the user computing entity 10 may include outdoor positioning aspects, such as a positioning module suitable for obtaining, for example, latitude, longitude, altitude, geocoding, heading, position, direction, speed, UTC, date and / or various other information / data. In one embodiment, the positioning module can obtain data by identifying the number of satellites in the field of view and the relative positions of these satellites, sometimes referred to as ephemeris data. These satellites can be a variety of different satellites, including LEO satellite systems, DOD satellite systems, the European Union Galileo positioning system, China's Beidou satellite navigation system, India's regional navigation satellite system, etc. Alternatively, the location information / data can be determined by triangulating the user computing entity 10 positioning in combination with various other systems (including cellular towers, Wi-Fi access points, etc.). Similarly, the user computing entity 10 may include indoor positioning aspects, such as a positioning module suitable for obtaining, for example, latitude, longitude, altitude, geocoding, heading, position, direction, speed, time, date and / or various other information / data. Some of these indoor aspects may use various positioning or location technologies, including RFID tags, indoor beacons or transmitters, Wi-Fi access points, cellular towers, nearby computing devices (e.g., smartphones, laptops), etc. For example, such technologies may include iBeacons, Gimbal proximity beacons, BLE transmitters, near field communication (NFC) transmitters, etc. These indoor positioning aspects may be used in a variety of settings to determine the location of someone or something to within inches or centimeters.

[0069] The user computing entity 10 may also include a user interface device including one or more user input / output interfaces (e.g., a display 416 and / or a speaker / speaker driver coupled to the processing element 408 and a touch screen, keyboard, mouse, and / or microphone coupled to the processing element 408). For example, the user output interface may be configured to provide an application, browser, user interface, dashboard, screen, web page, page, and / or similar words used interchangeably herein executed on and / or accessible via the user computing entity 10 to display or audibly present information / data and for user interaction with the application, etc. via one or more user input interfaces. The user input interface may include any of a number of devices that allow the user computing entity 10 to receive data, such as a keypad 418 (hard or soft), a touch display, a sound / voice or motion interface, a scanner, a reader, or other input device. In an embodiment including a keypad 418, the keypad 418 may include (or cause to be displayed) conventional numeric keys (0-9) and related keys (#, *) and other keys for operating the user computing entity 10, and may include a complete set of alphabetic keys or a set of keys that can be activated to provide a complete set of alphanumeric keys. In addition to providing input, the user input interface may also be used, for example, to activate or deactivate certain functions, such as a screen saver and / or sleep mode. Through such input, the user computing entity 10 may collect information / data, user interaction / input, etc.

[0070] The user computing entity 10 may also include an embedded and / or removable volatile storage device or memory 422 and / or a non-volatile storage device or memory 424. For example, the non-volatile memory may be a ROM, a PROM, an EPROM, an EEPROM, a flash memory, an MMC, an SD memory card, a memory stick, a CBRAM, a PRAM, a FeRAM, a RRAM, a SONOS, a racetrack memory, etc. The volatile memory may be a RAM, a DRAM, a SRAM, a FPM DRAM, an EDO DRAM, a SDRAM, a DDR SDRAM, a DDR2 SDRAM, a DDR3 SDRAM, a RDRAM, a RIMM, a DIMM, a SIMM, a VRAM, a cache memory, a register memory, etc. The volatile and non-volatile storage devices or memories may store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, byte code, compiled code, interpreted code, machine code, executable instructions, etc. to implement the functions of the user computing entity 10.

[0071] In an exemplary embodiment, user computing entities 10 may communicate with other user computing entities 10 and / or a controller 500 of a quantum computer.

[0072] VII. Exemplary Quantum Computers

[0073] like Figure 6 As shown, in various embodiments, the quantum computer 30 includes a controller 30 and one or more qubit management systems 550. For example, the one or more qubit management systems 550 may include a thermal control system (e.g., a cryogenic cooling system), a vacuum system (e.g., a pressure control system), a qubit confinement system (e.g., in the case of a trapped ion quantum computer, an ion trap and a voltage source connected to the ion trap), one or more gate systems (e.g., in the case of a trapped ion quantum computer, a laser and corresponding optical devices), a measurement system (e.g., in the case of a trapped ion quantum computer, including optical devices, photodetectors, etc.), etc. The controller 30 is configured and / or programmed to cause the one or more qubit management systems 550 to manipulate and / or evolve one or more qubits according to a quantum circuit, thereby enabling the quantum computer 30 to perform calculations, simulations, generative models, etc. In various embodiments, the qubit management system 550 is configured to control, contain, manipulate, manage, and / or cause the controlled evolution of one or more physical qubits 555 of the quantum computer 30.

[0074] In various embodiments, the controller 500 may include various controller elements, including a processing device 505, a memory 510, a driver controller element t15, a communication interface 520, an analog-to-digital converter element 525, and the like. For example, the processing device 505 may include a programmable logic device (CPLD), a microprocessor, a co-processing entity, an application specific instruction set processor (ASIP), an integrated circuit, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic array (PLA), a hardware accelerator, other processing devices and / or circuits, controllers, and the like. The term circuit may refer to a complete hardware implementation or a combination of hardware and a computer program product. In an exemplary embodiment, the processing device 505 of the controller 500 includes a clock and / or communicates with a clock. For example, memory 510 may include non-transitory memory, such as volatile and / or non-volatile memory storage devices, such as hard disks, ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. In various embodiments, memory 510 may store qubit records corresponding to qubits of a quantum computer (e.g., in a qubit record data storage device, a qubit record database, a qubit record table, etc.), calibration tables, executable queues, computer program code (e.g., in one or more computer languages, a dedicated controller language, etc.), etc. In an exemplary embodiment, execution of at least a portion of the computer program code stored in memory 510 (e.g., by processing device 505) causes controller 500 to perform one or more steps, operations, processes, procedures, etc. described herein for receiving a quantum circuit, executing the quantum circuit (e.g., slice by slice), and providing results of executing the quantum circuit.

[0075] In various embodiments, the driver controller element 515 may include one or more drivers and / or controller elements each configured to control one or more drivers. In various embodiments, the driver controller element 515 may include a driver and / or a driver controller. For example, the driver controller may be configured to cause one or more corresponding drivers to operate one or more corresponding drivers according to executable instructions, commands, etc. scheduled and executed by the controller 500 (e.g., by the processing device 505). In various embodiments, the driver controller element 515 may enable the controller 500 to operate one or more qubit management systems 550 to manipulate, manage, and / or evolve one or more physical qubits 555 of the quantum computer according to the quantum circuit 100. In various embodiments, the driver may be a laser driver; a vacuum component driver; a driver for controlling the flow of current and / or voltage applied to DC, RF, and / or other electrodes used to maintain and / or control, manage, and / or evolve the physical qubit 555; a cryogenic and / or vacuum system component driver; and the like. In various embodiments, the controller 500 includes a device for transmitting and / or receiving signals from one or more optical receiver components, such as a camera, a MEMs camera, a CCD camera, a photodiode, a photomultiplier tube, etc. For example, the controller 500 may include one or more analog-to-digital converter elements 525, which are configured to receive signals from one or more optical receiver components, calibration sensors, etc. In various embodiments, the controller 500 may include a communication interface 520 for interacting and / or communicating with the user computing entity 10. For example, the controller 500 may include a communication interface 520 for receiving executable instructions, command sets, etc. from the user computing entity 10, and providing the user computing entity 10 with outputs received from the quantum computer 30 (e.g., from the optical collection system) and / or the results of processing the outputs. In various embodiments, the user computing entity 10 and the controller 500 may communicate via a direct wired and / or wireless connection and / or one or more wired and / or wireless networks.

[0076] It should be understood that one or more of the components of the controller 500 may be located away from other controller 500 components, such as in a distributed system. In addition, one or more of these components may be combined, and additional components that perform the functions described herein may be included in the controller 500. Therefore, the controller 500 may be adapted to accommodate a variety of needs and situations. For example, although described as a single computing entity, in an exemplary embodiment, the controller 30 may be a distributed system and / or include multiple computing entities. For example, in an exemplary embodiment, the controller 500 may include a server and custom-built hardware components configured to drive and / or control the operation of one or more quantum bit management systems 550.

[0077] in conclusion

[0078] Many modifications and other embodiments of the invention set forth herein will occur to those skilled in the art having the benefit of the foregoing description and the teachings presented in the associated drawings. Therefore, it should be understood that the invention is not limited to the particular embodiments disclosed, and modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

1. A method, the method comprising: Receiving, by a controller of a quantum computer, a quantum circuit, the quantum computer including a qubit management system and a plurality of physical qubits, the quantum circuit including a plurality of circuit slices, wherein a first slice of the plurality of circuit slices includes a causal cone of a first system qubit line at a fully evolved level of the quantum circuit, and an i-th slice of the plurality of circuit slices is defined to include all gates not within a causal cone of any system qubit line of the quantum circuit, the system qubit line reaching the fully evolved level of the quantum circuit in slice i-j, where 0≤j<i is an integer, but now executing the gates by activating one or more physical qubits that have reached the fully evolved level during the execution of slice i-1, have optionally been measured, and are reset to the system qubit line at a base level of slice i; Causing, by the controller, the i-th slice of the quantum circuit to be executed using the physical qubits of the quantum computer; Optionally measuring, by the controller, physical qubits that evolve as the system qubits fully evolved via the execution of the i-th slice, and re-initializing and re-introducing them to the system qubit line at the base level of the i+m-th slice, where m is a positive integer; And Causing, by the controller, the quantum computer to execute the i+m-th slice of the quantum circuit using the physical qubits.

2. The method according to claim 1, wherein executing the i-th slice of the quantum circuit includes executing all gates for which the incoming and outgoing lines are within the i-th slice, so as to propagate the system qubits forward in time.

3. The method according to claim 2, wherein the quantum circuit includes at least one auxiliary line, and executing the i-th slice of the quantum circuit includes interacting, via a unitary gate, one or more system qubits at the bottom of the i-th slice with at least one auxiliary qubit, so as to introduce an initial correlation between the one or more system qubits at the bottom of the i-th slice and system qubits at the bottom of one or more other slices.

4. The method according to claim 1, wherein the quantum circuit encodes interactions governed by a Hamiltonian characterized by local interactions.

5. The method according to claim 1, wherein each system qubit line corresponds to a degree of freedom associated with a section of the physical domain being simulated.

6. The method according to claim 5, wherein executing the i-th slice of the quantum circuit includes evolving the degree of freedom according to an operator.

7. The method according to claim 6, wherein the operator is a Hamiltonian.

8. The method according to claim 5, wherein the physical domain is one of a one-dimensional physical domain, a two-dimensional physical domain, or a three-dimensional physical domain.

9. The method according to claim 5, wherein the quantum circuit simulates the dynamics of the evolution of a quantum state defined on a lattice representing the physical domain.

10. The method of claim 5, further comprising performing one or more measurements of at least one physical qubit in the plurality of qubits to determine a value corresponding to at least one degree of freedom within the physical domain.

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