Holographic quantum dynamics simulation

Abstract

A quantum computer controller receives a quantum circuit comprising circuit slices. The first slice comprises a past causal cone of a first system qubit wire at a fully evolved level of the circuit. An i-th slice contains all gates that are within a past causal cone of a system qubit wire that reaches the fully evolved level in slice i that are not in the past causal cone of a system qubit wire that reaches the fully evolved level in slice i−j. The controller causes execution of the i-th slice using the physical qubits; causes a physical qubit that was evolved along a system qubit wire to the fully evolved level via execution of the i-th slice to be reinitialized and reintroduced onto a system qubit wire at a base level of the i+m-th slice; and causes the quantum computer to use the physical qubit to execute the i+m-th slice.

That which is claimed: 
     
         1 . A method for generating a quantum circuit, the method comprising:
 defining a plurality of system qubit wires and interactions therebetween configured for performing a quantum algorithm;   identifying a past causal cone of a first system qubit wire of the plurality of system qubit wires;   defining a first slice containing the past causal cone of the first system qubit wire;   identifying a second causal cone of a second system qubit wire of the plurality of system qubit wires; and   defining a second slice containing a portion of the second causal cone that is not within the first slice.   
     
     
         2 . The method of  claim 1 , wherein the quantum circuit is configured such that each gate of the first slice is performed prior to beginning to perform the second slice. 
     
     
         3 . The method of  claim 1 , wherein the quantum circuit is configured such that executing an i-th slice of the quantum circuit comprises executing all gates for which incoming and outgoing wires lie within the i-th slice to propagate the system qubits forward in a dimension. 
     
     
         4 . The method of  claim 3 , wherein the quantum circuit comprises at least one ancilla wire and the quantum circuit is configured such that an i-th slice of the quantum circuit comprises interacting one or more system qubits at a bottom of the i-th slice with at least one ancilla qubit via unitary gates in order to introduce initial correlations 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. 
     
     
         5 . The method of  claim 1 , wherein the quantum circuit encodes interactions governed by a Hamiltonian characterized by local interactions. 
     
     
         6 . The method of  claim 1 , wherein each system qubit wire corresponds to a degree of freedom associated with a section of a physical domain being simulated. 
     
     
         7 . The method of  claim 6 , wherein an i-th slice of the quantum circuit is configured to, upon execution by a quantum processor, evolve the degree of freedom in accordance with an operator. 
     
     
         8 . The method of  claim 7 , wherein the operator is a Hamiltonian. 
     
     
         9 . The method of  claim 6 , wherein the physical domain is one of a one dimensional, two dimensional, or three dimensional physical domain. 
     
     
         10 . The method of  claim 6 , wherein the quantum circuit simulates the dynamics of the evolution of quantum states defined on a lattice representing the physical domain. 
     
     
         11 . The method of  claim 6 , further comprising causing the quantum circuit to be configured to cause measurement of at least one physical qubit of the plurality of qubits to determine a value corresponding to at least one degree of freedom within the physical domain. 
     
     
         12 . The method of  claim 1 , wherein at least one system qubit wire of the quantum circuit extends through multiple slices of quantum circuit. 
     
     
         13 . A computing entity comprising at least one processor and a memory storing computer-executable instructions, the computer executable-instructions configured, when executed by the at least one processor, to cause the apparatus to at least:
 generate a quantum circuit divided into slices by:
 defining a plurality of system qubit wires and interactions therebetween configured for performing a quantum algorithm; 
 identifying a past causal cone of a first system qubit wire of the plurality of system qubit wires; 
 defining a first slice containing the past causal cone of the first system qubit wire; 
 identifying a second causal cone of a second system qubit wire of the plurality of system qubit wires; and 
 defining a second slice containing a portion of the second causal cone that is not within the first slice. 
   
     
     
         14 . The computing entity of  claim 13 , wherein the quantum circuit is configured such that each gate of the first slice is performed prior to beginning to perform the second slice. 
     
     
         15 . The computing entity of  claim 13 , wherein the quantum circuit is configured such that executing an i-th slice of the quantum circuit comprises executing all gates for which incoming and outgoing wires lie within the i-th slice to propagate the system qubits forward in a dimension. 
     
     
         16 . The computing entity of  claim 15 , wherein the quantum circuit comprises at least one ancilla wire and the quantum circuit is configured such that an i-th slice of the quantum circuit comprises interacting one or more system qubits at a bottom of the i-th slice with at least one ancilla qubit via unitary gates in order to introduce initial correlations 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. 
     
     
         17 . The computing entity of  claim 13 , wherein the quantum circuit encodes interactions governed by an operator characterized by local interactions. 
     
     
         18 . The computing entity of  claim 13 , wherein each system qubit wire corresponds to a degree of freedom associated with a section of a physical domain being simulated. 
     
     
         19 . The computing entity of  claim 18 , wherein an i-th slice of the quantum circuit is configured to, upon execution by a quantum processor, evolve the degree of freedom in accordance with an operator. 
     
     
         20 . The computing entity of  claim 18 , wherein the quantum circuit simulates the dynamics of the evolution of quantum states defined on a lattice representing the physical domain.