Method and system for optimal decomposition of single-qubit quantum circuits using standard quantum gates

Abstract

The current application is directed to methods and systems which produce a design for an optimal approximation of a target single-qubit quantum operation comprising a representation of a quantum-circuit generated from a discrete, quantum-gate basis. The discrete quantum-gate basis comprises standard, implementable quantum gates. The methods and systems employ a database of canonical-form quantum circuits, an efficiently organized canonical-form quantum-circuit, and efficient searching to identify a minimum-cost design for decomposing and approximating an input target quantum operation.

1 . A method, carried out in a computer system, that creates a design for a target quantum operation u in a standard-quantum-gate basis, the method comprising:
 receiving, by the computer system, the target quantum operation u;   searching, by the computer system, a database of canonical-form quantum circuits to identify a canonical-form quantum circuit from which a minimum-cost design within a distance-metric-value distance to the target quantum operation u can be generated;   generating, by the computer system, the minimum cost design from the identified canonical-form quantum circuit; and   storing, by the computer system, the generated minimum-cost design in one or more of an electronic memory and physical data-storage device.   
     
     
         2 . The method of  claim 1  wherein each canonical-form quantum circuit is represented as a sequence of representations of TH and SH gates that contains no adjacent SH gates, that ends in TH, and in which no SH gate occurs before the fifth gate. 
     
     
         3 . The method of  claim 1  wherein the database of canonical-form quantum circuits is partitioned into one or more trace-level partitions, each associated with a range of absolute trace-level values. 
     
     
         4 . The method of  claim 3  wherein the trace-level partitions are distributed across multiple computational and data-storage nodes of a distributed quantum-circuit-design system. 
     
     
         5 . The method of  claim 1  wherein searching the database of canonical-foam quantum circuits to identify the canonical-form quantum circuit from which the minimum-cost design within the distance-metric-value distance to the target quantum operation u can be generated further comprises:
 transforming the target quantum operation u by a right-coset operation followed by an adjoint operation to generate up to a first maximum number of search neighborhoods within a trace space; and 
 searching the up to the first maximum number of search neighborhoods within the trace space to identify the minimum-cost design within the distance-metric-value distance to the target quantum operation u. 
 
     
     
         6 . The method of  claim 5   wherein the right-coset operation generates up to a second maximum number of trace-level neighborhoods;   wherein the adjoint operation generates up to a third maximum number of symmetrically related search neighborhoods within each trace-level neighborhood; and   wherein the first maximum number of search neighborhoods is the product of the second and third maximum numbers.   
     
     
         7 . The method of  claim 5  wherein the right-hand coset and adjoint operations employ elements of the CPH group. 
     
     
         8 . The method of  claim 1  wherein generating the minimum cost design from the identified canonical-form quantum circuit further comprises:
 applying an adjoint operation followed by a right-coset operation to the identified canonical-form quantum circuit. 
 
     
     
         9 . A database-search-based quantum-circuit design system comprising:
 a number of distributed system nodes, each including one or more processors, one or more electronic memories, and one or more physical data-storage devices; and   computer instructions stored in one or more electronic memories and physical data-storage devices within each system node that, when executed on the one or more processors within the system node, control the system node to
 receive a target quantum operation u; 
 search a portion of a database of canonical-form quantum circuits to identify a canonical-form quantum circuit from which a minimum-cost design within a distance-metric-value distance to the target quantum operation u can be generated; and 
 when the canonical-form quantum circuit is identified,
 generate the minimum cost design, from the identified canonical-form quantum circuit, 
 store the generated minimum-cost design in one or more of an electronic memory and physical data-storage device, and 
 provide an indication that the canonical-form quantum circuit is identified. 
 
   
     
     
         10 . The database-search-based quantum-circuit design system of  claim 9  wherein each canonical-form quantum circuit is represented as a sequence of representations of TH and SH gates that that contains no adjacent SH gates, that ends in TH, and in which no SH gate occurs before the fifth gate. 
     
     
         11 . The database-search-based quantum-circuit design system of  claim 9  wherein the database of canonical-fore quantum circuits is partitioned into one or more trace-level partitions, each associated with a range of absolute trace-level values. 
     
     
         12 . The database-search-based quantum-circuit design system of  claim 11  wherein the trace-level partitions are distributed across the number of distributed system nodes. 
     
     
         13 . The database-search-based quantum-circuit design system of  claim 11  wherein the target quantum operation u is transformed by a right-coset operation to generate up to a first maximum number of trace-level neighborhoods and the up to the first maximum number of trace-level neighborhoods are each searched by one or more distributed system nodes. 
     
     
         14 . The database-search-based quantum-circuit design system of  claim 9  wherein a distributed system node searches a trace-level neighborhood by:
 transforming the target quantum operation u transformed by the right-coset operation by an adjoint operation to generate up to a second maximum number of search neighborhoods within a trace space; and 
 searching the up to the second maximum number of search neighborhoods within the trace space to identify the minimum-cost design within the distance-metric-value distance to the target quantum operation u. 
 
     
     
         15 . The database-search-based quantum-circuit design system of  claim 14  wherein the right-hand coset and adjoint operations employ elements of the CPH group. 
     
     
         16 . The database-search-based quantum-circuit design system of  claim 9  wherein a distributed system node generates the minimum cost design from the identified canonical-form quantum circuit by:
 applying an adjoint operation followed by a right-coset operation to the identified canonical-form quantum circuit. 
 
     
     
         17 . The database-search-based quantum-circuit design system of  claim 9  wherein the database-search-based quantum-circuit design system selects as a design for the target quantum operation u the minimum-cost design identified by the distributed system nodes. 
     
     
         18 . A database-search-based quantum-circuit design system comprising:
 one or more processors, one or more electronic memories, and one or more physical data-storage devices; and   computer instructions stored in one or more electronic memories and physical data-storage devices within each system node that, when executed on the one or more processors within the system node, control the system to
 receive the target quantum operation u; 
 search a database of canonical-form quantum circuits to identify a canonical-form quantum circuit from which a minimum-cost design within a distance-metric-value distance to the target quantum operation u can be generated; 
 generate the minimum cost design from the identified canonical-form quantum circuit; and 
 store the generated minimum-cost design in one or more of an electronic memory and physical data-storage device. 
   
     
     
         19 . The database-search-based quantum-circuit design system of  claim 18  wherein each canonical-form quantum circuit is represented as a sequence of representations of TH and SH gates that that contains no adjacent SH gates, that ends in TH, and in which no SH gate occurs before the fifth gate. 
     
     
         20 . The method of  claim 1  wherein the database of canonical-foam quantum circuits is partitioned into one or more trace-level partitions, each associated with a range of absolute trace-level values.