{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:48:32Z","timestamp":1747190912232,"version":"3.40.5"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T00:00:00Z","timestamp":1663718400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum Engineering"],"published-print":{"date-parts":[[2022,9,21]]},"abstract":"<jats:p>Quantum computation based on a gate model is described. This model initially creates a superposition <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mi>|<\/a:mi>\n                        <a:msub>\n                           <a:mrow>\n                              <a:mi>\u03c8<\/a:mi>\n                           <\/a:mrow>\n                           <a:mrow>\n                              <a:mn>0<\/a:mn>\n                           <\/a:mrow>\n                        <\/a:msub>\n                        <a:mi>\u232a<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula> consisting of <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <c:mi>N<\/c:mi>\n                        <c:mo>=<\/c:mo>\n                        <c:msup>\n                           <c:mrow>\n                              <c:mn>2<\/c:mn>\n                           <\/c:mrow>\n                           <c:mrow>\n                              <c:mi>n<\/c:mi>\n                           <\/c:mrow>\n                        <\/c:msup>\n                     <\/c:math>\n                  <\/jats:inline-formula> states, and these states are labeled by an <jats:inline-formula>\n                     <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <e:mi>n<\/e:mi>\n                     <\/e:math>\n                  <\/jats:inline-formula> qubit index value <jats:inline-formula>\n                     <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <g:mi>j<\/g:mi>\n                     <\/g:math>\n                  <\/jats:inline-formula>. Two working qubits <jats:inline-formula>\n                     <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\">\n                        <i:mi>|<\/i:mi>\n                        <i:mn>0<\/i:mn>\n                        <i:msub>\n                           <i:mrow>\n                              <i:mi>\u232a<\/i:mi>\n                           <\/i:mrow>\n                           <i:mrow>\n                              <i:mi>w<\/i:mi>\n                              <i:mi>k<\/i:mi>\n                              <i:mn>0<\/i:mn>\n                           <\/i:mrow>\n                        <\/i:msub>\n                     <\/i:math>\n                  <\/jats:inline-formula> and <jats:inline-formula>\n                     <k:math xmlns:k=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\">\n                        <k:mi>|<\/k:mi>\n                        <k:mn>0<\/k:mn>\n                        <k:msub>\n                           <k:mrow>\n                              <k:mi>\u232a<\/k:mi>\n                           <\/k:mrow>\n                           <k:mrow>\n                              <k:mi>w<\/k:mi>\n                              <k:mi>k<\/k:mi>\n                              <k:mn>1<\/k:mn>\n                           <\/k:mrow>\n                        <\/k:msub>\n                     <\/k:math>\n                  <\/jats:inline-formula> are added for a measurement. Moreover, one marking qubit <jats:inline-formula>\n                     <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\">\n                        <m:mi>|<\/m:mi>\n                        <m:mn>0<\/m:mn>\n                        <m:msub>\n                           <m:mrow>\n                              <m:mi>\u232a<\/m:mi>\n                           <\/m:mrow>\n                           <m:mrow>\n                              <m:mi>m<\/m:mi>\n                              <m:mi>k<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:msub>\n                     <\/m:math>\n                  <\/jats:inline-formula> is added to discriminate between states in a superposition. Thus, <jats:inline-formula>\n                     <o:math xmlns:o=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\">\n                        <o:mi>|<\/o:mi>\n                        <o:msub>\n                           <o:mrow>\n                              <o:mi>\u03c8<\/o:mi>\n                           <\/o:mrow>\n                           <o:mrow>\n                              <o:mn>1<\/o:mn>\n                           <\/o:mrow>\n                        <\/o:msub>\n                        <o:mi>\u232a<\/o:mi>\n                        <o:mo>=<\/o:mo>\n                        <o:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <o:mrow>\n                              <o:mrow>\n                                 <o:mn>1<\/o:mn>\n                                 <o:mo>\/<\/o:mo>\n                                 <o:mrow>\n                                    <o:msqrt>\n                                       <o:mi>N<\/o:mi>\n                                    <\/o:msqrt>\n                                 <\/o:mrow>\n                              <\/o:mrow>\n                           <\/o:mrow>\n                        <\/o:mfenced>\n                        <o:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <o:mrow>\n                              <o:mstyle displaystyle=\"true\">\n                                 <o:msubsup>\n                                    <o:mrow>\n                                       <o:mo stretchy=\"false\">\u2211<\/o:mo>\n                                    <\/o:mrow>\n                                    <o:mrow>\n                                       <o:mi>j<\/o:mi>\n                                       <o:mo>=<\/o:mo>\n                                       <o:mn>0<\/o:mn>\n                                    <\/o:mrow>\n                                    <o:mrow>\n                                       <o:mi>N<\/o:mi>\n                                       <o:mo>\u2212<\/o:mo>\n                                       <o:mn>1<\/o:mn>\n                                    <\/o:mrow>\n                                 <\/o:msubsup>\n                                 <o:mrow>\n                                    <o:mrow>\n                                       <o:mi>|<\/o:mi>\n                                       <o:mrow>\n                                          <o:mi>j<\/o:mi>\n                                          <o:mi>\u232a<\/o:mi>\n                                       <\/o:mrow>\n                                    <\/o:mrow>\n                                 <\/o:mrow>\n                              <\/o:mstyle>\n                           <\/o:mrow>\n                        <\/o:mfenced>\n                        <o:mo>\u2297<\/o:mo>\n                        <o:mi>|<\/o:mi>\n                        <o:mn>0<\/o:mn>\n                        <o:msub>\n                           <o:mrow>\n                              <o:mi>\u232a<\/o:mi>\n                           <\/o:mrow>\n                           <o:mrow>\n                              <o:mi>w<\/o:mi>\n                              <o:mi>k<\/o:mi>\n                              <o:mn>0<\/o:mn>\n                           <\/o:mrow>\n                        <\/o:msub>\n                        <o:mo>\u2297<\/o:mo>\n                        <o:mi>|<\/o:mi>\n                        <o:mn>0<\/o:mn>\n                        <o:msub>\n                           <o:mrow>\n                              <o:mi>\u232a<\/o:mi>\n                           <\/o:mrow>\n                           <o:mrow>\n                              <o:mi>w<\/o:mi>\n                              <o:mi>k<\/o:mi>\n                              <o:mn>1<\/o:mn>\n                           <\/o:mrow>\n                        <\/o:msub>\n                        <o:mo>\u2297<\/o:mo>\n                        <o:mi>|<\/o:mi>\n                        <o:mrow>\n                           <o:mn>0<\/o:mn>\n                           <o:msub>\n                              <o:mrow>\n                                 <o:mi>\u232a<\/o:mi>\n                              <\/o:mrow>\n                              <o:mrow>\n                                 <o:mi>m<\/o:mi>\n                                 <o:mi>k<\/o:mi>\n                              <\/o:mrow>\n                           <\/o:msub>\n                        <\/o:mrow>\n                     <\/o:math>\n                  <\/jats:inline-formula>. The Hadamard transformation is applied to <jats:inline-formula>\n                     <y:math xmlns:y=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\">\n                        <y:mi>|<\/y:mi>\n                        <y:mn>0<\/y:mn>\n                        <y:msub>\n                           <y:mrow>\n                              <y:mi>\u232a<\/y:mi>\n                           <\/y:mrow>\n                           <y:mrow>\n                              <y:mi>w<\/y:mi>\n                              <y:mi>k<\/y:mi>\n                              <y:mn>0<\/y:mn>\n                           <\/y:mrow>\n                        <\/y:msub>\n                     <\/y:math>\n                  <\/jats:inline-formula> and <jats:inline-formula>\n                     <ab:math xmlns:ab=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\">\n                        <ab:mi>|<\/ab:mi>\n                        <ab:mn>0<\/ab:mn>\n                        <ab:msub>\n                           <ab:mrow>\n                              <ab:mi>\u232a<\/ab:mi>\n                           <\/ab:mrow>\n                           <ab:mrow>\n                              <ab:mi>w<\/ab:mi>\n                              <ab:mi>k<\/ab:mi>\n                              <ab:mn>1<\/ab:mn>\n                           <\/ab:mrow>\n                        <\/ab:msub>\n                     <\/ab:math>\n                  <\/jats:inline-formula>. <jats:inline-formula>\n                     <cb:math xmlns:cb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\">\n                        <cb:mi>|<\/cb:mi>\n                        <cb:msub>\n                           <cb:mrow>\n                              <cb:mi>\u03c8<\/cb:mi>\n                           <\/cb:mrow>\n                           <cb:mrow>\n                              <cb:mn>2<\/cb:mn>\n                           <\/cb:mrow>\n                        <\/cb:msub>\n                        <cb:mi>\u232a<\/cb:mi>\n                        <cb:mo>=<\/cb:mo>\n                        <cb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <cb:mrow>\n                              <cb:mrow>\n                                 <cb:mn>1<\/cb:mn>\n                                 <cb:mo>\/<\/cb:mo>\n                                 <cb:mrow>\n                                    <cb:msqrt>\n                                       <cb:mi>N<\/cb:mi>\n                                    <\/cb:msqrt>\n                                 <\/cb:mrow>\n                              <\/cb:mrow>\n                           <\/cb:mrow>\n                        <\/cb:mfenced>\n                        <cb:msup>\n                           <cb:mrow>\n                              <cb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <cb:mrow>\n                                    <cb:mrow>\n                                       <cb:mn>1<\/cb:mn>\n                                       <cb:mo>\/<\/cb:mo>\n                                       <cb:mrow>\n                                          <cb:msqrt>\n                                             <cb:mn>2<\/cb:mn>\n                                          <\/cb:msqrt>\n                                       <\/cb:mrow>\n                                    <\/cb:mrow>\n                                 <\/cb:mrow>\n                              <\/cb:mfenced>\n                           <\/cb:mrow>\n                           <cb:mrow>\n                              <cb:mn>2<\/cb:mn>\n                           <\/cb:mrow>\n                        <\/cb:msup>\n                        <cb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <cb:mrow>\n                              <cb:mstyle displaystyle=\"true\">\n                                 <cb:msubsup>\n                                    <cb:mrow>\n                                       <cb:mo stretchy=\"false\">\u2211<\/cb:mo>\n                                    <\/cb:mrow>\n                                    <cb:mrow>\n                                       <cb:mi>j<\/cb:mi>\n                                       <cb:mo>=<\/cb:mo>\n                                       <cb:mn>0<\/cb:mn>\n                                    <\/cb:mrow>\n                                    <cb:mrow>\n                                       <cb:mi>N<\/cb:mi>\n                                       <cb:mo>\u2212<\/cb:mo>\n                                       <cb:mn>1<\/cb:mn>\n                                    <\/cb:mrow>\n                                 <\/cb:msubsup>\n                                 <cb:mrow>\n                                    <cb:mrow>\n                                       <cb:mi>|<\/cb:mi>\n                                       <cb:mrow>\n                                          <cb:mi>j<\/cb:mi>\n                                          <cb:mi>\u232a<\/cb:mi>\n                                       <\/cb:mrow>\n                                    <\/cb:mrow>\n                                 <\/cb:mrow>\n                              <\/cb:mstyle>\n                           <\/cb:mrow>\n                        <\/cb:mfenced>\n                        <cb:mo>\u2297<\/cb:mo>\n                        <cb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <cb:mrow>\n                              <cb:mrow>\n                                 <cb:mi>|<\/cb:mi>\n                                 <cb:mrow>\n                                    <cb:mn>0<\/cb:mn>\n                                    <cb:msub>\n                                       <cb:mrow>\n                                          <cb:mi>\u232a<\/cb:mi>\n                                       <\/cb:mrow>\n                                       <cb:mrow>\n                                          <cb:mi>w<\/cb:mi>\n                                          <cb:mi>k<\/cb:mi>\n                                          <cb:mn>0<\/cb:mn>\n                                       <\/cb:mrow>\n                                    <\/cb:msub>\n                                 <\/cb:mrow>\n                              <\/cb:mrow>\n                              <cb:mo>+<\/cb:mo>\n                              <cb:mrow>\n                                 <cb:mi>|<\/cb:mi>\n                                 <cb:mrow>\n                                    <cb:mn>1<\/cb:mn>\n                                    <cb:msub>\n                                       <cb:mrow>\n                                          <cb:mi>\u232a<\/cb:mi>\n                                       <\/cb:mrow>\n                                       <cb:mrow>\n                                          <cb:mi>w<\/cb:mi>\n                                          <cb:mi>k<\/cb:mi>\n                                          <cb:mn>0<\/cb:mn>\n                                       <\/cb:mrow>\n                                    <\/cb:msub>\n                                 <\/cb:mrow>\n                              <\/cb:mrow>\n                           <\/cb:mrow>\n                        <\/cb:mfenced>\n                        <cb:mo>\u2297<\/cb:mo>\n                        <cb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <cb:mrow>\n                              <cb:mrow>\n                                 <cb:mi>|<\/cb:mi>\n                                 <cb:mrow>\n                                    <cb:mn>0<\/cb:mn>\n                                    <cb:msub>\n                                       <cb:mrow>\n                                          <cb:mi>\u232a<\/cb:mi>\n                                       <\/cb:mrow>\n                                       <cb:mrow>\n                                          <cb:mi>w<\/cb:mi>\n                                          <cb:mi>k<\/cb:mi>\n                                          <cb:mn>1<\/cb:mn>\n                                       <\/cb:mrow>\n                                    <\/cb:msub>\n                                 <\/cb:mrow>\n                              <\/cb:mrow>\n                              <cb:mo>+<\/cb:mo>\n                              <cb:mrow>\n                                 <cb:mi>|<\/cb:mi>\n                                 <cb:mrow>\n                                    <cb:mn>1<\/cb:mn>\n                                    <cb:msub>\n                                       <cb:mrow>\n                                          <cb:mi>\u232a<\/cb:mi>\n                                       <\/cb:mrow>\n                                       <cb:mrow>\n                                          <cb:mi>w<\/cb:mi>\n                                          <cb:mi>k<\/cb:mi>\n                                          <cb:mn>1<\/cb:mn>\n                                       <\/cb:mrow>\n                                    <\/cb:msub>\n                                 <\/cb:mrow>\n                              <\/cb:mrow>\n                           <\/cb:mrow>\n                        <\/cb:mfenced>\n                        <cb:mo>\u2297<\/cb:mo>\n                        <cb:mi>|<\/cb:mi>\n                        <cb:mn>0<\/cb:mn>\n                        <cb:msub>\n                           <cb:mrow>\n                              <cb:mi>\u232a<\/cb:mi>\n                           <\/cb:mrow>\n                           <cb:mrow>\n                              <cb:mi>m<\/cb:mi>\n                              <cb:mi>k<\/cb:mi>\n                           <\/cb:mrow>\n                        <\/cb:msub>\n                     <\/cb:math>\n                  <\/jats:inline-formula>. After a computation, a set of states is divided into two subsets; one is a subset bad (B) and the other is a subset good (G). <jats:inline-formula>\n                     <vb:math xmlns:vb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\">\n                        <vb:mi>|<\/vb:mi>\n                        <vb:msub>\n                           <vb:mrow>\n                              <vb:mi>\u03c8<\/vb:mi>\n                           <\/vb:mrow>\n                           <vb:mrow>\n                              <vb:mn>3<\/vb:mn>\n                           <\/vb:mrow>\n                        <\/vb:msub>\n                        <vb:mi>\u232a<\/vb:mi>\n                        <vb:mo>=<\/vb:mo>\n                        <vb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <vb:mrow>\n                              <vb:mrow>\n                                 <vb:mn>1<\/vb:mn>\n                                 <vb:mo>\/<\/vb:mo>\n                                 <vb:mrow>\n                                    <vb:msqrt>\n                                       <vb:mi>N<\/vb:mi>\n                                    <\/vb:msqrt>\n                                 <\/vb:mrow>\n                              <\/vb:mrow>\n                           <\/vb:mrow>\n                        <\/vb:mfenced>\n                        <vb:msup>\n                           <vb:mrow>\n                              <vb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <vb:mrow>\n                                    <vb:mrow>\n                                       <vb:mn>1<\/vb:mn>\n                                       <vb:mo>\/<\/vb:mo>\n                                       <vb:mrow>\n                                          <vb:msqrt>\n                                             <vb:mn>2<\/vb:mn>\n                                          <\/vb:msqrt>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                 <\/vb:mrow>\n                              <\/vb:mfenced>\n                           <\/vb:mrow>\n                           <vb:mrow>\n                              <vb:mn>2<\/vb:mn>\n                           <\/vb:mrow>\n                        <\/vb:msup>\n                        <vb:mfenced open=\"{\" close=\"}\" separators=\"|\">\n                           <vb:mrow>\n                              <vb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <vb:mrow>\n                                    <vb:mstyle displaystyle=\"true\">\n                                       <vb:msub>\n                                          <vb:mrow>\n                                             <vb:mo stretchy=\"false\">\u2211<\/vb:mo>\n                                          <\/vb:mrow>\n                                          <vb:mrow>\n                                             <vb:mi>j<\/vb:mi>\n                                             <vb:mo>\u2208<\/vb:mo>\n                                             <vb:mi>B<\/vb:mi>\n                                          <\/vb:mrow>\n                                       <\/vb:msub>\n                                       <vb:mrow>\n                                          <vb:mrow>\n                                             <vb:mi>|<\/vb:mi>\n                                             <vb:mrow>\n                                                <vb:mi>j<\/vb:mi>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                          <\/vb:mrow>\n                                       <\/vb:mrow>\n                                    <\/vb:mstyle>\n                                 <\/vb:mrow>\n                              <\/vb:mfenced>\n                              <vb:mo>\u2297<\/vb:mo>\n                              <vb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <vb:mrow>\n                                    <vb:mrow>\n                                       <vb:mi>|<\/vb:mi>\n                                       <vb:mrow>\n                                          <vb:mn>0<\/vb:mn>\n                                          <vb:msub>\n                                             <vb:mrow>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                             <vb:mrow>\n                                                <vb:mi>w<\/vb:mi>\n                                                <vb:mi>k<\/vb:mi>\n                                                <vb:mn>0<\/vb:mn>\n                                             <\/vb:mrow>\n                                          <\/vb:msub>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                    <vb:mo>+<\/vb:mo>\n                                    <vb:mrow>\n                                       <vb:mi>|<\/vb:mi>\n                                       <vb:mrow>\n                                          <vb:mn>1<\/vb:mn>\n                                          <vb:msub>\n                                             <vb:mrow>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                             <vb:mrow>\n                                                <vb:mi>w<\/vb:mi>\n                                                <vb:mi>k<\/vb:mi>\n                                                <vb:mn>0<\/vb:mn>\n                                             <\/vb:mrow>\n                                          <\/vb:msub>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                 <\/vb:mrow>\n                              <\/vb:mfenced>\n                              <vb:mo>\u2297<\/vb:mo>\n                              <vb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <vb:mrow>\n                                    <vb:mrow>\n                                       <vb:mi>|<\/vb:mi>\n                                       <vb:mrow>\n                                          <vb:mn>0<\/vb:mn>\n                                          <vb:msub>\n                                             <vb:mrow>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                             <vb:mrow>\n                                                <vb:mi>w<\/vb:mi>\n                                                <vb:mi>k<\/vb:mi>\n                                                <vb:mn>1<\/vb:mn>\n                                             <\/vb:mrow>\n                                          <\/vb:msub>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                    <vb:mo>+<\/vb:mo>\n                                    <vb:mrow>\n                                       <vb:mi>|<\/vb:mi>\n                                       <vb:mrow>\n                                          <vb:mn>1<\/vb:mn>\n                                          <vb:msub>\n                                             <vb:mrow>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                             <vb:mrow>\n                                                <vb:mi>w<\/vb:mi>\n                                                <vb:mi>k<\/vb:mi>\n                                                <vb:mn>1<\/vb:mn>\n                                             <\/vb:mrow>\n                                          <\/vb:msub>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                 <\/vb:mrow>\n                              <\/vb:mfenced>\n                              <vb:mo>\u2297<\/vb:mo>\n                              <vb:mrow>\n                                 <vb:mi>|<\/vb:mi>\n                                 <vb:mrow>\n                                    <vb:mn>0<\/vb:mn>\n                                    <vb:msub>\n                                       <vb:mrow>\n                                          <vb:mi>\u232a<\/vb:mi>\n                                       <\/vb:mrow>\n                                       <vb:mrow>\n                                          <vb:mi>m<\/vb:mi>\n                                          <vb:mi>k<\/vb:mi>\n                                       <\/vb:mrow>\n                                    <\/vb:msub>\n                                 <\/vb:mrow>\n                              <\/vb:mrow>\n                              <vb:mo>+<\/vb:mo>\n                              <vb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <vb:mrow>\n                                    <vb:mstyle displaystyle=\"true\">\n                                       <vb:msub>\n                                          <vb:mrow>\n                                             <vb:mo stretchy=\"false\">\u2211<\/vb:mo>\n                                          <\/vb:mrow>\n                                          <vb:mrow>\n                                             <vb:mi>j<\/vb:mi>\n                                             <vb:mo>\u2208<\/vb:mo>\n                                             <vb:mi>G<\/vb:mi>\n                                          <\/vb:mrow>\n                                       <\/vb:msub>\n                                       <vb:mrow>\n                                          <vb:mrow>\n                                             <vb:mi>|<\/vb:mi>\n                                             <vb:mrow>\n                                                <vb:mi>j<\/vb:mi>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                          <\/vb:mrow>\n                                       <\/vb:mrow>\n                                    <\/vb:mstyle>\n                                 <\/vb:mrow>\n                              <\/vb:mfenced>\n                              <vb:mo>\u2297<\/vb:mo>\n                              <vb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <vb:mrow>\n                                    <vb:mrow>\n                                       <vb:mi>|<\/vb:mi>\n                                       <vb:mrow>\n                                          <vb:mn>0<\/vb:mn>\n                                          <vb:msub>\n                                             <vb:mrow>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                             <vb:mrow>\n                                                <vb:mi>w<\/vb:mi>\n                                                <vb:mi>k<\/vb:mi>\n                                                <vb:mn>0<\/vb:mn>\n                                             <\/vb:mrow>\n                                          <\/vb:msub>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                    <vb:mo>+<\/vb:mo>\n                                    <vb:mrow>\n                                       <vb:mi>|<\/vb:mi>\n                                       <vb:mrow>\n                                          <vb:mn>1<\/vb:mn>\n                                          <vb:msub>\n                                             <vb:mrow>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                             <vb:mrow>\n                                                <vb:mi>w<\/vb:mi>\n                                                <vb:mi>k<\/vb:mi>\n                                                <vb:mn>0<\/vb:mn>\n                                             <\/vb:mrow>\n                                          <\/vb:msub>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                 <\/vb:mrow>\n                              <\/vb:mfenced>\n                              <vb:mo>\u2297<\/vb:mo>\n                              <vb:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <vb:mrow>\n                                    <vb:mrow>\n                                       <vb:mi>|<\/vb:mi>\n                                       <vb:mrow>\n                                          <vb:mn>0<\/vb:mn>\n                                          <vb:msub>\n                                             <vb:mrow>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                             <vb:mrow>\n                                                <vb:mi>w<\/vb:mi>\n                                                <vb:mi>k<\/vb:mi>\n                                                <vb:mn>1<\/vb:mn>\n                                             <\/vb:mrow>\n                                          <\/vb:msub>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                    <vb:mo>+<\/vb:mo>\n                                    <vb:mrow>\n                                       <vb:mi>|<\/vb:mi>\n                                       <vb:mrow>\n                                          <vb:mn>1<\/vb:mn>\n                                          <vb:msub>\n                                             <vb:mrow>\n                                                <vb:mi>\u232a<\/vb:mi>\n                                             <\/vb:mrow>\n                                             <vb:mrow>\n                                                <vb:mi>w<\/vb:mi>\n                                                <vb:mi>k<\/vb:mi>\n                                                <vb:mn>1<\/vb:mn>\n                                             <\/vb:mrow>\n                                          <\/vb:msub>\n                                       <\/vb:mrow>\n                                    <\/vb:mrow>\n                                 <\/vb:mrow>\n                              <\/vb:mfenced>\n                              <vb:mo>\u2297<\/vb:mo>\n                              <vb:mrow>\n                                 <vb:mi>|<\/vb:mi>\n                                 <vb:mrow>\n                                    <vb:mn>1<\/vb:mn>\n                                    <vb:msub>\n                                       <vb:mrow>\n                                          <vb:mi>\u232a<\/vb:mi>\n                                       <\/vb:mrow>\n                                       <vb:mrow>\n                                          <vb:mi>m<\/vb:mi>\n                                          <vb:mi>k<\/vb:mi>\n                                       <\/vb:mrow>\n                                    <\/vb:msub>\n                                 <\/vb:mrow>\n                              <\/vb:mrow>\n                           <\/vb:mrow>\n                        <\/vb:mfenced>\n                     <\/vb:math>\n                  <\/jats:inline-formula>. After a marking, a superposition is measured by POVM. The measurement is described by a collection of four measurement operators. The measurement transforms <jats:inline-formula>\n                     <cd:math xmlns:cd=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\">\n                        <cd:mi>|<\/cd:mi>\n                        <cd:msub>\n                           <cd:mrow>\n                              <cd:mi>\u03c8<\/cd:mi>\n                           <\/cd:mrow>\n                           <cd:mrow>\n                              <cd:mn>3<\/cd:mn>\n                           <\/cd:mrow>\n                        <\/cd:msub>\n                        <cd:mi>\u232a<\/cd:mi>\n                     <\/cd:math>\n                  <\/jats:inline-formula> into <jats:inline-formula>\n                     <ed:math xmlns:ed=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\">\n                        <ed:mi>|<\/ed:mi>\n                        <ed:msub>\n                           <ed:mrow>\n                              <ed:mi>\u03c8<\/ed:mi>\n                           <\/ed:mrow>\n                           <ed:mrow>\n                              <ed:mn>4<\/ed:mn>\n                           <\/ed:mrow>\n                        <\/ed:msub>\n                        <ed:mi>\u232a<\/ed:mi>\n                        <ed:mo>=<\/ed:mo>\n                        <ed:mfenced open=\"(\" close=\")\" separators=\"|\">\n                           <ed:mrow>\n                              <ed:mn>1<\/ed:mn>\n                              <ed:mo>\/<\/ed:mo>\n                              <ed:mrow>\n                                 <ed:msqrt>\n                                    <ed:mi>N<\/ed:mi>\n                                 <\/ed:msqrt>\n                              <\/ed:mrow>\n                           <\/ed:mrow>\n                        <\/ed:mfenced>\n                        <ed:mfenced open=\"{\" close=\"}\" separators=\"|\">\n                           <ed:mrow>\n                              <ed:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <ed:mrow>\n                                    <ed:mstyle displaystyle=\"true\">\n                                       <ed:msub>\n                                          <ed:mrow>\n                                             <ed:mo stretchy=\"false\">\u2211<\/ed:mo>\n                                          <\/ed:mrow>\n                                          <ed:mrow>\n                                             <ed:mi>j<\/ed:mi>\n                                             <ed:mo>\u2208<\/ed:mo>\n                                             <ed:mi>B<\/ed:mi>\n                                          <\/ed:mrow>\n                                       <\/ed:msub>\n                                       <ed:mrow>\n                                          <ed:mrow>\n                                             <ed:mi>|<\/ed:mi>\n                                             <ed:mrow>\n                                                <ed:mi>j<\/ed:mi>\n                                                <ed:mi>\u232a<\/ed:mi>\n                                             <\/ed:mrow>\n                                          <\/ed:mrow>\n                                       <\/ed:mrow>\n                                    <\/ed:mstyle>\n                                 <\/ed:mrow>\n                              <\/ed:mfenced>\n                              <ed:mo>\u2297<\/ed:mo>\n                              <ed:mrow>\n                                 <ed:mi>|<\/ed:mi>\n                                 <ed:mrow>\n                                    <ed:mn>0<\/ed:mn>\n                                    <ed:msub>\n                                       <ed:mrow>\n                                          <ed:mi>\u232a<\/ed:mi>\n                                       <\/ed:mrow>\n                                       <ed:mrow>\n                                          <ed:mi>w<\/ed:mi>\n                                          <ed:mi>k<\/ed:mi>\n                                          <ed:mn>0<\/ed:mn>\n                                       <\/ed:mrow>\n                                    <\/ed:msub>\n                                 <\/ed:mrow>\n                              <\/ed:mrow>\n                              <ed:mo>\u2297<\/ed:mo>\n                              <ed:mrow>\n                                 <ed:mi>|<\/ed:mi>\n                                 <ed:mrow>\n                                    <ed:mn>0<\/ed:mn>\n                                    <ed:msub>\n                                       <ed:mrow>\n                                          <ed:mi>\u232a<\/ed:mi>\n                                       <\/ed:mrow>\n                                       <ed:mrow>\n                                          <ed:mi>w<\/ed:mi>\n                                          <ed:mi>k<\/ed:mi>\n                                          <ed:mn>1<\/ed:mn>\n                                       <\/ed:mrow>\n                                    <\/ed:msub>\n                                 <\/ed:mrow>\n                              <\/ed:mrow>\n                              <ed:mo>\u2297<\/ed:mo>\n                              <ed:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <ed:mrow>\n                                    <ed:msub>\n                                       <ed:mrow>\n                                          <ed:mi>p<\/ed:mi>\n                                       <\/ed:mrow>\n                                       <ed:mrow>\n                                          <ed:mn>0<\/ed:mn>\n                                       <\/ed:mrow>\n                                    <\/ed:msub>\n                                    <ed:mi mathvariant=\"normal\">sin<\/ed:mi>\n                                    <ed:mtext>\u2009<\/ed:mtext>\n                                    <ed:mtext>\u2009<\/ed:mtext>\n                                    <ed:mi>\u03b8<\/ed:mi>\n                                 <\/ed:mrow>\n                              <\/ed:mfenced>\n                              <ed:mrow>\n                                 <ed:mi>|<\/ed:mi>\n                                 <ed:mrow>\n                                    <ed:mn>0<\/ed:mn>\n                                    <ed:msub>\n                                       <ed:mrow>\n                                          <ed:mi>\u232a<\/ed:mi>\n                                       <\/ed:mrow>\n                                       <ed:mrow>\n                                          <ed:mi>m<\/ed:mi>\n                                          <ed:mi>k<\/ed:mi>\n                                       <\/ed:mrow>\n                                    <\/ed:msub>\n                                 <\/ed:mrow>\n                              <\/ed:mrow>\n                              <ed:mo>+<\/ed:mo>\n                              <ed:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <ed:mrow>\n                                    <ed:mstyle displaystyle=\"true\">\n                                       <ed:msub>\n                                          <ed:mrow>\n                                             <ed:mo stretchy=\"false\">\u2211<\/ed:mo>\n                                          <\/ed:mrow>\n                                          <ed:mrow>\n                                             <ed:mi>j<\/ed:mi>\n                                             <ed:mo>\u2208<\/ed:mo>\n                                             <ed:mi>G<\/ed:mi>\n                                          <\/ed:mrow>\n                                       <\/ed:msub>\n                                       <ed:mrow>\n                                          <ed:mrow>\n                                             <ed:mi>|<\/ed:mi>\n                                             <ed:mrow>\n                                                <ed:mi>j<\/ed:mi>\n                                                <ed:mi>\u232a<\/ed:mi>\n                                             <\/ed:mrow>\n                                          <\/ed:mrow>\n                                       <\/ed:mrow>\n                                    <\/ed:mstyle>\n                                 <\/ed:mrow>\n                              <\/ed:mfenced>\n                              <ed:mo>\u2297<\/ed:mo>\n                              <ed:mrow>\n                                 <ed:mi>|<\/ed:mi>\n                                 <ed:mrow>\n                                    <ed:mn>0<\/ed:mn>\n                                    <ed:msub>\n                                       <ed:mrow>\n                                          <ed:mi>\u232a<\/ed:mi>\n                                       <\/ed:mrow>\n                                       <ed:mrow>\n                                          <ed:mi>w<\/ed:mi>\n                                          <ed:mi>k<\/ed:mi>\n                                          <ed:mn>0<\/ed:mn>\n                                       <\/ed:mrow>\n                                    <\/ed:msub>\n                                 <\/ed:mrow>\n                              <\/ed:mrow>\n                              <ed:mo>\u2297<\/ed:mo>\n                              <ed:mrow>\n                                 <ed:mi>|<\/ed:mi>\n                                 <ed:mrow>\n                                    <ed:mn>0<\/ed:mn>\n                                    <ed:msub>\n                                       <ed:mrow>\n                                          <ed:mi>\u232a<\/ed:mi>\n                                       <\/ed:mrow>\n                                       <ed:mrow>\n                                          <ed:mi>w<\/ed:mi>\n                                          <ed:mi>k<\/ed:mi>\n                                          <ed:mn>1<\/ed:mn>\n                                       <\/ed:mrow>\n                                    <\/ed:msub>\n                                 <\/ed:mrow>\n                              <\/ed:mrow>\n                              <ed:mo>\u2297<\/ed:mo>\n                              <ed:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <ed:mrow>\n                                    <ed:msub>\n                                       <ed:mrow>\n                                          <ed:mi>p<\/ed:mi>\n                                       <\/ed:mrow>\n                                       <ed:mrow>\n                                          <ed:mn>1<\/ed:mn>\n                                       <\/ed:mrow>\n                                    <\/ed:msub>\n                                    <ed:mi mathvariant=\"normal\">cos<\/ed:mi>\n                                    <ed:mtext>\u2009<\/ed:mtext>\n                                    <ed:mtext>\u2009<\/ed:mtext>\n                                    <ed:mi>\u03b8<\/ed:mi>\n                                 <\/ed:mrow>\n                              <\/ed:mfenced>\n                              <ed:mrow>\n                                 <ed:mi>|<\/ed:mi>\n                                 <ed:mrow>\n                                    <ed:mn>1<\/ed:mn>\n                                    <ed:msub>\n                                       <ed:mrow>\n                                          <ed:mi>\u232a<\/ed:mi>\n                                       <\/ed:mrow>\n                                       <ed:mrow>\n                                          <ed:mi>m<\/ed:mi>\n                                          <ed:mi>k<\/ed:mi>\n                                       <\/ed:mrow>\n                                    <\/ed:msub>\n                                 <\/ed:mrow>\n                              <\/ed:mrow>\n                           <\/ed:mrow>\n                        <\/ed:mfenced>\n                        <ed:mo>\/<\/ed:mo>\n                        <ed:mi>D<\/ed:mi>\n                     <\/ed:math>\n                  <\/jats:inline-formula>; here, <jats:inline-formula>\n                     <ee:math xmlns:ee=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M15\">\n                        <ee:mi>D<\/ee:mi>\n                        <ee:mo>=<\/ee:mo>\n                        <ee:msqrt>\n                           <ee:mrow>\n                              <ee:mtext>card<\/ee:mtext>\n                              <ee:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <ee:mrow>\n                                    <ee:mi>B<\/ee:mi>\n                                 <\/ee:mrow>\n                              <\/ee:mfenced>\n                              <ee:msubsup>\n                                 <ee:mi>p<\/ee:mi>\n                                 <ee:mn>0<\/ee:mn>\n                                 <ee:mi>\u2217<\/ee:mi>\n                              <\/ee:msubsup>\n                              <ee:msub>\n                                 <ee:mrow>\n                                    <ee:mi>p<\/ee:mi>\n                                 <\/ee:mrow>\n                                 <ee:mrow>\n                                    <ee:mn>0<\/ee:mn>\n                                 <\/ee:mrow>\n                              <\/ee:msub>\n                              <ee:msup>\n                                 <ee:mrow>\n                                    <ee:mtext>sin<\/ee:mtext>\n                                 <\/ee:mrow>\n                                 <ee:mrow>\n                                    <ee:mn>2<\/ee:mn>\n                                 <\/ee:mrow>\n                              <\/ee:msup>\n                              <ee:mi>\u03b8<\/ee:mi>\n                              <ee:mo>+<\/ee:mo>\n                              <ee:mtext>card<\/ee:mtext>\n                              <ee:mfenced open=\"(\" close=\")\" separators=\"|\">\n                                 <ee:mrow>\n                                    <ee:mi>G<\/ee:mi>\n                                 <\/ee:mrow>\n                              <\/ee:mfenced>\n                              <ee:msubsup>\n                                 <ee:mi>p<\/ee:mi>\n                                 <ee:mn>1<\/ee:mn>\n                                 <ee:mi>\u2217<\/ee:mi>\n                              <\/ee:msubsup>\n                              <ee:msub>\n                                 <ee:mrow>\n                                    <ee:mi>p<\/ee:mi>\n                                 <\/ee:mrow>\n                                 <ee:mrow>\n                                    <ee:mn>1<\/ee:mn>\n                                 <\/ee:mrow>\n                              <\/ee:msub>\n                              <ee:msup>\n                                 <ee:mrow>\n                                    <ee:mtext>cos<\/ee:mtext>\n                                 <\/ee:mrow>\n                                 <ee:mrow>\n                                    <ee:mn>2<\/ee:mn>\n                                 <\/ee:mrow>\n                              <\/ee:msup>\n                              <ee:mi>\u03b8<\/ee:mi>\n                           <\/ee:mrow>\n                        <\/ee:msqrt>\n                     <\/ee:math>\n                  <\/jats:inline-formula>, and <jats:inline-formula>\n                     <me:math xmlns:me=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M16\">\n                        <me:msubsup>\n                           <me:mi>p<\/me:mi>\n                           <me:mn>0<\/me:mn>\n                           <me:mi>\u2217<\/me:mi>\n                        <\/me:msubsup>\n                        <me:msub>\n                           <me:mrow>\n                              <me:mi>p<\/me:mi>\n                           <\/me:mrow>\n                           <me:mrow>\n                              <me:mn>0<\/me:mn>\n                           <\/me:mrow>\n                        <\/me:msub>\n                        <me:msup>\n                           <me:mrow>\n                              <me:mtext>sin<\/me:mtext>\n                           <\/me:mrow>\n                           <me:mrow>\n                              <me:mn>2<\/me:mn>\n                           <\/me:mrow>\n                        <\/me:msup>\n                        <me:mi>\u03b8<\/me:mi>\n                        <me:mo>+<\/me:mo>\n                        <me:msubsup>\n                           <me:mi>p<\/me:mi>\n                           <me:mn>1<\/me:mn>\n                           <me:mi>\u2217<\/me:mi>\n                        <\/me:msubsup>\n                        <me:msub>\n                           <me:mrow>\n                              <me:mi>p<\/me:mi>\n                           <\/me:mrow>\n                           <me:mrow>\n                              <me:mn>1<\/me:mn>\n                           <\/me:mrow>\n                        <\/me:msub>\n                        <me:msup>\n                           <me:mrow>\n                              <me:mtext>cos<\/me:mtext>\n                           <\/me:mrow>\n                           <me:mrow>\n                              <me:mn>2<\/me:mn>\n                           <\/me:mrow>\n                        <\/me:msup>\n                        <me:mi>\u03b8<\/me:mi>\n                        <me:mo>=<\/me:mo>\n                        <me:mn>2<\/me:mn>\n                     <\/me:math>\n                  <\/jats:inline-formula> which is derived from the completeness equation. The state <jats:inline-formula>\n                     <oe:math xmlns:oe=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M17\">\n                        <oe:mi>|<\/oe:mi>\n                        <oe:mn>0<\/oe:mn>\n                        <oe:msub>\n                           <oe:mrow>\n                              <oe:mi>\u232a<\/oe:mi>\n                           <\/oe:mrow>\n                           <oe:mrow>\n                              <oe:mi>m<\/oe:mi>\n                              <oe:mi>k<\/oe:mi>\n                           <\/oe:mrow>\n                        <\/oe:msub>\n                     <\/oe:math>\n                  <\/jats:inline-formula> and the state <jats:inline-formula>\n                     <qe:math xmlns:qe=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M18\">\n                        <qe:mi>|<\/qe:mi>\n                        <qe:mn>1<\/qe:mn>\n                        <qe:msub>\n                           <qe:mrow>\n                              <qe:mi>\u232a<\/qe:mi>\n                           <\/qe:mrow>\n                           <qe:mrow>\n                              <qe:mi>m<\/qe:mi>\n                              <qe:mi>k<\/qe:mi>\n                           <\/qe:mrow>\n                        <\/qe:msub>\n                     <\/qe:math>\n                  <\/jats:inline-formula> before the measurement are transformed into <jats:inline-formula>\n                     <se:math xmlns:se=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M19\">\n                        <se:msub>\n                           <se:mrow>\n                              <se:mi>p<\/se:mi>\n                           <\/se:mrow>\n                           <se:mrow>\n                              <se:mn>0<\/se:mn>\n                           <\/se:mrow>\n                        <\/se:msub>\n                        <se:mtext>sin<\/se:mtext>\n                        <se:mi>\u03b8<\/se:mi>\n                        <se:mi>|<\/se:mi>\n                        <se:mn>0<\/se:mn>\n                        <se:msub>\n                           <se:mrow>\n                              <se:mi>\u232a<\/se:mi>\n                           <\/se:mrow>\n                           <se:mrow>\n                              <se:mi>m<\/se:mi>\n                              <se:mi>k<\/se:mi>\n                           <\/se:mrow>\n                        <\/se:msub>\n                     <\/se:math>\n                  <\/jats:inline-formula> and <jats:inline-formula>\n                     <ue:math xmlns:ue=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M20\">\n                        <ue:msub>\n                           <ue:mrow>\n                              <ue:mi>p<\/ue:mi>\n                           <\/ue:mrow>\n                           <ue:mrow>\n                              <ue:mn>1<\/ue:mn>\n                           <\/ue:mrow>\n                        <\/ue:msub>\n                        <ue:mtext>cos<\/ue:mtext>\n                        <ue:mi>\u03b8<\/ue:mi>\n                        <ue:mi>|<\/ue:mi>\n                        <ue:mn>1<\/ue:mn>\n                        <ue:msub>\n                           <ue:mrow>\n                              <ue:mi>\u232a<\/ue:mi>\n                           <\/ue:mrow>\n                           <ue:mrow>\n                              <ue:mi>m<\/ue:mi>\n                              <ue:mi>k<\/ue:mi>\n                           <\/ue:mrow>\n                        <\/ue:msub>\n                     <\/ue:math>\n                  <\/jats:inline-formula>, respectively. This paper describes these measurement operators.<\/jats:p>","DOI":"10.1155\/2022\/4819682","type":"journal-article","created":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T19:35:19Z","timestamp":1663788919000},"page":"1-5","source":"Crossref","is-referenced-by-count":0,"title":["Transformation of Superposed Quantum States Using Measurement Operators"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0155-625X","authenticated-orcid":true,"given":"Hideaki","family":"Ito","sequence":"first","affiliation":[{"name":"School of Engineering, Chukyo University, Toyota, Aichi, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saburou","family":"Iida","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Chukyo University, Ret., Toyota, Aichi, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"article-title":"Quantum amplitude amplification and estimation","year":"2000","author":"G. Brassard","key":"1"},{"key":"2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84628-887-6","volume-title":"Explorations in Quantum Computing","author":"C. Williams","year":"2011"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1142\/s1230161214500115"},{"volume-title":"Quantum Computation and Quantum Information","year":"2010","author":"M. Nielsen","key":"4"},{"article-title":"A fast quantum mechanical algorithm for database search","author":"L. Grover","key":"5","doi-asserted-by":"crossref","DOI":"10.1145\/237814.237866"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.86.5188"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1038\/46503"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/s0375-9601(02)01803-0"},{"volume-title":"Combinatorial Optimization","year":"2008","author":"B. Korte","key":"9"},{"volume-title":"Quantum Information Theory","year":"2017","author":"M. M. Wilde","key":"10"}],"container-title":["Quantum Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/que\/2022\/4819682.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/que\/2022\/4819682.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/que\/2022\/4819682.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T19:35:25Z","timestamp":1663788925000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/que\/2022\/4819682\/"}},"subtitle":[],"editor":[{"given":"Shi Hai","family":"Dong","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,9,21]]},"references-count":10,"alternative-id":["4819682","4819682"],"URL":"https:\/\/doi.org\/10.1155\/2022\/4819682","relation":{},"ISSN":["2577-0470"],"issn-type":[{"type":"electronic","value":"2577-0470"}],"subject":[],"published":{"date-parts":[[2022,9,21]]}}}