Quantum query complexity of Boolean functions under indefinite causal order
The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum syst...
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| Vydáno v: | Physical review research Ročník 6; číslo 3; s. L032020 |
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| Jazyk: | angličtina |
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American Physical Society
26.07.2024
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| ISSN: | 2643-1564, 2643-1564 |
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| Abstract | The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher-order quantum computations. To this end, we generalize the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps. |
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| AbstractList | The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several ad hoc computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher-order quantum computations. To this end, we generalize the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps. The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher-order quantum computations. To this end, we generalize the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps. The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher-order quantum computations. To this end, we generalize the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps. Published by the American Physical Society 2024 |
| ArticleNumber | L032020 |
| Author | Mhalla, Mehdi Pocreau, Pierre Abbott, Alastair A. |
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| Cites_doi | 10.1038/ncomms2076 10.1016/0034-4877(72)90011-0 10.1088/1367-2630/aafef7 10.1103/PRXQuantum.2.010320 10.1103/PhysRevLett.123.210502 10.1145/502090.502097 10.1103/PhysRevLett.124.190503 10.1103/PhysRevLett.101.060401 10.1137/S0097539796300933 10.1063/5.0075919 10.1103/PhysRevA.88.022318 10.1103/PhysRevLett.127.110402 10.1088/1367-2630/17/10/102001 10.23638/LMCS-15(3:15)2019 10.1103/PRXQuantum.2.030335 10.1016/0024-3795(75)90075-0 10.1006/jcss.2002.1826 10.1103/PhysRevA.80.022339 10.1103/PhysRevLett.130.070803 10.1088/1367-2630/18/9/093020 10.1103/PhysRevA.109.062435 10.1088/1367-2630/aaf352 10.1007/s00453-013-9826-8 10.1103/PhysRevLett.127.200504 10.1016/S0304-3975(01)00144-X 10.1103/PhysRevLett.113.250402 10.1103/PhysRevA.86.040301 10.1103/PhysRevLett.117.100502 10.1038/nphoton.2011.35 10.22331/q-2017-04-26-10 10.1209/0295-5075/83/30004 10.1007/s10957-016-0892-3 10.1038/s41467-023-36893-3 10.1103/PhysRevLett.128.230503 10.1103/PhysRevA.96.052315 10.1016/j.jcss.2005.06.006 10.22331/q-2022-03-31-679 10.1137/050644719 |
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| Title | Quantum query complexity of Boolean functions under indefinite causal order |
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