Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumpti...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.6.010319 |
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| author | Antonio Anna Mele Yaroslav Herasymenko |
| author_facet | Antonio Anna Mele Yaroslav Herasymenko |
| author_sort | Antonio Anna Mele |
| collection | DOAJ |
| description | The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard. Here, we present an efficient algorithm for learning states on n fermion modes prepared by any number of Gaussian and at most t non-Gaussian gates. By Jordan-Wigner mapping, this also includes n-qubit states prepared by nearest-neighbor matchgate circuits with at most t swap gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of our algorithm is poly(n,2^{t}); thus if t=O(log(n)), it is efficient. We also show that, if t scales slightly more than logarithmically, any learning algorithm to solve the same task must be inefficient, under common cryptographic assumptions. We also provide an efficient property-testing algorithm that, given access to copies of a state, determines whether such a state is far or close to the set of states for which our learning algorithm works. In addition to the outputs of quantum circuits, our tomography algorithm is efficient for some physical target states, such as those arising in time dynamics and low-energy physics of impurity models. Beyond tomography, our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity, enabling an efficient circuit-compilation method. |
| format | Article |
| id | doaj-art-600d4aec8bc84ec39dc349f036292442 |
| institution | Kabale University |
| issn | 2691-3399 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-600d4aec8bc84ec39dc349f0362924422025-01-28T15:07:44ZengAmerican Physical SocietyPRX Quantum2691-33992025-01-016101031910.1103/PRXQuantum.6.010319Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian GatesAntonio Anna MeleYaroslav HerasymenkoThe experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard. Here, we present an efficient algorithm for learning states on n fermion modes prepared by any number of Gaussian and at most t non-Gaussian gates. By Jordan-Wigner mapping, this also includes n-qubit states prepared by nearest-neighbor matchgate circuits with at most t swap gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of our algorithm is poly(n,2^{t}); thus if t=O(log(n)), it is efficient. We also show that, if t scales slightly more than logarithmically, any learning algorithm to solve the same task must be inefficient, under common cryptographic assumptions. We also provide an efficient property-testing algorithm that, given access to copies of a state, determines whether such a state is far or close to the set of states for which our learning algorithm works. In addition to the outputs of quantum circuits, our tomography algorithm is efficient for some physical target states, such as those arising in time dynamics and low-energy physics of impurity models. Beyond tomography, our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity, enabling an efficient circuit-compilation method.http://doi.org/10.1103/PRXQuantum.6.010319 |
| spellingShingle | Antonio Anna Mele Yaroslav Herasymenko Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates PRX Quantum |
| title | Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates |
| title_full | Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates |
| title_fullStr | Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates |
| title_full_unstemmed | Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates |
| title_short | Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates |
| title_sort | efficient learning of quantum states prepared with few fermionic non gaussian gates |
| url | http://doi.org/10.1103/PRXQuantum.6.010319 |
| work_keys_str_mv | AT antonioannamele efficientlearningofquantumstatespreparedwithfewfermionicnongaussiangates AT yaroslavherasymenko efficientlearningofquantumstatespreparedwithfewfermionicnongaussiangates |