Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem |
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Authors: | Ocko Samuel A Chen Xie Zeng Bei Yoshida Beni Ji Zhengfeng Ruskai Mary Beth Chuang Isaac L |
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Institution: | Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. |
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Abstract: | It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems. |
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