In [[quantum computing]], '''Quantum-Selected Configuration Interaction (QSCI)''' is a hybrid quantum-classical algorithm that leverages a [[quantum computer]] to assist in the diagonalization of quantum [[observables]]. While initially proposed in the context of [[quantum chemistry]] to calculate the [[electronic structure]] of [[molecules]] and [[solids]], its core principle is expected to have broader applications in various scientific and engineering domains.
From the perspective of developing methods in quantum chemistry, QSCI can be understood as a technique that uses the sampling results from a quantum computer to inform the selection of configurations for [[Configuration_interaction|Configurationconfiguration Interactioninteraction]] calculation.<ref name=":qsci"/>.
It was originally proposed in 2023 by a Japanese quantum computing company QunaSys,<ref name=":qsci">{{Cite arXiv |last1=Kanno |first1=Keita |last2=Kohda |first2=Masaya |last3=Imai |first3=Ryosuke |last4=Koh |first4=Sho |last5=Mitarai |first5=Kosuke |last6=Mizukami |first6=Wataru |last7=Nakagawa |first7=Yuya O. |date=2023 |title=Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers |volume=abs/2302.11320 |class=quant-ph |eprint=2302.11320}}</ref>, which was followed by wider research.<ref name="adapt-qsci">{{Cite journal |last1=Nakagawa |first1=Yuya O. |last2=Kamoshita |first2=Masahiko |last3=Mizukami |first3=Wataru |last4=Sudo |first4=Shotaro |last5=Ohnishi |first5=Yu-ya |date=2024 |title=ADAPT-QSCI: Adaptive Construction of an Input State for Quantum-Selected Configuration Interaction |journal=Journal of Chemical Theory and Computation |volume=20 |issue=24 |pages=10817–10825 |doi=10.1021/acs.jctc.4c00846 |pmid=39642269 }}</ref>. For example, [[IBM]] later performed a large-scale practical experiment based on this approach.<ref name="ibm-sqd-experi">{{Cite journal |last1=Robledo-Moreno |first1=Javier |last2=Motta |first2=Mario |last3=Haas |first3=Holger |last4=Javadi-Abhari |first4=Ali |last5=Jurcevic |first5=Petar |last6=Kirby |first6=William |last7=Martiel |first7=Simon |last8=Sharma |first8=Kunal |last9=Sharma |first9=Sandeep |last10=Shirakawa |first10=Tomonori |last11=Sitdikov |first11=Iskandar |last12=Sun |first12=Rong-Yang |last13=Sung |first13=Kevin J. |last14=Takita |first14=Maika |last15=Tran |first15=Minh C. |last16=Yunoki |first16=Seiji |last17=Mezzacapo |first17=Antonio |date=2025 |title=Chemistry beyond the scale of exact diagonalization on a quantum-centric supercomputer |journal=Science Advances |volume=11 |number=25 |pages=eadu9991 |doi=10.1126/sciadv.adu9991 |pmid=40532014 |arxiv=2405.05068 |bibcode=2025SciA...11.9991R }}</ref>. They refer to the method as '''Samplesample-based quantum diagonalization''' ('''SQD'''). The experiment served as a notable demonstration of this hybrid approach, marking the largest-scale chemical computation on a quantum computer as of 2024.
== Methodology ==
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The QSCI involves a two-step process<ref name=":qsci"/>:
# '''Quantum Selectionselection:''' A quantum computer is used to prepare and measure a reference [[Quantum_state|state]]. By analyzing the measurement outcomes, the quantum computer can efficiently identify the most dominant or "important" basis states (e.g., [[electronic configuration]]s or other relevant [[Space_(mathematics)|subspace]]s) that are essential for accurately describing the system's [[ground state]]. The number of states to be selected is determined by a classical algorithm.
# '''Classical Diagonalizationdiagonalization:''' The selected basis states are then used as input for a subsequent [[Diagonalizable_matrix#Diagonalization|diagonalization]] performed on a [[classical computer]]. Because the quantum selection process has already identified the most physically relevant subspace, the size of the classical calculation is reduced.
