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Quantum Comple­xity Theory (e.g. BQP)

Quantum Comple­xity Theory classi­fies how diffi­cult compu­ta­tio­nal problems are for quantum compu­ters. It focuses on classes like Bounded‑Error Quantum Polyno­mial Time (BQP) i.e. problems solva­ble by quantum compu­ters in polyno­mial time, and inves­ti­ga­tes whether quantum machi­nes can truly solve problems that are impos­si­ble for classi­cal ones.

Topics in the Subfield Founda­ti­ons:

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Dequan­tiza­tion (e.g. dynami­cal Lie algebra)

When an exponen­tial speedup over classi­cal methods is claimed for a quantum algorithm, resear­chers seek to deter­mine whether…

Measu­res and metrics for quantum advan­tage (e.g. magic, entan­gle­ment) and explainability

To demons­trate that a quantum compu­ter is “better” than classi­cal compu­ta­tio­nal methods, metrics such as…

Circuit cutting and circuit knitting

To execute a large program on limited hardware, circuit cutting and circuit knitting techni­ques are used, in which…

Quantum Tomogra­phy Methods

Quantum tomogra­phy methods are proce­du­res for recon­s­truc­ting the unknown state of a quantum system or the…

Quantum circuit design / quantum archi­tec­ture search

Instead of manually desig­ning quantum circuits, quantum archi­tec­ture search…

Classi­cal optimi­zers (e.g. quantum natural descent)

Even on quantum hardware, the “brain” that drives the optimiza­tion is typically…

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