towards a unified picture of complexity for quantum fields
play

Towards a unified picture of complexity for quantum fields Michal P - PowerPoint PPT Presentation

Towards a unified picture of complexity for quantum fields Michal P . Heller aei.mpg.de/GQFI Path integral optimization as circuit complexity Michal P . Heller aei.mpg.de/GQFI based on 1904.02713 with H. Camargo R. Jefferson J. Knaute


  1. Towards a unified picture of complexity for quantum fields Michal P . Heller aei.mpg.de/GQFI

  2. Path integral optimization as circuit complexity Michal P . Heller aei.mpg.de/GQFI based on 1904.02713 with H. Camargo R. Jefferson J. Knaute

  3. <latexit sha1_base64="yltBqzk/Dm3W+BwptubuWE/TSDM=">AB83icdVDLSsNAFJ3UV62vqks3g0VwFSZpc1GCt24rGAf0IQymU7aoZNJmJkIJfQ3LhQxK0/486/cfoQVPTAhcM593LvPWHKmdIfViFjc2t7Z3ibmlv/+DwqHx80lVJgntkIQnsh9iRTkTtKOZ5rSfSorjkNeOG0t/N49lYol4k7PUhrEeCxYxAjWRvJzn2AOW/Nh3p0PyxVkex5CrgeRXatXPadhCKq6V24DOjZaogLWaA/L7/4oIVlMhSYcKzVwUKqDHEvNCKfzkp8pmIyxWM6MFTgmKogX948hxdGcEokaEhkv1+0SOY6VmcWg6Y6wn6re3EP/yBpmOGkHORJpKshqUZRxqBO4CACOmKRE85khmEhmboVkgiUm2sRUMiF8fQr/J13XdpDt3NYqzet1HEVwBs7BJXBAHTBDWiDiAgBQ/gCTxbmfVovVivq9aCtZ45BT9gvX0CRHiR0w=</latexit> <latexit sha1_base64="yltBqzk/Dm3W+BwptubuWE/TSDM=">AB83icdVDLSsNAFJ3UV62vqks3g0VwFSZpc1GCt24rGAf0IQymU7aoZNJmJkIJfQ3LhQxK0/486/cfoQVPTAhcM593LvPWHKmdIfViFjc2t7Z3ibmlv/+DwqHx80lVJgntkIQnsh9iRTkTtKOZ5rSfSorjkNeOG0t/N49lYol4k7PUhrEeCxYxAjWRvJzn2AOW/Nh3p0PyxVkex5CrgeRXatXPadhCKq6V24DOjZaogLWaA/L7/4oIVlMhSYcKzVwUKqDHEvNCKfzkp8pmIyxWM6MFTgmKogX948hxdGcEokaEhkv1+0SOY6VmcWg6Y6wn6re3EP/yBpmOGkHORJpKshqUZRxqBO4CACOmKRE85khmEhmboVkgiUm2sRUMiF8fQr/J13XdpDt3NYqzet1HEVwBs7BJXBAHTBDWiDiAgBQ/gCTxbmfVovVivq9aCtZ45BT9gvX0CRHiR0w=</latexit> <latexit sha1_base64="yltBqzk/Dm3W+BwptubuWE/TSDM=">AB83icdVDLSsNAFJ3UV62vqks3g0VwFSZpc1GCt24rGAf0IQymU7aoZNJmJkIJfQ3LhQxK0/486/cfoQVPTAhcM593LvPWHKmdIfViFjc2t7Z3ibmlv/+DwqHx80lVJgntkIQnsh9iRTkTtKOZ5rSfSorjkNeOG0t/N49lYol4k7PUhrEeCxYxAjWRvJzn2AOW/Nh3p0PyxVkex5CrgeRXatXPadhCKq6V24DOjZaogLWaA/L7/4oIVlMhSYcKzVwUKqDHEvNCKfzkp8pmIyxWM6MFTgmKogX948hxdGcEokaEhkv1+0SOY6VmcWg6Y6wn6re3EP/yBpmOGkHORJpKshqUZRxqBO4CACOmKRE85khmEhmboVkgiUm2sRUMiF8fQr/J13XdpDt3NYqzet1HEVwBs7BJXBAHTBDWiDiAgBQ/gCTxbmfVovVivq9aCtZ45BT9gvX0CRHiR0w=</latexit> <latexit sha1_base64="yltBqzk/Dm3W+BwptubuWE/TSDM=">AB83icdVDLSsNAFJ3UV62vqks3g0VwFSZpc1GCt24rGAf0IQymU7aoZNJmJkIJfQ3LhQxK0/486/cfoQVPTAhcM593LvPWHKmdIfViFjc2t7Z3ibmlv/+DwqHx80lVJgntkIQnsh9iRTkTtKOZ5rSfSorjkNeOG0t/N49lYol4k7PUhrEeCxYxAjWRvJzn2AOW/Nh3p0PyxVkex5CrgeRXatXPadhCKq6V24DOjZaogLWaA/L7/4oIVlMhSYcKzVwUKqDHEvNCKfzkp8pmIyxWM6MFTgmKogX948hxdGcEokaEhkv1+0SOY6VmcWg6Y6wn6re3EP/yBpmOGkHORJpKshqUZRxqBO4CACOmKRE85khmEhmboVkgiUm2sRUMiF8fQr/J13XdpDt3NYqzet1HEVwBs7BJXBAHTBDWiDiAgBQ/gCTxbmfVovVivq9aCtZ45BT9gvX0CRHiR0w=</latexit> <latexit sha1_base64="2nZ/9qZvC+D5JDkKqrCV8Mn5jHk=">AB83icdVDLSsNAFJ3UV62vqks3g0VwFSZiNlIpRuXFewDmlAm0k7dDIJMxOhP6GxeKuPVn3Pk3Th+Cih64cDjnXu69J8o4UxqhD6u0srq2vlHerGxt7+zuVfcP2irNJaEtkvJUdiOsKGeCtjTnHYzSXEScdqJxo2Z37mnUrFU3OlJRsMEDwWLGcHaSEREMxhY9ovrqf9ag3ZF6HfASR7freueMa4vue7vQsdEcNbBEs19DwYpyRMqNOFYqZ6DMh0WGpGOJ1WglzRDJMxHtKeoQInVIXF/OYpPDHKAMapNCU0nKvfJwqcKDVJItOZYD1Sv72Z+JfXy3XshQUTWa6pItFc6hTuEsADhgkhLNJ4ZgIpm5FZIRlphoE1PFhPD1KfyftM9sB9nO7XmtfrWMowyOwDE4BQ64BHVwA5qgBQjIwAN4As9Wbj1aL9brorVkLWcOwQ9Yb59MOZHa</latexit> <latexit sha1_base64="2nZ/9qZvC+D5JDkKqrCV8Mn5jHk=">AB83icdVDLSsNAFJ3UV62vqks3g0VwFSZiNlIpRuXFewDmlAm0k7dDIJMxOhP6GxeKuPVn3Pk3Th+Cih64cDjnXu69J8o4UxqhD6u0srq2vlHerGxt7+zuVfcP2irNJaEtkvJUdiOsKGeCtjTnHYzSXEScdqJxo2Z37mnUrFU3OlJRsMEDwWLGcHaSEREMxhY9ovrqf9ag3ZF6HfASR7freueMa4vue7vQsdEcNbBEs19DwYpyRMqNOFYqZ6DMh0WGpGOJ1WglzRDJMxHtKeoQInVIXF/OYpPDHKAMapNCU0nKvfJwqcKDVJItOZYD1Sv72Z+JfXy3XshQUTWa6pItFc6hTuEsADhgkhLNJ4ZgIpm5FZIRlphoE1PFhPD1KfyftM9sB9nO7XmtfrWMowyOwDE4BQ64BHVwA5qgBQjIwAN4As9Wbj1aL9brorVkLWcOwQ9Yb59MOZHa</latexit> <latexit sha1_base64="2nZ/9qZvC+D5JDkKqrCV8Mn5jHk=">AB83icdVDLSsNAFJ3UV62vqks3g0VwFSZiNlIpRuXFewDmlAm0k7dDIJMxOhP6GxeKuPVn3Pk3Th+Cih64cDjnXu69J8o4UxqhD6u0srq2vlHerGxt7+zuVfcP2irNJaEtkvJUdiOsKGeCtjTnHYzSXEScdqJxo2Z37mnUrFU3OlJRsMEDwWLGcHaSEREMxhY9ovrqf9ag3ZF6HfASR7freueMa4vue7vQsdEcNbBEs19DwYpyRMqNOFYqZ6DMh0WGpGOJ1WglzRDJMxHtKeoQInVIXF/OYpPDHKAMapNCU0nKvfJwqcKDVJItOZYD1Sv72Z+JfXy3XshQUTWa6pItFc6hTuEsADhgkhLNJ4ZgIpm5FZIRlphoE1PFhPD1KfyftM9sB9nO7XmtfrWMowyOwDE4BQ64BHVwA5qgBQjIwAN4As9Wbj1aL9brorVkLWcOwQ9Yb59MOZHa</latexit> <latexit sha1_base64="2nZ/9qZvC+D5JDkKqrCV8Mn5jHk=">AB83icdVDLSsNAFJ3UV62vqks3g0VwFSZiNlIpRuXFewDmlAm0k7dDIJMxOhP6GxeKuPVn3Pk3Th+Cih64cDjnXu69J8o4UxqhD6u0srq2vlHerGxt7+zuVfcP2irNJaEtkvJUdiOsKGeCtjTnHYzSXEScdqJxo2Z37mnUrFU3OlJRsMEDwWLGcHaSEREMxhY9ovrqf9ag3ZF6HfASR7freueMa4vue7vQsdEcNbBEs19DwYpyRMqNOFYqZ6DMh0WGpGOJ1WglzRDJMxHtKeoQInVIXF/OYpPDHKAMapNCU0nKvfJwqcKDVJItOZYD1Sv72Z+JfXy3XshQUTWa6pItFc6hTuEsADhgkhLNJ4ZgIpm5FZIRlphoE1PFhPD1KfyftM9sB9nO7XmtfrWMowyOwDE4BQ64BHVwA5qgBQjIwAN4As9Wbj1aL9brorVkLWcOwQ9Yb59MOZHa</latexit> Motivation 1: holographic complexity proposals 1402.5674 by Susskind, 1509.07876 by Brown et al., … ~ Volume of codim-1 C V max volume bulk slice ~ Action in codim-0 C A bulk region with null bdries What do holography complexity proposals stand for in hQFT? 1/13

  4. <latexit sha1_base64="saibsGfyJruy1uaAeyz+TkpK7wY=">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</latexit> <latexit sha1_base64="ZCcwqe28+4fRSPwUVrRJBSOqaY=">AB83icbVDLSsNAFL3xWeur6tLNYBFclaQKupJKNy4r2Ac0oUymk3boZBLmIZSQ3DjQhG3/ow7/8Zpm4W2HrhwOde7r0nTDlT2nW/nbX1jc2t7dJOeXdv/+CwcnTcUYmRhLZJwhPZC7GinAna1kxz2kslxXHIaTecNGd+94lKxRLxqKcpDWI8EixiBGsr+ZlPMEfNfJDd5YNK1a25c6BV4hWkCgVag8qXP0yIianQhGOl+p6b6iDUjPCaV72jaIpJhM8on1LBY6pCrL5zTk6t8oQRYm0JTSaq78nMhwrNY1D2xljPVbL3kz8z+sbHd0EGROp0VSQxaLIcKQTNAsADZmkRPOpJZhIZm9FZIwlJtrGVLYheMsvr5JOveZd1uoPV9XGbRFHCU7hDC7Ag2towD20oA0EUniGV3hzjPivDsfi9Y1p5g5gT9wPn8AsFCRcQ=</latexit> <latexit sha1_base64="F63pPIR3kqXK+XdFpBoCh/Ev+y8=">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</latexit> <latexit sha1_base64="f2H0mBHGKfL4okRuPk/E+pxgF8M=">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</latexit> <latexit sha1_base64="wR9x6m2b5bgF4czvu9O8K0lCo2A=">ACDXicbVDLSsNAFJ34rPUVdelmsAoupCRV0JUunHhoJ9QFPCZDph04mYWYilCE/4MZfceNCEbfu3fk3TtostPXAhcM593LvPUHCqFSO820tLa+srq2XNsqbW9s7u/beflvGqcCkhWMWi26AJGUk5aipFuIgiKAkY6wbiR+50HIiSN+b2aJKQfoSGnIcVIGcm3j7WHEYONzNdehNRIRBoToRDlGfTO4K2va1nm2xWn6kwBF4lbkAo0PTtL28Q4zQiXGpOy5TqL6GglFMSNZ2UslSRAeoyHpGcpRGRfT7/J4IlRBjCMhSmu4FT9PaFRJOUkCkxnfrGc93LxP6+XqvCqrylPUkU4ni0KUwZVDPNo4IAKghWbGIKwoOZWiEdIKxMgGUTgjv/8iJp16ruebV2d1GpXxdxlMAhOAKnwAWXoA5uQBO0AaP4Bm8gjfryXqx3q2PWeuSVcwcgD+wPn8AUsSbsQ=</latexit> <latexit sha1_base64="gNjVQ3wGrFkeh5KMF5+YFGknai0=">AB83icbVDLSsNAFL2pr1pfVZduBovgqiRV0JUunFZwT6gCWUynbRDJ5MwD6GE/IYbF4q49Wfc+TdO2y09cCFwzn3cu89YcqZ0q7ZQ2Nre2d8q7lb39g8Oj6vFJVyVGEtohCU9kP8SKciZoRzPNaT+VFMchp71w2pr7vScqFUvEo56lNIjxWLCIEayt5Gc+wRy18mHWzYfVmlt3F0DrxCtIDQq0h9Uvf5QE1OhCcdKDTw31UGpWaE07ziG0VTKZ4TAeWChxTFWSLm3N0YZURihJpS2i0UH9PZDhWahaHtjPGeqJWvbn4nzcwOroNMiZSo6kgy0WR4UgnaB4AGjFJieYzSzCRzN6KyARLTLSNqWJD8FZfXifdRt27qjcermvNuyKOMpzBOVyCBzfQhHtoQwcIpPAMr/DmGOfFeXc+lq0lp5g5hT9wPn8A0DmRhg=</latexit> <latexit sha1_base64="014Y13VniyKr46JPZf8BRa25D1c=">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</latexit> Motivation 2: complexity in free QFTs To my taste, and looked a lot like calculating HRT surfaces before first C V C A works on entanglement entropy in QFT (pioneers: 1980s, explosion > 2004) Geometric approach to complexity (of operators): quant-ph/0502070 by Nielsen , … "Z κ 2 # R κ 2 I O I Y I ( κ ) | R i κ 1 d κ P X η I | Y I ( κ ) | | T i = P e − C L 1 ∼ min d κ κ 1 I First applications to free QFTs on a lattice / cMERA regularization: 1707.08582 , 1707.08570 by Jefferson & Myers, 1807.07075 , 1810.05151 , … • unitary gates (for bosons): O I ∼ i φ j φ l , i π j φ l and i φ ( j π l ) i π j π l • for very fine-tuned cost function, , one can get exact results C certain L 2 • circuits then also use very non-local gates, e.g. O I = i φ here φ other galaxy • the good: similar divergence structures to holography (universality?) • the bad (but expected): very different time dependence than holography 2/13

Recommend


More recommend