From 070f4135e742988bd9728e058e35dad5e5008ce4 Mon Sep 17 00:00:00 2001 From: qottmann Date: Mon, 14 Apr 2025 13:01:01 +0200 Subject: [PATCH 01/30] A game of surface codes demo --- ...torial_game_of_surface_codes.metadata.json | 54 ++++++++++++ .../tutorial_game_of_surface_codes.py | 84 +++++++++++++++++++ 2 files changed, 138 insertions(+) create mode 100644 demonstrations/tutorial_game_of_surface_codes.metadata.json create mode 100644 demonstrations/tutorial_game_of_surface_codes.py diff --git a/demonstrations/tutorial_game_of_surface_codes.metadata.json b/demonstrations/tutorial_game_of_surface_codes.metadata.json new file mode 100644 index 0000000000..c761b7363a --- /dev/null +++ b/demonstrations/tutorial_game_of_surface_codes.metadata.json @@ -0,0 +1,54 @@ +{ + "title": "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery", + "authors": [ + { + "username": "Qottmann" + } + ], + "dateOfPublication": "2025-06-30T00:00:00+00:00", + "dateOfLastModification": "2025-06-30T00:00:00+00:00", + "categories": [ + "Quantum Computing", + "Algorithms" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_fixed_depth_hamiltonian_simulation_via_cartan_decomposition.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_fixed_depth_hamiltonian_simulation_via_cartan_decomposition.png" + } + ], + "seoDescription": "A game of surface codes: Exploring space-time tradeoffs in surface code based quantum computation.", + "doi": "", + "references": [ + { + "id": "Litinski", + "type": "preprint", + "title": "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery", + "authors": "Daniel Litinski", + "year": "2021", + "publisher": "", + "journal": "", + "doi": "10.22331/q-2019-03-05-128", + "url": "https://arxiv.org/abs/1808.02892" + } + ], + "basedOnPapers": ["10.22331/q-2019-03-05-128"], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_toric_code", + "weight": 1.0 + }, + { + "type": "demonstration", + "id": "tutorial_mbqc", + "weight": 1.0 + } + ] +} diff --git a/demonstrations/tutorial_game_of_surface_codes.py b/demonstrations/tutorial_game_of_surface_codes.py new file mode 100644 index 0000000000..abf73e66e7 --- /dev/null +++ b/demonstrations/tutorial_game_of_surface_codes.py @@ -0,0 +1,84 @@ +r"""A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery +=============================================================================== + +asd + +.. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_fixed_depth_hamiltonian_simulation_via_cartan_decomposition.png + :align: center + :width: 70% + :target: javascript:void(0) + +Introduction +------------ + + +Rules of the game +----------------- + + +Data blocks design +------------------ + +Compact data blocks +^^^^^^^^^^^^^^^^^^^ + +Intermediate data blocks +^^^^^^^^^^^^^^^^^^^^^^^^ + +Fast data blocks +^^^^^^^^^^^^^^^^ + + +""" +import numpy as np +import pennylane as qml +from pennylane import X, Y, Z, I + +import matplotlib.pyplot as plt + + +############################################################################## +# + +############################################################################## +# + +############################################################################## +# + +############################################################################## +# + +############################################################################## +# + +############################################################################## +# + + + + +############################################################################## +# +# Conclusion +# ---------- +# +# asd + + +############################################################################## +# +# References +# ---------- +# +# .. [#Litinski] +# +# Daniel Litinski +# "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery" +# `arXiv:1808.02892 `__, 2018. +# +# + +############################################################################## +# About the author +# ---------------- From e01fb52596a4516836b382b08bbeca55ed2d2808 Mon Sep 17 00:00:00 2001 From: qottmann Date: Mon, 14 Apr 2025 17:00:38 +0200 Subject: [PATCH 02/30] A game of surface codes demo --- demonstrations/tutorial_game_of_surface_codes.py | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/demonstrations/tutorial_game_of_surface_codes.py b/demonstrations/tutorial_game_of_surface_codes.py index abf73e66e7..799d503986 100644 --- a/demonstrations/tutorial_game_of_surface_codes.py +++ b/demonstrations/tutorial_game_of_surface_codes.py @@ -15,6 +15,17 @@ Rules of the game ----------------- +Data qubits as surface code tiles +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Basic operations +^^^^^^^^^^^^^^^^ + +Surface codes +^^^^^^^^^^^^^ + + + Data blocks design ------------------ From c9957a9d1e076565faacaa9209b081a083a36ea8 Mon Sep 17 00:00:00 2001 From: qottmann Date: Tue, 22 Apr 2025 12:51:49 +0200 Subject: [PATCH 03/30] intro, context, qubit patches --- .../tutorial_game_of_surface_codes.py | 40 ++++++++++++++----- 1 file changed, 31 insertions(+), 9 deletions(-) diff --git a/demonstrations/tutorial_game_of_surface_codes.py b/demonstrations/tutorial_game_of_surface_codes.py index 799d503986..f63d9cd840 100644 --- a/demonstrations/tutorial_game_of_surface_codes.py +++ b/demonstrations/tutorial_game_of_surface_codes.py @@ -1,29 +1,51 @@ r"""A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery =============================================================================== -asd - -.. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_fixed_depth_hamiltonian_simulation_via_cartan_decomposition.png - :align: center - :width: 70% - :target: javascript:void(0) +abstract Introduction ------------ +The game of surface codes [#Litinski]_ is a high-level framework for designing surface code quantum computing architectures. +The game helps us understand space-time trade-offs, where e.g. designs with a higher qubit overhead allow for faster computations and vice versa. + +The game can be understood entirely from the rules described in the next section. +However, it still helps to understand the correspondences in physical fault tolerant quantum computing (FTQC) architectures. +First of all it is important to note that we consider surface codes that implement :doc:`(Clifford + T) ` circuits. +In particular, these circuits can be mapped entirely to just performing :doc:`Pauli product measurements `. +Hence, we mainly care about which types of measurements we can perform in the rule description below. + +We also note that the patches that represent qubits correspond to surface code qubits. +There is a detailed explanation in Appendix A in [#Litinski]_ that describes the surface code realizations of all operations that we are going to see. +These are useful to know in order to grasp the full depth of the game, but are not essential to understanding its rules and concluding design principles. Rules of the game ----------------- +The game is played on a board of tiles, where patches correspond to qubits. +Underlying these tiles are physical qubits that are statically arranged. +But we should view qubit patches as dynamic entities that appear, move around, deform and disappear again. + Data qubits as surface code tiles ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +Data qubits are realized by patches that at least occupy one tile, but potentially multiple. +They always have four distinct boundaries corresponding to X (dotted) and Z (solid) edges. +Two-qubit patches have 6 distinct boundaries, corresponding to the single X and Z operators of each qubit, as well as the two products XX and ZZ. +This is shown in the figure below. + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/qubit_definition.png + :align: center + :width: 50% + :target: javascript:void(0) + + Qubits are defined as patches of tiles on the board. + A single qubit can occupy one tile (a) or multiple tiles (b), where dotted lines correspond to X and solid lines to Z operators. + Two-qubit patches (c) have 6 boundaries corresponding to the single :math:`X`, :math:`Z` and :math:`XX` and :math:`ZZ` operators. + Basic operations ^^^^^^^^^^^^^^^^ -Surface codes -^^^^^^^^^^^^^ - From 6c33693649de66cc229a88e82405a6b33efd6110 Mon Sep 17 00:00:00 2001 From: qottmann Date: Tue, 22 Apr 2025 12:52:14 +0200 Subject: [PATCH 04/30] add figure --- .../game_of_surface_codes/qubit_definition.png | Bin 0 -> 84754 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 _static/demonstration_assets/game_of_surface_codes/qubit_definition.png diff --git a/_static/demonstration_assets/game_of_surface_codes/qubit_definition.png b/_static/demonstration_assets/game_of_surface_codes/qubit_definition.png new file mode 100644 index 0000000000000000000000000000000000000000..e02a2ff4e04c3dbbd74fa8f83aeb24472b76dc73 GIT binary patch literal 84754 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b1504b7f30343179799c77152a8bd8a1f49ceb3e Mon Sep 17 00:00:00 2001 From: qottmann Date: Tue, 22 Apr 2025 13:27:27 +0200 Subject: [PATCH 05/30] more details --- demonstrations/tutorial_game_of_surface_codes.py | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/demonstrations/tutorial_game_of_surface_codes.py b/demonstrations/tutorial_game_of_surface_codes.py index f63d9cd840..181821111d 100644 --- a/demonstrations/tutorial_game_of_surface_codes.py +++ b/demonstrations/tutorial_game_of_surface_codes.py @@ -8,6 +8,8 @@ The game of surface codes [#Litinski]_ is a high-level framework for designing surface code quantum computing architectures. The game helps us understand space-time trade-offs, where e.g. designs with a higher qubit overhead allow for faster computations and vice versa. +One can draw a rough comparison to microchip design in classical computing, +where the equivalent game would be about how to arrange the transistors of a chip to perform fast and efficient computations. The game can be understood entirely from the rules described in the next section. However, it still helps to understand the correspondences in physical fault tolerant quantum computing (FTQC) architectures. @@ -25,6 +27,8 @@ The game is played on a board of tiles, where patches correspond to qubits. Underlying these tiles are physical qubits that are statically arranged. But we should view qubit patches as dynamic entities that appear, move around, deform and disappear again. +The goal of this demo will be to understand the design principles and space-time trade-offs for surface code architectures. +We are going to introduce the necessary rules of the game in this section. Data qubits as surface code tiles ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -46,6 +50,9 @@ Basic operations ^^^^^^^^^^^^^^^^ +Every operation in the game has an associated time cost that we measure in units of 🕒. These correspond more or less to surface code cycles. +There are some discrepancies but the correspondance is close enough to weigh out space-time trade-offs in architecture designs. + From cec3353b3bb52cf561de5aa04f45fcb9f1449b5e Mon Sep 17 00:00:00 2001 From: qottmann Date: Tue, 22 Apr 2025 13:51:05 +0200 Subject: [PATCH 06/30] more high level stuff, really like the examples from the paper --- demonstrations/tutorial_game_of_surface_codes.py | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/demonstrations/tutorial_game_of_surface_codes.py b/demonstrations/tutorial_game_of_surface_codes.py index 181821111d..22c6875652 100644 --- a/demonstrations/tutorial_game_of_surface_codes.py +++ b/demonstrations/tutorial_game_of_surface_codes.py @@ -8,6 +8,10 @@ The game of surface codes [#Litinski]_ is a high-level framework for designing surface code quantum computing architectures. The game helps us understand space-time trade-offs, where e.g. designs with a higher qubit overhead allow for faster computations and vice versa. +E.g., a space-efficient design might allow a computation with :math:`10^8` qubits to run in :math:`4` hours using :math:`55k` physical qubits, +whereas and intermediate design may run the same computation in :math:`22` minutes using :math:`120k` physical qubits, +or a time-optimized design in :math:`1` second using :math:`1500` interconnected quantum computers with :math:`220k` physical qubits, each. + One can draw a rough comparison to microchip design in classical computing, where the equivalent game would be about how to arrange the transistors of a chip to perform fast and efficient computations. @@ -55,7 +59,6 @@ - Data blocks design ------------------ From aa7b2f52accba7bf7e660c2aa5b7994bf150ec50 Mon Sep 17 00:00:00 2001 From: qottmann Date: Tue, 22 Apr 2025 17:29:32 +0200 Subject: [PATCH 07/30] more updates --- demonstrations/tutorial_game_of_surface_codes.py | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/demonstrations/tutorial_game_of_surface_codes.py b/demonstrations/tutorial_game_of_surface_codes.py index 22c6875652..b01bf4c8f6 100644 --- a/demonstrations/tutorial_game_of_surface_codes.py +++ b/demonstrations/tutorial_game_of_surface_codes.py @@ -8,7 +8,7 @@ The game of surface codes [#Litinski]_ is a high-level framework for designing surface code quantum computing architectures. The game helps us understand space-time trade-offs, where e.g. designs with a higher qubit overhead allow for faster computations and vice versa. -E.g., a space-efficient design might allow a computation with :math:`10^8` qubits to run in :math:`4` hours using :math:`55k` physical qubits, +E.g., a space-efficient design might allow a computation with :math:`10^8` T gates to run in :math:`4` hours using :math:`55k` physical qubits, whereas and intermediate design may run the same computation in :math:`22` minutes using :math:`120k` physical qubits, or a time-optimized design in :math:`1` second using :math:`1500` interconnected quantum computers with :math:`220k` physical qubits, each. @@ -18,12 +18,14 @@ The game can be understood entirely from the rules described in the next section. However, it still helps to understand the correspondences in physical fault tolerant quantum computing (FTQC) architectures. First of all it is important to note that we consider surface codes that implement :doc:`(Clifford + T) ` circuits. -In particular, these circuits can be mapped entirely to just performing :doc:`Pauli product measurements `. -Hence, we mainly care about which types of measurements we can perform in the rule description below. +In particular, these circuits can be mapped to just performing :doc:`Pauli product measurements `. +This is because all Clifford operations can be moved to the end of the circuit and merged with measurements. +The remaining non-Clifford gates are realized by :doc:`magic state injection ` and more Clifford operations that can again be merged with measurements again. +Hence, we mainly care about performing measurements on qubits in arbitrary bases. We also note that the patches that represent qubits correspond to surface code qubits. There is a detailed explanation in Appendix A in [#Litinski]_ that describes the surface code realizations of all operations that we are going to see. -These are useful to know in order to grasp the full depth of the game, but are not essential to understanding its rules and concluding design principles. +These are useful to know in order to grasp the full depth of the game, but are not essential to understanding its rules and concluding design principles explained in this demo. Rules of the game ----------------- @@ -56,6 +58,10 @@ Every operation in the game has an associated time cost that we measure in units of 🕒. These correspond more or less to surface code cycles. There are some discrepancies but the correspondance is close enough to weigh out space-time trade-offs in architecture designs. +We are not going to give an exhaustive overview of all possible operations, but focus on a few important ones and fill the remaining gaps necessary for the architecture designs in the respective sections below. + +- X and Z measurement +- Y measurement From 7648b500e82a20997c3f54752946d1aa086a472a Mon Sep 17 00:00:00 2001 From: qottmann Date: Wed, 23 Apr 2025 13:14:50 +0200 Subject: [PATCH 08/30] Basic operations --- .../game_of_surface_codes/PPM.png | Bin 0 -> 23962 bytes .../Y_measurement_protocol.png | Bin 0 -> 41049 bytes .../qubit_definition_cropped.png | Bin 0 -> 43498 bytes .../tutorial_game_of_surface_codes.py | 61 ++++++++++++++---- 4 files changed, 50 insertions(+), 11 deletions(-) create mode 100644 _static/demonstration_assets/game_of_surface_codes/PPM.png create mode 100644 _static/demonstration_assets/game_of_surface_codes/Y_measurement_protocol.png create mode 100644 _static/demonstration_assets/game_of_surface_codes/qubit_definition_cropped.png diff --git a/_static/demonstration_assets/game_of_surface_codes/PPM.png b/_static/demonstration_assets/game_of_surface_codes/PPM.png new file mode 100644 index 0000000000000000000000000000000000000000..367191456df168f299b566a2b9c3db8580e71544 GIT binary patch literal 23962 zcmbTdV{~Or*Df4(oQ`eVX2-VOv7K~mb=Qgw`Kx22DYX3^8q#tM(napv9?xfs9H~=D98ddypCXj9FfE zO8k&jG=~V9WaVdhmmGv`WN@xt#>$sEYL7Kem9qJu(KpBD1E&qpSL6_8R*+ovrb=NB zdRseNnQlx7rVu2IUyAi#WcHkB*#a*FUNfN{MLRPv+gi<0Q+~`?KG`!OW^5ggZ#?B; z(i|Z~KSQYr8z&4#LopGF%)b1Pa;Gc!|FY(lYP6ng1o!Vm0*VYCZ(O^4jo5$hQ$=3;0 zlQ3)}%*#79988{LPpe;$GQmCdCN@?xALIk#ByxAW!G7bJ{lY3LV+X2S-BeS`Oim7j z26zt*0vcus0s*`O1ztG73j_o_J`@BB_>Tg-M03IZPb#QdF8Kf4e@cJ|sfb8P0smEu zolH&boGt8K0?v~nfkiD?s%pAu%E|H=+uJf2n%EneGPv71e2ReZx$^*TZB1PaiQH{% z?3{Vr`APoC!2`Vie9cHg^iLKSYkm?}2WSVrg$j^jWTG=4nkMl!TlC6tB~c zhlq|m5*o0GpG%hcxkfLOtIij8)fyDB6qsyW&VC z6r1eycE{2ZNb|u1ydKUC7pwHR{NDNGvv|n;STE+vP#f*m01ZX!iystn=|sfDpt91& z3l&<2^W`b(X6=DMU2H-x!GV#>B=`M9CJh!$SIOY8bvXaaZL`{l!0&n66^ek%Ca-oN zgkD)CnY%xl^0i)h6HJXX)D!Nm9sbaE5(cQmfG7$7i9`zdOe%Pjoq=d*c=$Oks!Czk ziA-*2SXi)CiT<7tIChTxkWk`pxa)k5z%FTw?P_-1**rL)l-;eH6qw~At`xp|*zm)| znIcfX*&qKmcb5hrbgQonnBBkYkIzf6b9`T)D4kBDtnH9?2u;Vmigt@rkv6IRXDb{a z@X!O=J#O;Fqj7p}kBDU0Eztm+c7MBoI^Nvg4#eYjDs9~I_-6!cPC>hSdBNRKo>9#g zDwQ%A{L#&I{_#V-=-@x;m(Z$}+G<^!!wHmDnii^Mp7*C|-%2n1$=TV_K|w(S5otF# zReRO-6)QBEx8@YpytWT={05%yPV%0=dwY8`{W#ThIa^Vi2(pX8=M6RReS+-n?v8hw znaK6AmxGFUd%i=Jr%s5EC$l|l8PDWK-3}9}(5*Frd4D<}{1ub!bbWc*^@~`9$!d;j z&nP%F6xNvBM|V$DaL6R2)?%8ZxwVx>BY@+j$$lfIxtS}kN~u5`=b@M^8h%XCkJW6< z|JWPB#%|W+mYb-Y(5%#W_U3m;cVx~Hr~P^O6{SLU)XT$#2w~RHq*ApB z7cs$WI2NDhtt65@04(WPYS`!b_K2kH^?A|2uM9>NQ21uAe8uIwAC;MG*J!g$Ld9r} z!i34FuZr4pvEG3?P)4H|zStY~HKcWS*JNa5cDp|k5**5-y976%*X8gR)0e&0-@lpY z^jcMsN>$}E-pIa75wGEeGtICWIA1pYAh_jD<*-d}_&R$&SmIbjGohXH8%?90gul~D zV$>wE0=V`x)TO5uP1aujB~lW%w}aC)`xdaP4_$_>T*)mR81&>On^;BC8wovv28 z(i8lIRS6zI;W{!BLQ|={+GuN?9B_BBL72tsCf>KFMs=3ARLlhDOluO)>cs(J_eRi^ zFPN|W#@Gy7h|WjKpjx>}%(ac=>8l=O%i2uL#sepC!UG}}fyRsrUvEUKvI2f#Fqjry z(!dJP{KJM>s($^eS+OA=YU^ij>Dfg{vF$Nw7~DpNTi=0wwX^)JP*O)=&q4n`tAeZ; za7kB*+c~R10i9_e$F!BvARJKnfwd1!{Vc?X!LUk=<>CE!*^OLmGw-}BJP#m@efxU8 za;IaKwVOz-GF75LDEsDvzjFVkQ^N3Di+6&^3}!N6x_!___QM!`h_u7PC|js^YmEh> zS#ggr2wrG&_sK!kjt855^(#`(O{$FL$KiCr^-~{Zdsj%g(seuk`l;X#@QZcoC`m*D zK8x7d`Z8|EJS&yhQQt3Z9+Rf+vcB}PKV`EXPM3|7hvVGX_YyPn?J_EL?N1)4tCh)B zm=<00R?^XI}qo-j7UNxy%E=4w}zla(IWW~aQ|3fe{=Ss^$r zgWGCG9tery&K@mZ6M}AgTf(cD2^qX8M5|c!CDwCyE>0He+6p-?gKJ`TKDX0tGRk9j zTV{^>aIG^HK;~G7dty|S*Q%2g-2R~Bjd-GsrB2YCe>;+Cy7FV?+_{BZi?QkxG9RXk z_ABP`i;FR!5A(l8HE;2)EG}`oFrlHcUvIBVXD&l5bi_9Z4jtSaaV?8gQRB&mdVPD_ zW8&HysoFQ$2N&3$&uDVOv2L>*8*>{LngGxrz~gAI;h2)SxSlK|?RpGcLpwy$j2hdy z#CD`g9c)B?H9A{>E7i^`oIb0p31~70&1^xUAk+?lMc;j}Y)NCYM7chgj4l01 z+TvuU0LL5IRCL8rZa~2MRriZ6Wb>};4EGl&3sxT^PCOp`aKJn+Y)qdk$7a$|3{bsC zh>k0~xs2*TE52M=F;-BNAD6Slj#(#Gmd zD$h}Z7bJisST87!o0Sg2!?|Gp(`Xzblg>*z2_}H!ns4~PqHSNz;cTBjSOOs7P#!W|p3)Rr@C1qfjXW8&Lmo{)Z!4=$+nlIbv2dML z9h*~`YwSvGflh-JIu(xX&4gh7;BPH;G6a)|3@wQ01 zxk{(&OB|WK4EB@2v;LXz-9(4xa3Trm6F~*UFZdycJS&pJLXqYd2c~y@C#=;61EGlc z9YjxZ9s5oF)S9&>J7rKiI+P=E+(ocvJQ8%@u&;z17_gDkDy8>u8YDH|Z^AN=J=t5kQUiYI^#%UIkeudapv z<&{*Eujr3Yq;Em;)}-H8?BQi5C!ThTwR)1kz>CfGAg*2?v%!X+l^w@ z(p5tW-_#lew*BirVoc8K0 z(|+IvP*;jS$LP|WF2AuBFs3i4^l3iOsDT($*n@<`33yS1MV};b2G%(i7IJlZ-dNtd zAts2YQNorvlK%Fy($0!`G^D>LgfkN~QoB4zv^!yvjHQ6OxY zH=>XSXt#M{k7X^$Ferv&bJJrB=A*ysHWOB-5e66$oKq>WbxOTq&6HZV9ZQ-Jyf
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a/demonstrations/tutorial_game_of_surface_codes.py b/demonstrations/tutorial_game_of_surface_codes.py index b01bf4c8f6..6faeb0d5d9 100644 --- a/demonstrations/tutorial_game_of_surface_codes.py +++ b/demonstrations/tutorial_game_of_surface_codes.py @@ -17,15 +17,15 @@ The game can be understood entirely from the rules described in the next section. However, it still helps to understand the correspondences in physical fault tolerant quantum computing (FTQC) architectures. -First of all it is important to note that we consider surface codes that implement :doc:`(Clifford + T) ` circuits. -In particular, these circuits can be mapped to just performing :doc:`Pauli product measurements `. +First of all it is important to note that we consider surface codes that implement `(Clifford + T) `__ circuits. +In particular, these circuits can be compiled to circuits that just perform `Pauli product measurements `__. This is because all Clifford operations can be moved to the end of the circuit and merged with measurements. -The remaining non-Clifford gates are realized by :doc:`magic state injection ` and more Clifford operations that can again be merged with measurements again. -Hence, we mainly care about performing measurements on qubits in arbitrary bases. +The remaining non-Clifford gates are realized by `magic state injection `__ and more Clifford operations, which can be merged with measurements again. +Hence, we mainly care about performing measurements on qubits in arbitrary bases and efficiently distilling and injecting magic states. We also note that the patches that represent qubits correspond to surface code qubits. There is a detailed explanation in Appendix A in [#Litinski]_ that describes the surface code realizations of all operations that we are going to see. -These are useful to know in order to grasp the full depth of the game, but are not essential to understanding its rules and concluding design principles explained in this demo. +These are useful to know in order to grasp the full depth of the game, but are not essential to understanding its rules and concluding design principles that we cover in this demo. Rules of the game ----------------- @@ -36,22 +36,17 @@ The goal of this demo will be to understand the design principles and space-time trade-offs for surface code architectures. We are going to introduce the necessary rules of the game in this section. -Data qubits as surface code tiles -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - Data qubits are realized by patches that at least occupy one tile, but potentially multiple. They always have four distinct boundaries corresponding to X (dotted) and Z (solid) edges. -Two-qubit patches have 6 distinct boundaries, corresponding to the single X and Z operators of each qubit, as well as the two products XX and ZZ. This is shown in the figure below. -.. figure:: ../_static/demonstration_assets/game_of_surface_codes/qubit_definition.png +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/qubit_definition_cropped.png :align: center :width: 50% :target: javascript:void(0) Qubits are defined as patches of tiles on the board. A single qubit can occupy one tile (a) or multiple tiles (b), where dotted lines correspond to X and solid lines to Z operators. - Two-qubit patches (c) have 6 boundaries corresponding to the single :math:`X`, :math:`Z` and :math:`XX` and :math:`ZZ` operators. Basic operations ^^^^^^^^^^^^^^^^ @@ -60,6 +55,47 @@ There are some discrepancies but the correspondance is close enough to weigh out space-time trade-offs in architecture designs. We are not going to give an exhaustive overview of all possible operations, but focus on a few important ones and fill the remaining gaps necessary for the architecture designs in the respective sections below. +At the cost of 1🕒 we can measure patches in the X and Z basis. If two patches share a border, one can measure the product of their shared edges as highlighted by the blue region in the figure below. + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/ZZ_measurement.png + :align: center + :width: 20% + :target: javascript:void(0) + + Simultaneously measuring the patches of two adjacent patches corresponds to the product of their neighboring edges. Here, we measure $ZZ$. + +In particular, if the shared edge contains both Z and X edges, we can measure in the Y basis. In the following example, the upper qubit A has both operator edges $Z_A$ and $X_A$ exposed. +Measuring it together with the auxillary qubit B, initialized in the $|0\rangle$ state below, we measure $(Z_A X_A) \otimes Z_B \propto Y_A \otimes Z_B$ alltogether. + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/Y_measurement.png + :align: center + :width: 20% + :target: javascript:void(0) + + $Y$ operators can be measured by having both X and Z edges be exposed with an adjacent auxiliary qubit. The measurement corresponds to the product of all involved operators, involving $Z_A X_A \propto Y_A$. + +In practice, we measure a single qubit patch in the Y basis by utilizing an auxiliary qubit. If we start off from a single square patch we first need to deform it at the cost of 1🕒, initialize an auxiliary qubit at no cost, and perform the joint measurement as shown above (1🕒). +The entire protocol is shown below: + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/Y_measurement_protocol.png + :align: center + :width: 50% + :target: javascript:void(0) + + The protocol for measuring a single qubit in the Y basis involves deforming the patch (Step 2, 1🕒), initializing an auxillary qubit in $|0\rangle$ (0🕒), simultaneously measure both patches (1🕒) and deforming the qubit back again. + +Auxiliary qubits play an important role as they allow measuring products Pauli operators on different qubits, +which is the most crucial operation in this framework, since everything is mapped to `Pauli product measurements `__. + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/PPM.png + :align: center + :width: 30% + :target: javascript:void(0) + + Measuring $Y_1 X_3 Z_4 X_5$ via a joint auxiliary qubit in 1🕒. In principle multi-qubit measurements with many qubits come at the same cost as with fewer qubit, however the requirement of having an auxiliary region connecting all qubits may demand extra formations. + + + - X and Z measurement - Y measurement @@ -77,6 +113,9 @@ Fast data blocks ^^^^^^^^^^^^^^^^ +Distillation blocks design +-------------------------- + """ import numpy as np From b664d98161804c576091500cb64247f62b683eb4 Mon Sep 17 00:00:00 2001 From: qottmann Date: Wed, 23 Apr 2025 14:10:51 +0200 Subject: [PATCH 09/30] compact block --- .../game_of_surface_codes/Y_measurement.png | Bin 0 -> 9395 bytes .../game_of_surface_codes/ZZ_measurement.png | Bin 0 -> 4930 bytes .../clifford_rotation.png | Bin 0 -> 25610 bytes .../game_of_surface_codes/compact_block.png | Bin 0 -> 24122 bytes .../magic_state_injection.png | Bin 0 -> 27440 bytes .../non_clifford_rotation.png | Bin 0 -> 20564 bytes .../game_of_surface_codes/patch_rotation.png | Bin 0 -> 35394 bytes .../tutorial_game_of_surface_codes.py | 69 ++++++++++++++++-- 8 files changed, 64 insertions(+), 5 deletions(-) create mode 100644 _static/demonstration_assets/game_of_surface_codes/Y_measurement.png create mode 100644 _static/demonstration_assets/game_of_surface_codes/ZZ_measurement.png create mode 100644 _static/demonstration_assets/game_of_surface_codes/clifford_rotation.png create mode 100644 _static/demonstration_assets/game_of_surface_codes/compact_block.png create mode 100644 _static/demonstration_assets/game_of_surface_codes/magic_state_injection.png create mode 100644 _static/demonstration_assets/game_of_surface_codes/non_clifford_rotation.png create mode 100644 _static/demonstration_assets/game_of_surface_codes/patch_rotation.png diff --git a/_static/demonstration_assets/game_of_surface_codes/Y_measurement.png b/_static/demonstration_assets/game_of_surface_codes/Y_measurement.png new file mode 100644 index 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A single qubit can occupy one tile (a) or multiple tiles (b), where dotted lines correspond to X and solid lines to Z operators. -Basic operations -^^^^^^^^^^^^^^^^ - Every operation in the game has an associated time cost that we measure in units of 🕒. These correspond more or less to surface code cycles. There are some discrepancies but the correspondance is close enough to weigh out space-time trade-offs in architecture designs. We are not going to give an exhaustive overview of all possible operations, but focus on a few important ones and fill the remaining gaps necessary for the architecture designs in the respective sections below. + +Arbitrary Pauli product measurements +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + At the cost of 1🕒 we can measure patches in the X and Z basis. If two patches share a border, one can measure the product of their shared edges as highlighted by the blue region in the figure below. .. figure:: ../_static/demonstration_assets/game_of_surface_codes/ZZ_measurement.png @@ -94,19 +95,77 @@ Measuring $Y_1 X_3 Z_4 X_5$ via a joint auxiliary qubit in 1🕒. In principle multi-qubit measurements with many qubits come at the same cost as with fewer qubit, however the requirement of having an auxiliary region connecting all qubits may demand extra formations. +Non-Clifford Pauli rotations +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Non-Clifford Pauli rotations $e^{-i \frac{\pi}{8} P}$ for some Pauli word $P$ are realized via `magic state distillation and injection `__. +Magic state distillation blocks are a crucial part of the architecture design that we are going to cover later. +For the moment we assume that we have means to prepare magic states $|m\rangle = |0\rangle + e^{-i \frac{\pi}{4}} |1\rangle$ on special qubit tiles (distillation blocks). +Magic state injection in this case then refers to the following protocol: + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/magic_state_injection.png + :align: center + :width: 50% + :target: javascript:void(0) + + Performing a non-Clifford $\pi/8$ rotation corresponds to performing the joint measurement of the Pauli word and $Z$ on the magic state qubit. The additionally classically controlled Clifford rotations can be merged again with the measurements at the end of the circuit. +Take for example the Pauli word $P = Z_1 Y_2 X_4$ on the architecture layout below. +This design allows one to directly perform $e^{-i \frac{\pi}{8} P}$ as we have access to all of $X, Y, Z$ on each qubit, as well as the Z edge for the magic state qubit. -- X and Z measurement -- Y measurement +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/non_clifford_rotation.png + :align: center + :width: 50% + :target: javascript:void(0) + Performing $e^{-i \frac{\pi}{8} Z_1 Y_2 X_4}$ by measuring $Z_1 Y_2 X_4 Z_m$. The remaining Clifford Pauli rotations are merged with the terminal measurements at the end of the circuit via compilation. +We are going to see in the next section that one of the biggest problems is performing Y rotations and measurements (same thing, really, in this framework). Data blocks design ------------------ +We now have all the necessary tools to understand different designs and their space-time tradeoffs. + Compact data blocks ^^^^^^^^^^^^^^^^^^^ +The compact data block has the following form. The middle aisle is going to be used as an auxiliary qubit region. + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/compact_block.png + :align: center + :width: 50% + :target: javascript:void(0) + + The compact data block design is efficient in space. However, only one edge is exposed to the auxiliary qubit region in the middle. + +This design only uses $\frac{3}{2}n$ tiles and 3 additional ones for a magic state distillation block. +The biggest drawback is rather obvious: we can only access $Z$ measurements in the auxiliary qubit region. In order to perform joint $X$ measurements, +we can perform a patch rotation at a cost of 3🕒: + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/batch_rotation.png + :align: center + :width: 50% + :target: javascript:void(0) + + A patch rotation can be used to expose the $X$ edge to the auxiliary qubit region. + +An additional problem of this design is the fact that there is no space for qubits to deform to in order to perform Y measurements. +This can be remedied by making use of the identity + +.. math:: e^{i \frac{\pi}{8} Y} = e^{-i \frac{\pi}{4} Z} e^{i \frac{\pi}{8} X} e^{i \frac{\pi}{4} Z}. + +The second (first in the circuit) Clifford rotation $e^{i \frac{\pi}{4} Z}$ needs to be explicitly performed in this case. The first one can be merged again with the terminal measurements of the circuit. +Such a rotation $e^{i \frac{\pi}{4} P}$ can be performed with a joint measurement of $P \otimes Y$, similar to the magic state distillation circuit: + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/clifford_rotation.png + :align: center + :width: 50% + :target: javascript:void(0) + + A patch rotation can be used to expose the $X$ edge to the auxiliary qubit region. + + Intermediate data blocks ^^^^^^^^^^^^^^^^^^^^^^^^ From 0ead8d5840fba653b85c3e4754fdfffaeb9145ec Mon Sep 17 00:00:00 2001 From: qottmann Date: Wed, 23 Apr 2025 14:40:00 +0200 Subject: [PATCH 10/30] compact block --- .../tutorial_game_of_surface_codes.py | 32 +++++++++++++++++-- 1 file changed, 30 insertions(+), 2 deletions(-) diff --git a/demonstrations/tutorial_game_of_surface_codes.py b/demonstrations/tutorial_game_of_surface_codes.py index 49fd165616..d41da7fbfc 100644 --- a/demonstrations/tutorial_game_of_surface_codes.py +++ b/demonstrations/tutorial_game_of_surface_codes.py @@ -118,7 +118,7 @@ :width: 50% :target: javascript:void(0) - Performing $e^{-i \frac{\pi}{8} Z_1 Y_2 X_4}$ by measuring $Z_1 Y_2 X_4 Z_m$. The remaining Clifford Pauli rotations are merged with the terminal measurements at the end of the circuit via compilation. + Performing $e^{-i \frac{\pi}{8} Z_1 Y_2 X_4}$ by measuring $Z_1 Y_2 X_4 Z_m$. The additional measurement $X$ on the magic state qubit is not shown and has no additional cost. The remaining Clifford Pauli rotations are merged with the terminal measurements at the end of the circuit via compilation. We are going to see in the next section that one of the biggest problems is performing Y rotations and measurements (same thing, really, in this framework). @@ -150,6 +150,8 @@ A patch rotation can be used to expose the $X$ edge to the auxiliary qubit region. +The worst thing that can happen is to have two opposite qubits require an X measurement, e.g. qubits (3 and 4) or (5 and 6). If either or both occurs, it takes a total of 6🕒 to rotate the batches. + An additional problem of this design is the fact that there is no space for qubits to deform to in order to perform Y measurements. This can be remedied by making use of the identity @@ -163,7 +165,33 @@ :width: 50% :target: javascript:void(0) - A patch rotation can be used to expose the $X$ edge to the auxiliary qubit region. + A Clifford rotation $e^{i \frac{\pi}{4} P}$ is performed by measuring $P \otimes Y$ + +In particular, we still need to be able to perform a $Y$ measurement _somewhere_. +In this case we just outsourced it to another resource qubit, which we can use for all others and for which we left space in the bottom left corner of the compact data block. +For example, we can perform the rotation $e^{i \frac{\pi}{4} Z_3 Z_5 Z_6}$ at a cost of 1🕒 in the following way: + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/clifford_rotation_356.png + :align: center + :width: 50% + :target: javascript:void(0) + + A Clifford rotation $e^{i \frac{\pi}{4} Z_3 Z_5 Z_6}$ is performed by measuring $Z_3 Z_5 Z_6 \otimes Y_\text{resource}$ with the additional resource qubit in the bottom left corner of the compact block. + +The worst case here is having an even number of $Y$ operators in the Pauli word, as it requires two distinct $\frac{\pi}{4}$ rotations, each costing 2🕒. + +Overall, in the worst case scenario an operation can cost 9🕒. This consists of the base cost of 1🕒 for performing the Pauli measaurement, 2🕒 for having an even number of $Y$ operators, and 6🕒 when opposite qubit patches require $X$ measurements. +The following protocol shows such a scenario by performing $e^{i \frac{\pi}{8} Y_1 Y_3 Z_4 Y_5 Y_6}$, which is realized by $e^{i \frac{\pi}{4} X_1 X_3 Z_4 X_5 X_6} e^{i \frac{\pi}{4} Z_3 Z_5 Z_6} e^{i \frac{\pi}{4} Z_1}$. + +.. figure:: ../_static/demonstration_assets/game_of_surface_codes/compact_block_worst_case.png + :align: center + :width: 90% + :target: javascript:void(0) + + Worst case scenario in the compact block when performing $e^{i \frac{\pi}{8} Y_1 Y_3 Z_4 Y_5 Y_6}$. + Step 2 measures $Z_1$ together with $Y$ on the resource qubit in order to perform the $e^{i \frac{\pi}{4} Z_1}$ rotation at 1🕒. Step 3 performs the additional $X$ on the resource qubit at 0🕒. + Same for steps 4 and 5 for performing $e^{i \frac{\pi}{4} Z_3 Z_5 Z_6}$ at 1🕒 overall. + Steps 6 and 7 perform the patch rotations at 3🕒, each. And the final measurement of $X_1 X_3 Z_4 X_5 X_6 Z_m$ at another 1🕒 completes the computation. 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