Quantum Architecture more unknowns than knowns Mark Oskin University of Washington

Outline What / Why / How Design Rules and Technology Abstraction Quantum Architecture Simulation Infrastructure Programming languages

What is it? (1) The organization and optimization of quantum and classical structures (i.e. the micro-architecture) and the interface (i.e. the ISA) for the efficient execution of quantum- enabled software. (2) A dark vast babble-space Quantum Architecture:

Why? Quantum architecture research can –Identify the weak spots in technology Point the way to solutions for some of them Push the rest back to the physicists –Discover what we don’t know A surprisingly useful thing to know –Bring a reality check to this process Identify physical bounds that alter theoretical ones Quantify the “known” aspects => quite large –Maybe find the right abstraction? - Now?

How Need expertise in both disciplines –Quantum theorist and physicist –Architecture Engineers Funding is the easiest part –NSF Nanoscale initiative –DARPA QuIST Students are available –Lots of interest –Need only simple background in Architecture basic QC theory –Can stay away from the dicey parts at first

How It’s not exactly SimpleQubit but… Currently mathematical models Working on an architecture simulator Physicists working on component simulator “Applications” are well known: –Its 99%++ error correction –They have all the things we like: Locality Parallelism

Quantum Architecture I.Abstracting technologies II.Formulate design constraints III.Mold into building blocks IV.Form into architectures V.Simulate application performance

Technology abstraction First order assumptions: –Classical control of quantum gates –Silicon to interface and control –Individual control of quantum bits

Second order assumptions Choose a likely technology: Kane –Spin of 31P holds quantum state  20nm apart for quantum effect to occur  1.5Kelvin for reasonable coherence time –Local magnetic field arbitrates gates Controlled by “classical” pins –  5nm classical pitch Driven by high frequency (10-100Mhz) clock Gated by “lower” frequency (0.01 – 10) Mhz Similar to CMOS vs. TTL 1.5

Develop design rules 20nm spacing of qubits 5nm spacing of control lines 1.5 Kelvin cannot drive AC current –2 dimensions must be  100nm “pitch matching” issue –Implies sparseness of quantum state

Quantum architecture Abstractions –Interconnect –Memory –Processor Interfacing –Quantum ISA –Classical-Quantum interface

Specialization?

A Quantum Wire Short: swapping-channel –structural implications (sparseness) –Limited length Long: teleportation-channel –“Arbitrary” length –Architectural implications Overhead Latency / bandwidth

A short quantum wire Constructed from swap gates Unless the particle that holds the quantum state physically moves, the information “flows” in discrete steps from particle to particle. Each step requires 3 quantum controlled-not operations, effectively performing a “swap” of the quantum states.

Straightforward approach 5nm access points contain only a handful of quantum states for their electrons at temperatures less than 1K, compromising correct operation.

As two physical dimensions of the access point exceed 100nm thousands of electron states are held. Classically, these states are restricted to the access point, however, quantum mechanically they tunnel downward, guided by the via, thus enabling control. One solution…

100nm 5nm 20nm 100nm Classical access points Narrow tipped control 20nm 100nm

Incompleteness of lines

Top-down view

QCAD Cell Implications Minimum wire length –  200nm (10 qubits) –Excepting custom components Minimum junction point size –  44 qubits square Realistic sizes will be larger –Assumes deep 5nm vias

Why short wires are short Limited by decoherence Threshold theorem => distance –10 -8  1.8mm Key difference from classical: –quantum information must be protected, not just restored!! Can make longer with “repeater” –Essentially this is multiple short wires separated by error correction blocks

Architecting long wires Key insight: –EPR pairs are known states No need to protect them –Purify the good ones –Discard the bad

Architecture of a long wire EPR Generator Teleporation Unit Entropy Exchange Purification Coded Tele- Portation Classical control channel Quantum EPR channel EPR channel

Long wires Can be of “arbitrary” length –A 10mm wire sustains nearly peak bandwidth Low latency –Pre-communicate EPR pairs –Latency is constant: teleportation operation Code-conversation for “free” –Facilitates Processor Memory communication

Long wires Several architectural implications –EPR generation –Distributed entropy exchange (zero’s) –Purification –Teleportation

QCAD Cells Fundamental –Qubit –Zero –Measurement Basic –Line –Intersection Composite / Custom –Purify (custom error correct) –Error correct –Add? Multiply? Memory?

Building Block (I) Measurement unit – computational & Bell basis Measure Qubit to measure Zero qubit Classical control Classical {0,1} output with probability determined by 

Building Block Entropy exchange unit … EX P Polarized Light Polarized Electrons Electric Field Ground

Macro Block EPR generation unit EPR EPR Generator Zero qubits Classical control Quantum output of an EPR state

Macro Block Purification unit – error correction Pur Purification Unit EPR states to purify Classical control Purified EPR states Zero bits Garbage state (to Entropy Exch)

Quantum Memory

Quantum memory? Is dedicated memory viable? Yes –DRAM like (needs refreshing) –Hierarchical error codes? Quantum caches –DFS (Decoherence Free Subspace)? Really phase coherent subspace Need less error correction/qubit No –Qubit Refresh almost as complex as computation! –Big “Almost” => No T gate / all transversal

Quantum ALU / ISA

Quantum Functional Unit Complex, have to tightly integrate: –Measurement –Zeros –Quantum I/O –Irregular classical logic Maybe custom data-paths for: –H/X/Z –CNot –T –Complicated by hierarchical error coding

Processing Likely to use just-in-time compilation –Huge O(n*c^k) savings with error correction: Optimize overhead to data size Clustering –Smaller O(n*c) savings: Packing / unpacking Application specific error processing –Phase error independence –Bit-flip error independence

Flexible execution units Classic analogy: MMX (except more complicated to combine)

Interfacing and Control Quantum operations occur at different speeds –~ Mhz for single qubit rotations –~ Khz for two-qubit operations –~ 1Mhz on average (50/50 split) Even at 1Mhz operation –Ample opportunity for interesting classical work… –Error correction creates even more time for top-level control (5^k) –Low-level must simultaneously decide on the control of millions of qubits/Mhz

Controlling the classical control Highly parallel –O(n) operations per-cycle! –Required for fault-tolerant operation Specialized classical processors? –Certainly ASIC logic for drive/control –Quantum co-processor ISA interface?

Quantum ISA Single qubit rotations –rotate(qubit, axis, angle) Controlled operations –rotate(qubit, axis, angle, {on list}) Just-Enough-Compilation –Control error correction overhead –Invoke(program, input, input complexity)

Simulation Architecture Simulation –Abstraction layer QCAD Cells Macro blocks (memory, etc) –Classical interfacing Bolt onto SimpleScalar?? –Design path QVHDL -> Cell Layout

How? Quantum simulation is O(2^n) hard –Obtaining the right algorithmic answer is not going to happen “Symbolic” simulation is only O(n*t) –Classic n-body simulation –Eminently Parallelizable –Look for this in the Fall

Programming Abstractions Quantum computing lacks a clear abstraction for computer scientists –Matrix algebra just isn’t intuitive enough Difficult to abstract –2^n states for n bits –entanglement

A Classical Representation of Quantum Circuits Example: Quantum Teleportation H H XZ Not obvious that this measurement affects the probability distribution for this quantum bit Not explicit that these qubits are now entangled…

Critic + Concise + Familiar + Classical decisions are explicit - Super-position is hidden - Entanglement is hidden

Alternative Representation HHXCC

Critic - Not very concise (exponential!) - Not very familiar (where are the qubits?) - Classical decisions are implicit + Super-position is exposed + Entanglement is exposed

Ideal Programming Abstraction Concise Familiar within reason Integrates Classical/Quantum Exposes super-position and entanglement

Conclude Choose your area of interest and there is work to do: –Design rules / cell development –Architecture abstractions –Classical-Quantum interfacing –Programming languages

Notes / Graduate course homes/oskin/quantum-tutorial Notes based on book by Michael Nielsen and Isaac Chuang (with some info from John Preskill) Graduate course w/UG’s on request Geared for computer scientists –Begins with linear algebra review –Ends with error correction Sequence of programming assignments in QCL

QARC Project Quantum Architecture project –Isaac Chuang, MIT –Fred Chong, UC Davis –John Kubiatowicz, UC Berkeley –Mark Oskin, UW