ECE 497NC: Unconventional Computer Architecture

1. ECE 497NC: Unconventional Computer Architecture Nicholas Carter Lecture 12: Quantum Computers II – Implementation Issues

2. Outline • Hurdles to building quantum computers • Decoherence • Error Correction • Requirements for workable quantum computers • NMR quantum computers • Complete architecture proposal

3. Decoherence • Quantum computations rely on being able to operate on a set of qubits in an entangled/superimposed state • Allows computation on all possible inputs to a computation in parallel • Problem: Interaction of qubits with environment affects their state, causing them to not be entangled/superimposed • Can partially address this by designing computer to reduce interaction with environment, but this may make it impractical (for example, running at very low temperatures) • General result: a quantum computation can only proceed for a limited period of time before a measurement must be performed • Measurement forces the system into a more-stable classical state • Measurement destroys superposition • System limited by ratio of decoherence time to operation latency

4. Quantum Errors • Digital systems provide noise protection by mapping an analog signal onto two discrete states • Any error/noise that doesn’t cause the system to mis-interpret a signal gets corrected by the next circuit that reads the signal • Problem: qubits are analog • Need to be able to operate on qubits that are superpositions of multiple states • Observation of qubits collapses them into one state or another • Also, operations on qubits are unlikely to be perfect, another source of error • Need error correction

5. Classic Error Correction • Basic idea: encode n bits of data as n + m bits of error-detecting data. • For codes where the original n bits remain unchanged, the m bits are called the syndrome. • Example: Hamming codes • Well-understood trade-off between m and number of errors that can be corrected/detected • Whenever data is read, regenerate the m syndrome bits • Compare to syndrome from data to determine if error has occurred • Depending on the code, may be able to correct errors as well as just detect

6. Quantum Error Correction • Problem: reading qubits in a superimposed state collapses them to one state or the other. • Can’t use coding algorithms that require examining the data bits to detect errors • Solution: use codes based on measurements that only determine information about errors, not about data • Theoretical best code uses 5 qubits to encode 1 • Commonly-used code uses 7 qubits for each data qubit. • Can recursively apply encoding technique to tolerate higher error probabilities • For some codes, can build gates that operate on encoded data directly, without decoding • Code used in paper requires “about 153” physical gates to implement a fault-tolerant operation • Implementation parameter: error rate of technology determines how much logic can be done between error corrections, and thus overhead of error correction.

7. Requirements for Quantum Computer • Need to have something to represent qubits • Lots of physical phenomena that have two states • Must be able to address individual qubits, and qubits must be able to interact • Must be able to apply individual qubits as inputs to gates • Need to have gates with >1 input • Must be able to initialize qubits to a known state • Hard to write programs if you can’t set inputs • Must be able to observe/extract result from system • Yep, the answer’s in there somewhere, just can’t get it out • Coherence time must be long compared to gate delay • This basically determines how many operations we can do on a superposition before we have to do an observation • Implementation detail visible to programmer

8. NMR-Based Quantum Computers • Most advanced demonstrated technology for quantum computation • Use nuclei with spin ½ as qubits • Spin straight up = |0> • Spin straight down = |1> • Other directions indicate superpositions of |0> and |1> • Long coherence times (seconds) • Electron spins (alternate technology) have coherence times of nanoseconds • In a magnetic field, spin direction precesses about the field’s axis at a rate that is proportional to the field strength

9. NMR-Based Computers II • Bond atoms that represent qubits into molecules • Inter-atomic bonds provide mechanism for different qubits to interact. • Each molecule becomes an n-qubit computing system • Can operate on multiple molecules in parallel to reduce errors • Asymmetry of molecule causes different atoms to precess at different frequencies • Individual addressability

10. Structure of System Tube RF Coils Static field coils

11. Implementing Operations • Key ideas: • Radio energy applied perpendicular to magnetic field causes spins to rotate around axis of RF field if RF frequency is a resonant frequency of the precession frequency • Pulses of different durations cause different amounts of rotation • Position of spin of atom A affects precession rate of nearby atom B by altering the magnetic field seen by B • Differences between precession frequencies of different atoms in the molecule >> effect of nearby atom spins

12. Implementing Operations I • Can flip state of bit with appropriately-timed RF pulse, or set into superposition with shorter pulse • Can create multi-input gates by sending pulses at the frequency that the atom will precess at if appropriate other bits are in a given state. • CNOT operation • CNOT operation + set of operations on individual qubits = universal set of gates • “Machine language” is now set of frequency of RF pulses, duration of pulses, and time between pulses • Read state out by rotating qubit spins into horizontal plane, sensing the time-varying magnetic field they create as they precess

13. Results • Used NMR technology to implement the core of Shor’s algorithm on permutations of a four-element set. • Duration: 50-500ms, depending on permutation

14. Full System Architecture • Goal: extend thoughts on ways to do computation with quantum to something like a full system • Issues • Data storage • Communication/signalling • Error correction overhead • Basic idea: Couple quantum computing system with classical computer • Classical computer sequences operations through quantum computer, does dynamic compilation • Classical computer also does checking of results for probabilistic computations • System aimed at NP-complete problems where computing answer is hard but checking answer is easy.

15. Programming/Compiling • Two-phase process • Pre-compiler generates code that executes the algorithm with a specified error probability on an ideal quantum computer • Dynamic compiler creates instruction stream to meet the error probability on the actual computer • This compiler needs to know about the technology • Also needs estimate of program run time • #errors is proportional to run time. • Estimate either provided by user or generated using profiling • For example, can start with very conservative (strong) error correction and use lower levels once the running time is known

16. Error Correction • Problem: 7-bit codes only tolerate certain amounts of error • Can tolerate greater errors by recursive coding, at greatly increased cost • “Sawtooth” overhead as error rates cross critical thresholds • Solution: Cluster operations • Rather than performing error correction on each operation, group operations into clusters and only do error correction after each cluster. • Allows “fractional” levels of recursion, bringing error correction cost much closer to ideal.

17. Architecture • Quantum ALU/Ancilla generator • Performs actual computations and error correction • Implements set of universal quantum operations • Quantum Memories • Storage locations for qubits • Assumed to have 2 orders of magnitude lower error rates than CPU • Entropy Exchange Unit • Source of qubits in |0> or CAT state • Important, because many algorithms require many qubits in one of these states or the other • Inter-unit communication via quantum teleportation • Allows exact state of qubits to be transmitted • Extension to quantum teleportation allows conversion from one error-correcting code to another as part of teleportation

18. Conclusions/Thoughts • Quantum computing is still way out there, though people are starting to demonstrate actual systems • One issue: current designs expose implementation issues to programmer • Time that computation can run before decoherence becomes an issue • Number of steps that can be performed before need to do a measurement • Still big gaps between demonstrated results and the theoretical predictions people are using to do designs • My gut feelings: • We’ll see quantum computers being built for specific problems in the next decade or two • Quantum computing won’t move into the mainstream unless a vastly better implementation technology is developed and a much larger set of problems that are good for quantum are discovered